For Space Shuttle Orbiter Entry Trajectory Optimization Study: NASA MSC Memo ES32, June 21, 1971

...... *.*.*.*.*.*.-.*.*...... *...... MSC - 04217 ...... *...'...'.*.*.*.*.*.*...... REVISION B ......

.* NATIONAL AERONAUTICS AND SPACE ADMINISTRATION ...... PROJECT/SPACE SHUTTLE ...... SPACE SHUTTLE GUIDANCE, .....*...... NAVIGATION AND CONTROL ...... DESIGN EQUATIONS ...... ,...... VOLUME IV ...... a...... DEORBIT AND ATMOSPHERIC ...... *...... OPERATIONS ...... I...... *...... *.a ...... RNl SED ...... GECEMBER 1, 1971 ...... -._._._._._._. :::::I :::::I ... (MASA-Tfl-x-67709) SPACE SHUTTLB GUIDANCE, N72-23912 :-:.:.HAVIGATJO#...... AND CONTROL DESIGN EQUATIONS* ....:.:.:... JOLURE 4: DEORBIT AND ATHOSPUEBIC :.:.:.OPERATIONS...... K.J. Cox (NASA) 1 Dee. 1971 Unclas ::::::.94 p CSCL 176 63/31 26897 ......

SYSTEMS ANALYSIS BRANCH GUIDANCE AND CONTROL DIVISION MANNED SPACECRAFT CENTE HOUSTON,TEXAS

.'.....'.*...*...*.*.*. .*.....'.'.'.'.*.'.'.*..*..:...... :...*...*...... *.*.*.'.*.*.*.'.*...... MSC - 04217 REVISION B - NASA SPACE SHUTTLE PROGRAM WORKING PAPER

SPACE SHUTTLE GUIDANCE, NAVIGATION AND CONTROL DESIGN EQUATIONS

VOLUME IV DEORBIT AND ATMOSPHERIC OPERc'.TIONS

( Revised

NATIONAL AERONAUT1 CS AND SPACE ADMI NISTRATION MANNED SPACECRAFT CENTER HOUSTON, TEXAS

Prepared by Systems Analysis Branch Guidance ond Control Division

K. J. Cox, Chief Systems Anal pisBranch

FimeA. Fqpt I Direstor of Enginring and Developmrrt

i%L;CEDING PAGE BLANK NOT Fm

This second publication of the Space Shuttle GN&S Design Equation Document contains baseline equations for approdmately fifty parcent of the CWC computation requirements as spacified ia the GB&C S/IJ Functional Requirements Document (MSS-03690 Rev. B) . This document supercedes the original MSC-04217 and the subsequently published revision, Additions or corrections to this document since its original publication .are indicated in the Table of Contents by asterisks in the margin,

It is planned to republish this document in a new revision in approximately four months time. At that time it is anticipated that equations will bs available for virtually all requirements, The new revision will be issued with format changes intended to stress bterdependency of related s~lhmittals and to eliminate duplication to the greatest degree practicable,

This issue kxis been modified to reflect the shuttle-st~ct~eand avionics- configuration changes which have occurred subsequent to the first issue, A significant change is that orbiter control of the booster has been added as a requirement, Decentralization of the camputations and Ulocation to sub- systems is the current trend with the MARK I & MARK I1 shuttle configurations. The camputation requirements for shuttle vehicles asd missions may be much less than those alluued f9r in this document, However, since the configurations are v& fluid at this state in the shuttle development, the approach adopted in tMa document is to include as coniplete a set of design equations as possible to cover ressonable possibilities, Therefore, subsets of equstions may be ex- tracted from this documsnt to forn specifications for specific vehicles, cum- puters and missions, Tho GNM: %sign Equations d~cumentis the result of the efforts of numy people fkcsn NASA and support contractors. The list is too long to credit all con- tributors; however, contractors which made direct contributiw to the docu~~~t are as follows: a. TRW Systems Group, LC,,Houston Operations b. MIT/~harles Stark Draper Laboratory c, Lockheed Rectronics Co,, Inc,, Houston Aer08pa.w Systems Division d, The Boeing Co, , Houston, Texas The equations are revid by the GN&C Forntulation and Implementation Panel and their cnmments included on submittal forms where appropriate. The names . of equation submitters are included on the submittal sheet in each section, Comments on the aubanittals should be referred to the iadividw subnitter or to the responsible USA engineer, General cammnts on the document or proposed au!xdttals should be referred to the System Analysis Brsnch, Guidance aad Control Division,

TABLE OF COAWENTS

-PAGE 1. PURPOSE...... e 1-1 * 2. SCOPE ...... 2-1 * 3. APPLICABILITY...... 3-1 * VOLUME I 4. DEFINITION C@' TEW ...... 4-1 5. REFEHISNCE ~~~S ...... 5-1 *

7. GMSOFTWAN3 FiTNCTIONAL REQUIIU3EUS 7-1 * . - .. t 8. COORDINATE SYSTEB AND TRANSF'OILIJIATIONS ...... 8-1 * VOLUNE I1 - PREFLIGHT TIWOUI;H ORBIT INSE_!ION 9. DESCRIPTIOH OF EQUATIONS . . . . . 9-1 9.1 Preflight ...... 9.1-1 9.11 GN&C System Initialization, Monitor, Test and Checkout ...... TBD 9.1.2 Prelaunch Targeting ...... TBD 9.1.3 Sensor Calibration and Alignment ...... TBD 9.2 Boost Phase Program ...... 9.2-1 9.2.1 Rapid Real-Tins State Advancement During Specific Force Sensing ...... 9 2-4 9.2.2 Booster Control ...... 9.2-15 * 9.3 Separation ...... 9 3-1 9.3.1 Attitude Contra1 ...... TBD 9.4 Orbit Insertion Prqgram ...... : .. 9.4-1 9.4.1 Navigation (same as 9.2.1) ...... 9.4-1 9.4.2 Powered Ascent Guidance ...... 9.473 9.4.3 Thruat.Vector Control ...... 94-26 * *

PAGE

9.51 Abort Decision and Made Determ.tnatian ...... TBD 9.5.2 Abort Targeting ...... TBD TBD 9.5.3 Abort

9.7.1.2 Precision ...... 9.7.2 Navigation (same as 9.2.1) ...... 9.7.3 Powered Flight Guihce ...... 9.7.4 Thrust 'lector Control ...... 9.7.4.1 Fixed Eaes ...... 9.7.4.2 Gimballed Engines ...... 9.8 Rendezvous Mission Phase ...... 9 .8-1 9.8.1 Targeting ...... 9.8-1 9.8.1 .1 Rende~vousTargeting ...... 9.8-2 * 9.8.1.2 Braking ...... 9.8-56 * TABLE OF CONTENTS (CONTINUED) -PAGE 9.8.2 Relative State Updating ...... 9.8-87 9.8.3 Rendezvous Guidmca (same aa 9.7.3). ...9.8-129 9.8.4 Rendezvous Attitude Control ...... TBD 9.p statiod Keeping Mission Phase ...... 9.9-1 9.9.1 Relative State Estimation ...... TBD 9.9.2 Station Keeping Guidance. ..m...... TBD 9.9.3 Station Keeping Attitude Control ...... TBD 9.10 Docking and Undoclcing ...... 9.1&1 9.10.1 Docking and Undocking Yavigation ...... 9..'10-5 9.10 .2 Automatic Docking Control Law ...... 9.10-32 9.U Docked' Operations . (TBD) ...... , ..... 9.114

VOLUME IV - DEORBIT AND ATMOSPHERIC OPERATIONS 9.12 . Deorbit andEntrg ...... 9.12-1 9.12.1 Daorbit Targeting ...... 9.12-3 * 9.12.2 Entry .Navigation ...... TBD 9.12.3 EntqGuidance ...... 9.1231j* 9.12.4 Entry Autopilot ...... 9.1281 * 9.'13 Transition ...... 9.13-1 9.13.1 Transition Attitude Control ...... 9.13-2 * 9.14 Cruise and Ferry Cruise ...... 9.14-1 9.14.1 Navigation ...... TBD 9.14.2 Guidance ...... TBD . 9.14.3 Cruise Autopilot ...... 9.14-1 - -- - -.-- 9.14.3.1 M8p.a Modes ... 9.14-3 * 9.14.3.2 ~igitalControl ...... 9.16s' * 9.1 5 Approach and ~sniing ...... 9.1 5-1 9.15.1 Navigation r*aeeemae.a..a.TBD 9.13.2 Guihce ee.~~~~...me..9m15-1 TABLE OF CONTENTS (CONTINUU)) -PAGE

9.15.2.2 Final Apprmch ...... ,9.15-,59* 9.15.3 Control ...... TBD 9,16 Horizontal Takeoff ...... TBD

9.17 Communications and P~inting... , ,...... TBD , 9.18 FailureDatection ...... TBD

VOLUME v - now DIAGRAMS 10. Flow Diagram TBD ......

VOLUME VI - CONSTANTS AND KEYBOl! ACCESSIBLE PARAMETE-%

11.SWRYOFCONSTANTS 0.0 . TBD

12. REQUIRED KEYBOARD ACCESSIBLE PARAMETERS ...... TBD I 1, PURPOSE The p-mpose of this document is to specify the equations necessary to perform the guidance, navigation and control onboard computrtion functions for the apace shuttle orbiter vehicle, Thi~ equations document will provide as Comprehensive a set oi equstions as possible from which modules may be chosen to develop Part I Specifications for particular vehicles, computers and missions: This document is expected to be the source of any equations used to develop soltware for hardware/sof tware feasibility testing, for ground-based simulations or flight test demonstrations, This document defines a baseline set of equstiuns whicn fulfill the computation requirements for gufdanco, navigatLoAl and control of the space 3huttle orbiter vehicle. All shuttle mission phases are covered fram Prelaunch through ~an5inghkllout. The spacecraft flight mode and the aircraft flight. mods are addressed, Equations r *e included for the Mark I systems snd Mark I1 systems through the all-up shuttle configuation. Control of the booster during launch is covered, The baseline equations may be inplemented in a single GN&C computer Dr aybe distributed among several subsystem computers, depanding upon the outcome of cen- tralisatioa/decentralization deliberations currently in progress. APPLICABILITY

This document is applicable to the guidance, navigation ~nd control (GN&C) computation f unutions for the space shut5le orbiter .vehicle. It specffies a set of baaeline deaign equation8 which may be used for the shuttle program software epecification andl hardware sizing. It define8 the baseline equations for MSC G&C9 hardwarc:/sof tware simulation. 9. DESCRIPTIONS OF EQUATIONS

The detailed equatiorra for the GU&C ftmctioti~are defined in this section. The organization of thlr section is tentative and will be modified so as to present the equations as they are designed in as clear a faahion aa possible. As an introduction to each major subsection (usually a missionphase), the general GN6C software functions to be implemented will be identified and,'where appropriate, a conceptual discussion and top level flw of the coatputatians, inputs and outputs will be included in order to understand and strmrarize what is to be covered. This should be an order of miqgnitude less detailed than the flaw diagrams of tk equations which come later.

A GN&C Equation Submittal eheet will introduce each of the CNbC eqtration submittals and sunuaarize the GNbC functions, and identify the source and NASA tontact for each.

The detailed data to be presented for each GN&C function within each of the major subsections (usually a mission phase) is srnaarized belw. Although items 6 through 10 are to be referenced only in the equations document, they are required submittals before the equations can be approved and finalized for flight sof mare development .

1. Rmctioaal Requirements

The specific functiarrl requfrements (f roar t'he GN&C Software Rimtianal Requirements Document) vfrich are satisfied by the equations shau1.i be identified.

2. Pmcticmal Magram A brief functional explanation and description of the overall concept and approach. A functional block diagrcl~should be used where clarity is enhunced. Inputs, outputs, and Interfaces will be providdd. 3 . Equations and Flabm Detailed equations aad a descriptive text which guides the reader through the flawe of SectianlOshould be provided. The ahhm frequency if the capputations shall be specified and ratimrle given or referenced. 4. Coordinate S~Etern

The coordinate systems used shall be defined.

5. Constants/Variables Summary

Constants and variables shall be summarized in tabular form with the following information:

a. Variables/constants symbols and definitions b. Units c. Allowable quantization d. R-age of values

6. FORTRAN Coding

The FORTRAN coding of the function for verification wing the Space Shuttle Flight Simulation (SSFS) will be referenced . 7. Simulation

The SSFS specifications, description ant! user's guide used to verify each GNiC function will be referenced.

8. Testing

Test plans and test results will be referenced.

9. Derivation

The mathematical derivation of the equations including all mathematical assumptions si~allbe referenced . Assumptions

The following will be referenced:

a. Avionics baselige system assumed b. Reference missions assumed c. Vehicle mass properties assumed d. Propulsion models assumed e. Environment models assumed f. Error models assumed

The major subsections of this section are identified and partially expanded in the followillg . 9.12 DEORBIT AND ENTRY

The Deorbit and Entry phase of the Shuttle mission begins with the Shuttle performing the Deorbit Targeting for the Deorbit (or Deorbit phasing, if required) burn and terminates at the beginning of transition to low angle of attack. The primary landing point and the required orbit maneuvers have been detennlned from pre-phase planning computations. The GNCC Software functions to be perfonned 'during this phase are:

Deorbit Targeting will be perfonned in the coast period prior to the deorbit burn(s) . Targeting outputs (for a specified landing site input) will include parameters as time(s) of ignition, initial attitude for the bum(s), burn time, total AV for each burn, IERT realignment schedule, time of reentry, transition time, cross and downrange required, jet engines ignition time, and time of touchdown. . 2. Orbitalnavigationusinggroundbeacon or star/ horizon measurements as required to update Shuttle .State prior to thrusting maneuvers and aerodynamic entry augmented by available external measurements.

3. Powered Flight guidance resulting in co-ds to autopilot (attitude), thrust vector controls, or thrust throttle coarmands to achieve desired conditions (state and attitude) for transition and limit entry g-loading and heating.

4. Autopilot computations to compute reaction control system commands to achieve the proper attitude.

1 Figure 1 displays a functional flow diagram of the Deorbit and Entry Software Functions.

SPACE SHIJTTB GN&C SOFWARE EQUATION SUBMITTAL

Software Equation Section DeorbPt Taraetina Submittal No. 28 Function To determine the deorbit manuever as a function of entrv ram8 and fliht path mule, Modds No, _ -5 Function No. 1.2.L.5 (ISC-03690 Rev. A)

Submitted by: Brand & Brenn6n (name) Date : 24 Aunust 1471

NASA Contact C. Livelv Organization EG2 Approved by Pam1 111 3.- 0 S- S- Description: This routine has been desiened to step throwh successive aolutiane (valid o~DOFtunitieeto fulfill entm cdti0r.m wi~~constrainta).allouinjz the crew to make selection based on en* c~~~aranne,time-to ignition. reauired veldtv -. 1.8, li~htinlt coILdltio~8,urmncv of return. etc.

Shuttle Conf'iguration: (vehicle, Aero Ikta, Sensor, Et Cetera) This software is Mependent of shuttle confinuration. It8 utility reauires aidficant cross-rtanm cbabiut~.

(Verif icaticm Status) -- 9.12.1 Debabbt Tarnetinq (contd B)

1. INTRODUCTION

The large entry crossrange capability of the shuttle permits deorbit to a specified landing site to be accomplished with a single maneuver. Since the required velocity change is smallest when no plane change is made, the equations presented here are designed to target the Powered Flight Guidance Routines (Ref- erence 3) for an in-plane maneuver. The ignition time for this maneuver is selected to satisfy entry interface and landing site constraints with minimum fuel expenditure. If the shuttle had no crossrange capability, then an in-plane deorbit maneuver to a specified landing site could only occur when that landing site, which rotates with the earth, intersects the orbital plane of the vehicle. Assuming the landing site latitude is less than the orbital inclination angle, and neglecting the effects of precession, the landing site will intersect the orbital plane twice every twenty-four hours. However, the time difference between these two intersections is in general not twelve hours. In the case when the landing site latitude is equal to the orbital inclination there will be only one intersection every twenty-four hoars.

Since the shuttle has a high crossrange capability, deorbit does not require intersection of the landing site vector and the orbital plane. It is possible whenever the angle between the landhg site vector and the orbital plane is less than approximately 20 deg. In general, there will be two sets of opportunities every twenty-four hours. Within each set, there may be several deorbit opportunities occurring on consecutive orbits with varying croserange requirements. When the latitude of the landing site approaches the inclination of the orbit, these two sets merge to become one. It should be noted, in addition, that if the landing site latitude is greater than the orbital inclination, the landing site may still fall within the crossrange cakabi1ity of the vehicle. With these facts in mind, this routine has been designed to continue stepping through successive solutions, allowing the crew to select a particular deorbit opportunity based upon entry crossrange. time-to-ignition, required velocity change, landing site lighting conditions, urgency of the return, etc. The desired entry range and flight path angle will be considered inputs to this routine, since available data relating tn footprint size and shape, entry heating at various ranges, and optimal entry flight path angle are only preliminary. In future revisions, consideration should t 2 given to computing the optimum values of these quantities for the particular situation. 9.12.1 Deorbit Taraetinq (cont Id)

NOMENCLATURE

Semimajor axis

Alarm code-failure in AV miqimization loop

Alarm code-failure in Preeision Required Ve- locity Determination Routine

Semimajor axis of Fischer Ellipsoid

Estimated magnitude of the thrust acceleration

Semiminor axis cf Fischer Ellipsoid

Number of columns of navigation filter weighting matrix (set to 0 in this routine since the matrix is not required)

Maximum acceptable crossrange distance of Orbiter

Estimated entry cross-range distance

Entry downrange distance

Magnitude of the engine thrust

Magnitude of the attitude control system translational thrust

Magnitude of the orbital maneuvering system engine thrust

Entry interface altitude (400,000 ft) 9.12.1 Deorbit Tarnetin4 (cont ld)

Unit vector formed by the cross product of the angular momentum and the landing site vectors

Unit vector in the direction of

First estimate of fEI

2-component of the unit vector -i$ (z-axis assumed North)

Unit vectar in the direction of the angular momentum

Unit vector in the direction of the landing site projection into the orbital plane

Unit normal to the trajectory plane (in the direction of the angular momentum at ignition)

Sensitivity coefficient used ti compute adjustment to time-of-arrival at entry interface

Estimated vehicle mass

Iteration counter

n max Iteration limit

n rev Integral number of complete revolutions to be made in the transfer (set to zero in this routine)

"D Semilatus rectum of deorbit trajectory

P~ Secant squared of the desired entry flight path angle

Secant squared of the offset entry angle used by the PFY Powered Flight Guidance Routine

Precision position vector Entry interfacz position from Precision Required Velocity Determination Routine

Position of the impulsive deorbit maneuver

Entry interface position

Position vector at ignition

Estimated landing site position at the time of landing

~PFT Powered flight offset target vector

8 Engine select ewitch eng

fail Switch set to indicate non-convergence of Pre- cision Required Velocity Determination Routine

Switch set equal to one after the first pass through step one

Switch indicating which perturbations are to be included in the Precirion State and Filter Weighting Matrix Extrapolation Routine (See Reference 5)

Switch set when the target vector muat be projected into the plane defined by iN

Precision state vector time

Time of impuleive deorbit maneuver

Time-of-arrival at entry interface

Estimated time at which in-orbit porition vector ia coincident with the landing rite projection into the orbital plane ETL Desired earliest time-of-landing

Ignition time

Estimated time-of-landing

Desired latest time-of-landing

Precision velocity vector

Entry interface velocity from Precision Required Velocity Determination Routine

Pre- impulse velocity

Entry interface velocity

Ignition velocity vector

Velocity associated with the powered flight offset target vector

Post-impulse radial component of velocit:

-v req Required velocity v ' Required velocity on the coasting trajectory - req v HD Post-impulse horizontal component of velocity

%I Adjustment t 3 At 01 ad^^^ Increment added to the acceptable crossrange, used in rough crossrange check

Difference between the predicted and desired p A P~ Y Out-of-plane target mise due to the projection of the target vector

Transfer time i t - t )

Transfer time ( t - t l)

Transfer time ( t - t )

Estimated duration of the powered maneuver

Time-of-fligi,t difference between (1) the interval from deorbit through entry to landing, and (2) the time spent in orbit over the same total central angle

Time-of-flight required to transfer through the central angle BLp

Required velocity change

Previous value of I AX 1

Increment in in-plane angle 6 ,,

Initial increment in in-plane angle

Convek-gence criterion on A p Y

Convergence criterion on angle A8

Post-impulse flight path angle '

Desired entry flight path angle measured from the horizontal

Landing site longitude

In-plane angle between precision state vector and entry interface 9.12.1 Deorbit Tar~eting(cont'd)

In-plane angle between precision state vector and $0 1 deorbit position

OD In-plane angle over which search is made to find minimum deorbit Av

In-plane central angle traversed duricg entry

Angle between precision state vector and the projection of the landing eite into the orbital plane

Previous value of a ,,

Gravitational parameter of the earth (product of the earth's mass and universal gravitation constant)

Landing site latitude

Orbital period Deorbit Tamting (cont ' d)

2. FUBiCTIONdL FLOW DIAGR -4M

A functional flow diigrarr. presenting the basic approach to the deorbit targeting problem can be found in Figure 3. In addition to the state vector, the primary inputs to the routine are the landing site location (latitude and longitude), the entry downrange distance, the entry angle (at 400,003 ft) and the earliest desired time of landing. Since the high crossrange capability may make deorbit possible on two or more consecutive orbits, after each solution the crew has the option to recycle the program to determine the next possible deorbit opportunity. To give thz crew the flexibility to evaluate solutions in the future without stcppit~gthrough all earlier opportunitios, the earliest desired time-of-landing is included as an input. How- ever, the vehicle is assumed to be in coasting flight until the deorbit maneuver, and therefore the effects of any maneuvers prior to deorbit are not accounted for.

After the vehicle state vector is extrapolated forward to the earliest desired time-of-landing, the solution process is initiated. This consists of three major steps. During the first step the vehiclz state is further advanced until the landing site, which rotates with the earth, lies sufficiently near the orbital plane so that it is within the crossrange (or out-~f-plane)capability of the entry phase. During the next step an iterative process is used to select the ignition time for this aeorbit opportunity which requires the smallest velocity change, ths minimizing the fuel expznditurc. Since the first two steps involve several conic approximations to minimize the computer time used, the rhird step fine tunes the solrition by generating a precision trajecrory which satisfies the corstra.int on the desired entry angle while accounting for gravitational perturbations and the non-impulsive nature of the deorbit maneuver. After completion of this step the results are displayed to the crew. They may then elect to accept tile solution, recycie the routine to solve for the next deorbit opportunity, or exit. If they accept the solution, a few minor computations are required to initialize the Powered Flight Guidance Routines for a modified Lambert aimpoint maneuver. To aid the reader in understanding the functional fl~wdiagram, each of the three major steps in the solubon p-zocess is discussed in more detail below.

2.1 Determination of the Next Deorbit Opportunity (Step 1)

To determine the next pocsible deorbit opportunity, it is necessary to calculate the inertial location of the landing site (which rotates with the earth) at the time-of-landing. Then the angle between the orbital plane and the landing site can be used to estimate the crossrange required during entry. To accomplish this, an estimate of the time-of-flight difference A t DE between (1) the interval fy~rn deorbit through entry to landing, and (2) the time spent in orbit over the same t

central angle is used. Analysis has shown that a constant is probably adequate to

represent this difference since more p~'ecisecalculations 1.1 the following step will compensate for any error.

Upon completion of the initialization process, the state vector is extra- poiated forward to ihe earliest desired time-of-landing. Then the inertial location cf the landing site at the present state vector time, biased by the time difference At DE. is computed. 'This landing site vector is projected into the orbital plane, allowing the in-plane central angle BIp between the vehicle position and the pro- jectio~of the landing site io be determined.

Figure 1. Out-of-plane Geonietry

The conic routines can now be used to determine the time-of-flight At Ip required to coast in orbit through the central angle BIp . If the state was then propagated through this central angle, its position vector would be aligned with the previously determined projection of the landing site vector. Unfortunately, the landing site will movc slightly due to earth rotation while the vehicle transfers through the central angle. Therefore, the inertial location of the landing site must be recomputed, accounting for the time difference At DE explained previously. Thus, an iterative process is required to precisely determine the location of the landing site at the zxpected time-of-landing. During the first pass through the deorbit targeting routine, the previously described steps are repeated once to insure convergence. However, on subsequent passes no iteration is required, since the initial guess achieved by extrapolating the state vector one orbit beyond the previous solution guarantees a small value for the time-?f-flight correction AtIp. Assuming the deorbit maneuver 3 in-plane, the angle between tbe orbital plane and the landing site location at the estimated time-of-!anding can be wed tc measure the crossrange required during "Ae entry phase. If the croesrange is within the capability of the vehicle, the solution process continues on lo the next step. If not, the vehicle state is extrapolated forward one revolution to the next potential deorbit opportunity and the process of estimating the crossrange is repeated. It should be noted that the process used to determine the crossrange requirement ie only approximate, and therefore a small increment is added to the tolerance used in the crossrange check to allow for thir. A small number of cases which pass this check will actually lie outside the vehicle crossrange capability, how - ever, a more precise check later will screen these out.

2.2 Ignition Time Selection (Step 2)

During this step in the solution process, an ignition time is selected which minimizes the impulsive velocity change required. For these computations the projection of the landing site into the orbital plane is assumed to be the real landing site. Then, based upon the desired entry downrange distance, a target position at entry interface which also lies in the orbital plane can be defined. This target position is set 400,000 ft above the Fischer ellipsoid.

DEORBIT POSITION

ENIRY INTERME TARGET #)SIT ION RANGE LANDING SITE PROJUTION

Figure 2. In- plane Geometry

Using thia entry interface target, and the desired entry flight path angle, a search ia made on the central ~gleOD traversed between the deorbit maneuver and entry interface to locate the position and time of the minimum Av maneuver. Deorbit Tarneting ( con1td)

Then the time-of-flight required for the deorbit and entry phases can be accurately determined. Using this time-of-flight, an accurate calculation of the inertial location of the landing site at the time-of-landing can be made, and the entry interface target can also be updated. Tc preserve the central angle of the deorbit phase, the impulsive maneuver time is kdjusted. Then the ignition time is biased from the impulsive time by half the expected length of the maneuver and the state vector is extrapolated to this time.

Since the location of the landing site at the time-of-landing is now known accurately, the angle between the c -bital plane and the landing site is recomputed to precisely measure the entry crossrange required. Then a precision check is made, and any solution exceeding the crossrange capability is rejected, thus returning the routine to step one to search for the next opportunity.

Precision Solution- (Step 3)

During this step a precision integrated trajectory from deorbit to entry interface is generated which accounts for both the finite length of the thrusting maneuver and the effects of gravitational perturbations. Since the time-of-flight from deorbit to entry interface is known, the Precision Required Velocity Determination Routine can be used to generate this trajectory. However, the effects of conic approximations in the previous steps and the finite length of the maneuver can cause significant error in the reentry angle. Therefore, the resulting entry angle is checked and if it is in error. a slight modification is made in the time-of-flight from the deorbit maneuver to entry interface to adjust the entry angle. Then the precision trajectory is recomputed. After satisfying the flight path angle constraint , pertinent data relating to the maneuver can be displayed to the crew or transferred to the Mission Planning Module. ENTER

t . + Input state vector, target location. entr range, entry I angle, earliest timt -of-landing, acceptai: le crossrange . 1

t INITIA~XZ I ATION I Calculate the orbital period I I' I Set t equal to the earliest time-of-landing I!

Increment t by the ------t I- .. orbital perio%. ---7- Extrapolate state vector ahead to t I 3 Use At (the approximate time-of -flight 1 differenREbetween the sum of the deorbit and entry I times-of-flight and the time spent in orbit over the I same central angle) to calculate the inertial landing I site vector at the estimated time-of-landing t +At I

Find the conic propagation time At Ip correspond- I ing to this central angle d I I I Calculate inertial landing I site vector at time ,- STEP 1 t3 + AtIp + AtDE t f I I I I Recalculate inertial landing site vector at time I F 3 timate entry crossrange by calculating the .ngle between the landing site vector and the orbital plane I I

I I I e (rough check) I I

Figure 3a. Functional Flow Diagram 9.12.1 Deorbit Targeting (cont'd) -- --

Calculate the entry 7 projection of the landing site vector into the orbital plane. I the entry range angle 8 , the radius of the Fischer El- 1 lipsoid and the orbital pgne I a Search on OD (the central angle traversed between the I deorbit maneuver and entry interface) to find the minimu I fuel deorbit maneuver I I Estimate entry time-of-flight based on entry interface STEP 2 conditions I Update the estimated time-of -landing based on deorbit I and entry times -of-flight I Recalculate the inertial landing site vector at the time-of- landing and its projection into the orbital plane I I Recalculate the entry interface target position I Update the time of the impulsive deorbit maneuver 1 to preserve the central angle of the deorbit phase I Bias ignition time by half the expected length of the I maneuver I a Extrapolate the state vector to the ignition time I Recalculate the entry crossrange - 1 I I I I (precision check) I I

Use Precision Required Vel compute a precision traject

to give desired yEI

STEP 3

I FINAL CALCULATIONS

Flight Guidance

4 I

EXIT Figure 3b. Functional Flow Diagram 9.12-16 .9*12*1Bar bit Tm-Coont d)

3. INPUT AND OUTPUT VARIABLES

Input Variables

~ - --

0 Time associated with the vehicle state vector

To,10 State vector

ETL Earliest desired time-of-landing

LTL Latest desired time-of-landing

m Current estimated vehicle mass

s eng . Engine select switch

@LS Landing site latitude Landing site longitude

Desired inertial entry angle . Y EI

DR Desired entry downrange distance

d~~~ Maximum acceptable croesrange distance Output Variables

t. Ignition time I&?

t2 Time of arrival at entry interface and time associated with offset target

r Offset target vector - PFT Parameter defining the desired conic entry a~gle 'PFY

rev Integral number of complete 380° revolutions %ev = 0 for deorbit)

-Ui Unit normal to tran~ferplane in direction of angular momentum vector

s Switch indicating whether the initial and target proj vectors are to be projected into the plane defined by the unit normal AN Deorbit Tarnetinq ( cont d)

4. DESCRIPTION OF EQUATIONS To minimize the size of the Deorbit Targeting Routine, extensive use is made of other routines. Therefore, this routine consists primarily of simple equations, logical operations, and calls to other routines. Since most of the complicated equatio~~srequiring detailed explanation are contained in the description of the other routines, this section will be limited to a list of items not covered in the text describing the functional flow diagram. These items will he listed in their order of occurence, and are intended to supplement the detailed flow diagram in subsection 5. 4.1 Selection of Perturbing Acceleration during Precision State Extra~olation During the first step in the solution process, which may require long term state vector extrapolation, it is desirable to maximize accuracy by including all significant perturbing accelerations in the extrapolation process. Therefore, the switch spert , which controls the selection of perturbing accelerations in the Precision State Extrapolation Routine, is set to 2. During the later portion of the routine, referred to as step three, the switch is reset to 1, thus limiting the dis- turbing acceleration to the J term, the second harmonic of the earth's gravitational potential function. Since extrapolation during step three is limited to the interval from the deorbit maneuver to entry interface, the effects of smaller perturbing accelerations are not significant. In addition, extrapolation over this interval lies .uithin an iterative loop, and thus may be repeated several times. The simplified model can therefore significantly reduce the running time of this step.

4.2 Selection of 0 Ip Quadrant During the discussion of the functional flow diagram, it was mentioned that successive solutio,ls to the deorbit problem (when successive solutions exist) are about one revolution apart. To find succeeding solutions to the problem, the state vector is extrapolated forward one revolution and then the in-plane central angle oIP between the state vector and the projection of the landing site into the orbital plane is computed. Analysis has shown that for some selections of orbital inclination and landing site, the correction to the assumption of one revolution may be as large as 29'. A lower limit on 0 IP of -30' was chosen, thus allowing a small margin from the empirically determined limit of -29' . The upper limit on BIp is +330° Large positive values for 0 . IP only occur in situations where no solution existed on the previous revolution.

To determine eIp . the following equation is used, eIp = COS" [unit ( -r ) lisp sign (r,xLtmp) i I [ -h I 9.12.1 Deorbit Tar~etinq-(cont 'd) where r = vehicle position vector -0 = ~'LSP unit vector in the direction uf the landing site projection -hi = unit angular momentum vector

This places eIp between -180' and +180° and therefore an additional test, shown in Figure 4b. is made to force BIp between -30' and +330° . In order to make the first entry into step one compatible with subsequent entries, the state vector is initially extrapolated forward beyond the earliest desired time-of-landing tETL by one-twelfth of the orbital period, to the time t 3, where

%e-twelfth of the period in nearly equivalent to a central angle of 30' for typical (near circular) orbits, and hence makes the first entry into step one compatible with later entries.

4. 3 Effect of Approximate Entry and Deorbit Tirnes- of -Flight on Entry Crossrange Caicuration During the first step in the solution process, an estimate of the time of landing is necessary to compute the inertial location of the landing site and the associated entry crossrange. Since the parameters of the deorbit trajectory have not been computed, the deorbit and entry times-of-flight are not known. To estimate the landing time, a constant At DE is used to approximately represent the difference between the sum of the deorbit and entry times-of-flight and the time spent in orbit over the same total central angle. Preliminary analysis has show9 that if an average value is selected for thiu time difference, the maximum error will be about 6 minutes. This analysis, described in Reference 7, did not include ariations in entry time-of-flight for the particular ectry range, but further analysis is ex ected to show this effect is small. During the first step in the solution, this error will affect the calculation of the inertial landing site vector and subsequent entry crossrange computati~n. This effect on the crossrange estimate will be largest for deorbit from a polar orbit, and result in a maximum error of less than 90 n.mi. To insure that potentially acceptable solutions are not rejected due to errors in the initial crossrange estimate, the rough check on croasrange during the first step uses a test criterion 90 n.mi. larger than the acceptable croserange input to the routine. In step two, after the time-of-landing has been refined, the crossrange is recomputed and a precision check ia made. Thus a few cases which pass the firat test will be rejected later. 9.12.1 Deorbit Tarmtiq (conttd)

4.4 Velocity Change Minimization Method Step two oi the routine includes an iterative search to determine the location of the impulsive maneuver which minimizca the velocity change Av. As shown in Figure 4d.this iteration uses OD, the central angle traversed between the impulsive maneuver and entry inte~*face,as the inaependent variable. A very simple halving step iterator is used to search for the minitnum. Although this does not converge quickly, it is safe and reliable. The more efficient technique of using a slope iteration was not selected because analysis has shown that inflection points exist in the relationship of Av and OD' These tnflection points would greatly complicate any fteration designed to determine the minimum by driving 'he slope to zero.

4.5 Required Velocity Equations The equations used in the previously described iterative loop to determine the required velocity can be found in Reference 2. Theee equations, shown in Figure 4d of the detailed flow diagram, use the initial vehicle position 5 D, the entry interface position r -EI ' and the desired entry angle YEI as follows. First the tangent of he initial (post-impulse) flight path angle Y ie computed by

tan T = (1 - r ) cot ( B D/2 - rDIrEItan(YEI) where eD is the central angle between r and zEIand also the independent variable in the search. The semilatus rectum p ,, of the deorbit trajectory can then be determined from

The parameter p , the secant squared of the desired entry angle, is comprited once during initialization of the routine. The horizontal and radial components of the required velocity are then obtained from

v = v HD tan Yl RD

The required velocity is then formed and differenced with the premaneuver velocity to obtain the impulsive Av.

v = v unit (:I,) + vHD unit D~ yD)xf - req -RD J Deorbit Tarpetinq (cont'd)

4.6 Entry Time-of-Flight Computation (TBD)

In Figure 4e of the detailed flow diagram. the time-of-flight At 23 from entry interface to landing is shown as a function of entry velocity, flight path angle, and range. Functionalization of this time-of-flight will be included later when entry guidance analysis is complete.

4.7 In-Piane Effect of A roximate Deorbit and Entry Times-4kght o P

As discussed in subsection 4. 3, the first eetimate of the inertial location of the landing ~iteis dependent upon an estimate sf the time-of-landing. A constant time differerxe At DE' used to estimate the landing time. may be in error by as much as 6 minutes. This led to a significant error in the crossrange estimate for a high Inclination orbit. For orbits of lower inclination, where the movement of the landing site can be neariy parallel tc the orbital plane, this same error can affect the definition of the entry interface location used in the Av minimization iteration. The entry interface location, computed early in step two. is based upon the projection of the lzndirig site vector into the orbital plane and the desired entry

' range. After the minimization process is complete, the deorbit and entry times- of-flight can be accurately calculated. As shown in Figure 4e, another calculation of the inertial landing site position is made, thus removing the error due to the A t DE approximation. To maintain the desired entry range input to the routine, the entry interface position is recalculated. This new position will be. at most, 1.5' (equivalent to 6 minutes of earth rotation) from the entry interface us

where -i' EI is a unit vector in the direction of the entry interface position ueed during minimization. LEI is the new value, lhis a unit angular momentum vector, and r/ 2 r is the inverse of the mean orbital rate. The cross product of the unit vector8 is nearly equivalent to the angle between them, and the dot product gives the proper sign. The mean orbital rate is used to calculate the deorbit time adjustment from the angular adjustment. Following thie adjustment to the impulsive deorbit time, the ignition time for the maneuver is biased from the impulsive time by one-half the expected length of the maneuver, thus ceirtering the finite thrust maneuver about the impulsive maneuver. 9.12.1 Deorbit Targeting (contld)

4.8 Com~ensationfor Oblatenesa and Finite -Maneuver Length Step three of the solution proceso contains calculations which account for the finite length of the thrusting maneuver on the required velocity change, and compensate ior the effects of the J gravitztional perturbation or. the deorbit trajectory. The Precision Required Velocity Det,*rmination Routine is used to accomplish these objectives, and the reader sh~uldrefer to Reference 1 for a description of the technique. That routine. however, is designed to maintain the terminal (entry inierface) time-of-arrival, and this ?an cause change8 in the entry angle. Preliminary analysis, described in Reference 7, has shown that the nominal erltry flight path angle error resulting from the oblateness and ,^initr!maneuver length is about 0.2', but can be as large as 0.6' in extreme cases. Therefore, to preserve the desired entry angle, the time-of-arrival at entry interface is adjusted slightly. Delaying tne time-of-arrival tends to lofi the trajectory and thug increase the entry angle. An earlier time-of-arrival will depress the trajectory and result in a shallower flight path angle. To determine the time-of-arrival adjustment, the approximate senr .ivity of changes in time-of-flight to changes in entry angle is used. Analysis has shown that this sensitivity varies by a factor of about 13, depending an the characteristics of the pre-maneuver trajectory. However, the sensitivity rrivided by the deorbit time-of-flight varies by a factor of less than 3. This variation is sufficiently mnali such that a constant can be used as the sensitivity coefficient for all cases. To reduce the computations required to constrain entry angle, both here and in the Powered Flight Gcidance Ftoutints*, the secant squared of the entry angle is used rathcr than the actual angle. In particular, no inverse trigonometric Y Pinction evaluations are required. The sequence of calculations designed to reduce the entry angle error are shown in Figures 4f and 4g. First the error Ap in the secafit squared of the entry jl flight path angle is computed from the follawing equation: 1 Apy = 1 - [unit ( -rl; ) unit ( vtt -2 )I2 -py where -ri and -v'a are the terminal position and velocity determined by the Precision Required Velocity Determination Routine and p is the desired value. If the error is too large, the entry interface time-of-arrival, t is adjusted as follows:

* The Powered Flight Guidance Routines, aescribed in Reference 3, use the same basic technique described here to maintain entry angle in the event of off-nominal thrusting conditions. where kY is the sensitivity coefficient described earlier and At lZ is the time-of- flight from deorbit to entry interface. After adjusting the time-of-arrival, .the Precision Required Velocity 3ctermination Routine is recalled with the adjusted time-of-arrival and the results are checked.

In the process of computing a required velocity, the Precision Required Velocity Determination Routine computes an offset target for use during the powered flight. For the deorbit maneuver, the powered flight guidance also requires an offset entry angle. This offset entry angle, actually the secant squared of the angle, is computed from the following equation

- 1 PPPY unit ( rpFr1 unit ( pm )I2 where r - PFT is the offset target for the powered flight guidance and kPFT is the associated velocity. 5. DETAILED FLOW DLAGRAM

This section contains detailed flow diagrams of the Deorbit Targeting Rou- tine. Each hput and output variable in the routine and suSroutine call statements can be fo:lowed by a symbol in brackets. This symbol identifies the notation for the corresponding variable in the detailed description and flow diagrams of the called routine. When identical notation ia used, the bracketed symbol is omitted. UNWERSA L PROGRAM CONSTANTS CONSTANTS INPUT VARIABLES

Set f according to s I eng - -f I m I = tan (YEI) tan EI I I I I IMTIA LIZA TION I

n rev = 0

Call Precision State Extrapolation Routine (Ref. 5) '.

STEP 1 I I I I

Figure 4a. Detailed Flow Diagram I I I I I I I . ETXrr I Call Geodetic to Reference Coordinates Routine (TBD) I I I 1 I -hi = r t(rOXvO)- gLsP= unit [(ih~5LS)Xih] I - 1 lB~~= cos knit ( E~) eign [(TOX!uP) Lh] I I STEP 1

- l~allConic State Extrapola- 1 I?:Ition (Theta) Routine'Ipl']l (R-ef. 4)] output: At Ip [M ,]

Figure 4b. Detailed Flow Diagram 9.12.1 Deorbit Tsrneting (conttd)

C I i 1 Call Geodetic to Reference 1 1 Coordinates Routine (TBD) 1 I Input: Output: f -r J STEP 1 I I I I I I (Figure 4a ) ------i = unit(LhXfU) ~LSP= -ixih -1 coa fiLSP*flLSp) sign (itLSP x -Up)i . I~I Ip =- [- @IP - @IP+ 4~ 0~.- d~~Ir~, sin0 = sin ( 0 E) cosBE = cos( BE) - cos gE - i sin BE 2 I llE1 ~LSP -L STFP I I I I I

Figure 4c. Detailed Flow Diagram 9.12.1 Deorbit Tarnet- (cont'd) I I I 8 = 8 -8 TP E I n= 0 I = lr OD A0 = Ago I J I = 0-OD I i I Call Conic State Extrapola- tion (Theta) Routine (Ref. 4) I Input: ro,x0,801 8 I ..Qut: ED [.I. I t STEP 2 D = IEDI I

t :an = (1 rD/rEI ) cot (9D/2) rD/rEI tan Y EI I Y 1 - - I I - I P~ - - (1 + tany12) - v HD = v tan Y RD HD I - v-req - "RD unit (r- D)+vHDunit I Ax = v -req - XT) I AV = (Ax ( 1 = 8 +Ae I 'D D = OD I OP I AVp = AV I I I v I

Figure 4d. Detailed Flow Diagram Call Conic State Extrapolation (Theta) Routine (Ref. 4) Input: tD [ OU'PU':

At 23 f ( 7 vEI s dDR ) tL * to+ At01+At12+At23 STEP 2 i I Call Geodetic to Reference Coordinate Routine (TBD) I 1 I Output: -r I I I I

unit (ihX rLS) I

-i Xih I BE, 8 I LLSP coe -1ain F I I I I I I I I Figure 4e. Detailed Flow Diagram $2 ' I:Deorbit Tarnatilrq (cont 'd)

1 I Call Precision State Extrapolation Routine (Ref. 5)

STEP 2

i I I (Figure 4a) ------yo+ At 1l + At l2 4-I

I 1 Call Precision Required Velocity Detemination 1 I Routine (Ref. 1 ) I STEP 3 I I TEI 1'1 1' rev ' ' a eng I I Output: .XIreq [xto]# [~i]1; [xi] a I 8 TPFT [TIC]' XPFT klC]'1~' proj ' I Arproj ' 'fail I I I I I Set Alarm Code a2 I

v Figure 4f. Detailed Flow Diagram I I I I AP,, - - STEP 3 I I I - -- $- I I

Yee I =-, I I I FINA L = CALC LATIONS 'pert 2.4 Y I I (Figure 4a) EXIT 1 I 1 I Pp~ys1 - [unit (1 PFT 1- unit pFT I ,

OWPUT VARIABLES ------1 ( 'ig* ;:* 'P~Y PPP~* I "rev proj -N

Figure 4g. Detailed Flow Diagram Deorbit Targeting (cont'd)

6. SUPPLEMENTARY INFORMATION As mentioned in Subsection 4.6, the equation necessary to determine entry time-of-flight is not specified. This must necessarily be postponed until further entry guidance design and analysis makes functionalization of this parameter poe - sible. The effect of different azimuths on the entry phase has not be considered in this design. Since the crossrange capability of the vehicle is dependent on azimuth, and thus may be larger in one direction than the other, this skould be considered in the acceptable crossrange criterion. I.1 addition, varying entry azimuths also effect the required inertial flight path ingle, and hence it may be more desirable to constrain the relative flight paw angle at entry interface. The deorbit target:.:g technique presented here requires long term atate vector extrapolation to select a deorbit opportunity several revolutions later. The accuracy of tk-s ext dpolation is dependent upon accurate knowledge of the current state vector. Any errors due to imperfect navigation will tend to be magnified by the long term extrapolation. Fortunately, the out-of-plane component of error tends to oscillate, and thue can be expected to remain below about 1 n.mi. Con- sequently, the prediction of crossrange for a deorbit opportunity several revolutions later is not significantly affected by the expected state vector error. Mission planning functions, which are sensitive to croeerange requirements, can be carried out without being significantly affected by the navigation error. The in-plane component of state vector error does increase during long term extrapolation, at a rate of about 1 n.mi. per revolution. Therefore the targeting should be repeated during the revolution prior to the deorbit maneuver, taking advantage of more precise knowledge of the vehicle state vector. The deorbit targeting equations presented here are designed to target a single minimum fuel maneuver which satisfies entry interface and landing site constraints. Since deorbit is the final major?maneuver, it may be logical to use all the remaining fuel to either effect a faster return or to reduce the entry crossrange requirement. This could be accomp18.hed by (I) thrusting out -of -plane or (2) using multiple maneuvers to place the vehicle in a phasing orbit prior to landing. The first alternative could easily be added to the design presented here. The eecond alternative, using phasing orbits to adjust the timing and hence inertial landing site location, would require an additional logical structure to eelect the proper phasing orbit; however, targeting for the final deorbit maneu--er could still be accomplished with the equations presented here. REFERENCES

1. Brand, Timothy J. , 11Precision acquired Velocity Determination1', Space Shuttle GN & C Equation Document No. 13, Rev. 1, M. I. T. /DL, September 1971.

2. Marscher, William, "A Unified Method of Generating Conic Sections ", R-479, M.I.T. /IL, Febru~ry1965.

3. Pu, Chung L., Higgins, John P., Brand, Timothy J. , "Powered Flight Guidance", Space Shuttle GN & C Equation Document No. 11, Rev. 1, M. I. T. /DL, September 1971.

4. Robertson, William M. , "Conic State ~xtrapolation'~,Space Shuttle GN & C Equation Document No. 3-71, M.I.T. /DL, Febru~ry1971.

5. Robertson, William M., I I Precision State and Filter Weighting Matrxi Extra- polation", Space Shuttle GN & C Equation Document No. 4, Rev. 1. M. I. T. /DLl Tb be published.

6. Robertson, William M. , I I Conic Required Velocity ~eternin;rtion", Space Shuttle GN & C Equation Document No. 10, Rev. 1 , M.I.T. /DL, September 1971.

7. Brsnnan, P. J., "~eorbitTargeting Design ~nalysis", 23A STS Msmo No. 55-71,. To be pubiished. SPACE SHUTTLE:

GN&C SOFTWAIE EQUATION SUBMITTAL

Software Equatior, Secbion: Ently Guidance Subndttal No. 39 * Function: Provide guidance commands during entry

Module No. OG-5 Function Yo. '7.8.9 (MSC-03690 Rev. A) Submitted by: W.H. Peters (%c) J.K. WillouerhZj~(UC) - MSG - 051'1

Date : 10-21 -71 NASA Contact: W. H. Peters Organization: EG2 -_ - (name ) ., Approved by Panel I11 LJ, Ly ~~t~ t"hihl ( chairman)

Smmary Description: Update to previously submitted fast time internation 'I @dance method for orbiter entry. Incorpcrates numerous new features, the moat notable of which is the ability to simultaneously control heatim and both c3m- ponents of fiiul rrinae error, - Shuttle Configuration: (~ehicl.;, Xero Data, Sensor, Et Cetera)

Testine: to date primarily on Nit ~olCorbiter but method not ssnsitive to vehicle confiwation. .. . Comments: (Design Status) Preliminam design complete

(Verification Status Successfully followed TPS weight-optimum trajectory

* l~evioualybaselined as subrd.ttal No. 2. 1. I NTRODUCm * 3N The fast-time integration (FTI) guidance approach was originally developed for the MSC straight-wing orbiter reentry vehicle as a candid-te guidance logic. The background study leading to the development sf the original FTI subroutine was documented in reference 3. The details of the guidance algorithn as it applied to the single-control variable straight-wing orbiter appear in references 4 and 5. Exten- sions and significant modifications to the original rcutine have followed the decision to apply the method to the high- crossrange vehicle designs. These modifications incluiie the addition of a second control variable with the resulting capability of controlling not only range but also any other parameter which depends only on the trajectory state variables. This report is intended to provide current docuraenta- tion of the prediction, the sensitivity, and the guidance equations. Also included are a fxmc:ional flow cnart of the logic and a listing of the current FTI subroutine. Preliri- nary simulation results appear in reference 7 which is a collection of viewgraphs used for an oral presentation of the method. Additional simulation results will appear in future memoranda. A discussion of the relationship of the FTI guidance approach to onboard optimization and to parametric guidance methods is provided in reference 6.

The prediction and sensitivity equations -re presented in Section 2. Sec~ion3 discusses the control equations.

The Appendix provide^ a f-ictiod flow chart of the guidance ccm- putational procedure and a listing of the current FTI ~.outines. (The listing is 8uppUed for defkitim of factors used, but not otherwise defined in the text.) 3.12.3 Entry Guidance (cont'd;

SYMBOL DEFINITION OR DESCRIPTION

Break r i quency in dampirig filter . Control variable used to shift the angle of sttack profile. Weighting factor used in minimum effort control logic to scale relative magnitudes of Aa and A$ Drag coefficient.

Lift coefficient.

Constant in damping logic equal to eaT . Aerodynamic drag. Determinant of ( ) . Surface gravitational cor.stant used in predictions. Impulse response of the damping-loop transfer function. Altitude. Instantaneous orbit inclination. Constant used to define the range (heating rate) error when minimum effort heating rate (range) control is desired. See Section 3. Gain in altitude rate damping logic.

Great circle crossrange distance. Lift to drag ratio. Vehicle mass. 9.12.3 Ea.h Guidance (cont'd)

SYMBOL DEFINITION OR DESCRIPTION

F Guidance sensitivity matrix defined by equation 3.1. Elemenr from row i and column j of the P matrix.

I 6 Reference convective heating rate at thc stagnation point of a unit sphere;

Predicted downrange distance at the catoff condition; i.e., R = XI

Earth radius.

Reference area. Laplace transform variable. Guidance cycle time. Nondimensional horizontal velocity;

-U v cos y v. v. Total vehicle velority relative to a rotating earth and atmosphere. Circular satellite velocity at 400,000 feet altitude. Great circle dgwnrosge distance. Angle of attack. Specified angle of attack profile used in guidance predictions and sensitivity calculations. 9.12.3 Entry Guidance (cont'd)

SYMBOL DEFINITION OR DESCRIPTION

B Reciprocal of atmospheric scale height in exponential atmosphere used in guidance predictions. Flight path angle. Sampled flight path angle. Damping correction to bank angle. Bank angle; vehicle rotation about the velocity vector. Assumed sea-level density in exponential atmosphere model used in the guidance predictions. Instantaneous latitude. Heading with respect to the original downrange direction.

earl;;^ spin rate.

Nondimensional ( ) . 9,12,3 Entry Guidance (cont d)

2. PREDICTION AND SENSITIVITY EQUATIONS The equations of motion which form the basis of the guidance predictions and the sensitivity calculations are the following.

1 Y=ZmvOp eoBhv2sc, cos +

+ 2wE cos i

6 = vsiny

X = 7AE V COS y COS 1

1 p eoBhvscD(~/~sin +) + Zw sin i sin u $0 E 9.1 2.3 Entry Guidance ( cont d)

Note that these equations include rotating earth effects but are based on an exponential atmosphere. Computationally the atmosphere consists of two separate exponential fits with a contj-tuu1s junction at an altitude of 140,000 feet.

The eqations actually integrated by the guidance are exactly equivalent to those above but have been transformed sdb- stantially to permit rapid and efficient integration. Tke algebra of these transformations is tedious but straight- forward and therefore is not included here. However, the transformation procedure is itemized as follows:

1. Convert the dimensional equations to non-dimensional equations using the vehicle mass, the circular satellite velocity at 400,000 feet altitude and the circular orbit radius at 400,000 feet altitude as non-dimensionalizing factors.

2. Change the independent variable from time to non- diaensional horizontal velocity -u by dividing equatio?~~ (2.1) through (2.6) by equation (2.1) and multiplying the resulting equations by

-dc = 1 , diT cos i 1 - i? tan y & Z 9.12.3 Entry Guidance (cont d)

3. Factor the resulting equations extensively so that quantities appearing frequently in the equations are evaluated only once for each derivative evaluation. Although this factorization renders tt= equations almost unrecognizable in the guidance routine, it is perhaps the most imporrant coding detail to permit rapid integration.

In the guidance subroutine, the equations of motion appear as follows:

D (1) = (TS6) [ (T27) (LOD) - (TS) (T26) + 2 (T2) ] (2.9)

D(2) = (T56) [(VN) (TlO)] (2 .10)

D(4) = (T56) [((~27)/ (~7)) SIN(PPH1) (LOD)

+ Z(0MEGA) SIN (ANGLEI) SIN (XMU)] (2.12)

The factored "T" quantities are defined by the code itself which appra: in the Appendix of this report.- b. *'t The perturbation equations integrated by the guidance result from taking partial derivatives of equations (2.1) to (2.4) with respect to the quantities (L/D cos 6) and CD . These quantitizs are used instead of a rnd + directly t~ avoid algebraic sign reversals in the sensitivities as the bank angle goes through zero degrees. The sensitivities to (L/D cos 0) and CD are related to the sensitivities to a and @ by simple chain rule differentiation; i.e., 9.1 2.3 Entry Guidance ( cont d)

In the guidance subroutine, the perturbation equations for (L/D cos 4) take the form:

D(6) = (All) (Y (6)) + (Al2) (Y (7) ) + PFLODl (2.16)

D(7) + (A21) (Y(6)) + (A22) (Y(7)) + PFLOD2 (2.17)

D(8) = (A31)(Y(6)) + (A32)(Y(7)) + PFLOD3 . (2.18)

The perturbation equations for CD appear as

D(9) = (All) (Y (9)) + (A12) (Y (10) ) + PFCDl (2.19)

D(10) = (A21) (Y(9)) + (A22) (Y(10)) + PFCD2 (2.20)

Dfll) = (A31) (Y(9)) + (A32) (Y(10)) + PFCD3 . (2,21)

Thc values of the aerodynamic coefficients C, and CD and their derivatives with respect to a (C, and CD ) are a a included in tL? predictim and sensitivity integrations using cubic spline appr~ximations [reference 2). Interpolation using 9.1 2.3 Entry Guidance ( conk d)

splines is very nearly as efficient as using linear interpolation and provides accurate derivative information at no cost. It was found that very simple polynomial approximations for angle of attack dependence were too inaccurate to produce a net gain in guidance efficiency. Mach number effects are included using linear interpolation.

The crossrange equations (2.12) and (2.13) are integrated by the guidance with the bank angle'pxofile multiplied by -1 to predict the crossrange capability that remains if the bank angle were reversed at the current time. The crossrange logic commands reversals when the reversed-bank crossrange equations predict termination inside a shrinking interval about the target. As a result of using - in equations (2.12) and (2.18), the value of from the crossrange integration is not fed into the downrange equation. Instead, the value of $ used in equation (2.11) is obtained as foilows :

$=,, (L/D sin 0) (2.22)

dllr -i/v (L/D sin 4) (2.24) " dv

Assuming that L/D sin 4 is constant over each increment of velocity corresponding tc a single integration step

= 1. (L/D sin 0) Ln $i+i 1 - 9.1 2.3 Entry Guidance (cont 1 d)

This simple integration provides a $ value of sufficient accuracy to use in the downrange equation (2.11).

The value of the latitude used in equation (2.5) is calculated as in Figure 1.

A predictor-corrector integration method is used in the current FTI guidance routine to perform the numerical integration. Four steps of a fourth-order Runge-Kutta method are used to start the integration. The predictor is the fourth-order Adams Bashforth formula and the corrector is the fourth-order Adams-Moulton formula. Stepsizes are fixed at 50 feet per second. The integration code appears as an integral part of the guidance routine to avoid calls to external and overgeneralized integration subroutines.

To date, no attempt has been made to strip down either the eq~ationsof motion or the integration. The synthesis philosophy has been to build from formulae that are unques- tionably accurate enough and to do so with as n~uch efficiency as possible. Complete trajectory integrations are currently being performed in approximately 2 seconds of UNIVAC 1108 execution time. It is probable that an investigation of the following items would lead t~ a substantial reduction in computation time: 1. Simplification of the prediction and/or the sensitivity equations based on an order of magnitude examination of the terms.

2. Increase of the integration stepsize. 9.12.3 Entry Guidance (cont 'd)

3. Alteration of the order of the integration formulae. For example, with current rtepsizes, fourth-order formulae are probably not necessary. Elimination of the corrector alone would almost halve the integration time. Other investigators have recently recommended the use of higher-order integrators with very large stepsizes to improve efficiency. these suggestions should be investi- .gated. It is anticipated that by using state-of-the-art integration methods the integration efficiency could be improved by at least a factor of two. 9.12.3 Entry Guidance (contlci)

p LATITUDE AT POIlTl' B'

Figure 1. - Computation of latitude at point 8:. (1 of 2) 9.1 2.3 Entry Guidance (coat d)

sinA I sin(9~~-~~)I ccs Q O = sinA sin 90' sin(90°-vo) cos p o

cos C = cos X cos k

sin sinA - -s1n C

cos (go0-p) = sin p - cas c cos (9~'-pol + sin c sin(90~-p,)co~A" = cos c sin po + sin c cos po cos A"

Figure 1. - Computation of l~titudeat point B' . (2 of 2) 9.12.3 Entry Guidance (contld)

3. GUIDANCE EQUATIONS

As currently coded, the FTI subroutine issues angle of attack and bank angle commands based on the reference unit sphere convective heating rate at a future point and the downrange distance traveled when the vehicle reaches a speci-

fied cutoff altitude. It is apparent fi ll.1 reference 1 that approximate temperature control can be maintained by speci- fying an appropriate reference sphere heating rate profile for the nose panel of the orbiter. The guidance algorithm attempts to make the predicted reference heating rate at a future point on the trajectory equal to o desired value obtained from a specified profile. The prediction point is .determined by subtracting a fixed velocity decrement from the current velocity. For example, suppose the specified velocity decrement is 400 feet per second. At a guidance computation which begins at a velocity of 23,000 feet per second, the heating rate at 22,600 feet per second is predicted. Also calculated are the sensitivities of the heating rate at 22,600 feet per second to the ctirrent control values. Similarly, when the vehicle is traveling at 22,400 feet per second the predicted heating rate at 22,000 fze: per second is being controlled. Simultaneously, the predicted range at the cutoff altitude is being calculated along with its sensitivities to the current control values.

The guidance computes the elements af the sensitivity matrix P , where 9.12.3 Entry CizidanceU (cont d)

The sensitivities of R are evaluated at the cutoff condition and the sensitivities of 4 are evalu: ted at the prediction time appropriate for the current guidance call. Linear analysis leads to

where AR and AO are determined by diffezencing the predicted and desired values of R and d , respectively. The control commands are obtalned by solving this simple linear system simultaneously; i.e.,

To first order, the above control law finds the control pair which eliminates the range error and the heating rate error simultaneously.

It is easily seen from equations (2.14) and (2.1.5) that P is singular when $ = 0 or c) m 90' . In the subroutine, the magnitude of the determinant of P is calculated and if necessary limited to a value greater than a preset minimum. In addition, if the determinant of P gets small 9.12.3 Entry Guidance (contld)

causing large control changes to result from 3.3, these changes are limited so that IAal -< 3' and IAQ~ -< 10' . This allows the ccntroller to make the next prediction with a value of @ for which P is non-singulhr.

Since it is necessary to provide for upper and lower limits on both angle of attack and bank angle, special control saturation logic is used. Each forward integration is performed with control limicing logic. For example, if the controller has shifted the angle of attack profile so that in some segment of the trajectory a exceeds its maximum allowable value, the trajectory prediction and the sensitivity calculation are made using the maximum allowable value in that segment of the trajectory. Thus, all predictions and sensitivity calculations are based on perturbing the control only in regions where perturbations can be tolerated. This represents another major advantage of onbosrd sensitivity calculation. Other perturbation guidance schemes, such as the adjoint variable methods, cannot easily adapt to control saturation and therefore provide inaccurate sensitivities in those regions. If a co~trolis saturated and if the change given by (3.3) does not cause the control to leave the control boundary, the FTI control law recomputes the other control variable change based on the proper single-control vartable sensitivity. An exarnplc ,,auld help clarify this simple saturation procedure. Suppose

a = amax and Aa computed from (3.3) is positive. The commanded change in Q is then recomputed as either 9.12.3 Entry Guidance ( cont ' d) depending on the control segment in bhich the guidance is operating. Similarly, suppwe 4 is saturated and A@ computed from (3.3) does not bring 4 off its limit. The Aa command issued by the guidance is then recompated as

Again the equation chosen depends on the current control segment. Ncte that the recomputation of the commands during regions of control saturation requires only an additional division since the single-control gains are elements 22 the sensitivity matrix P which is already computed.

The coatrol segments referred to in the previous paragraph are defined as follows:

Segment 1 - From guidance startup at .05 gls deceleration to a fixed velocity point. The controls in this segment are calculated to eliminate the 6 error with minimum control effort,

Segment 2 - From the end of Segment 1 to the point on the trajectory where the predicted maximum heating rate first becomes less than a threshold value. The controls in this segment are calculated to eliminate the 6 error and the R error simultaneously. If a control saturates in this segment, range control is dropped temporarily and the 6 error is used to compute the other control. 9,12.3 Entry C;ui.d:ace-- (cont'd)

Segmeat 3 - From the end of ,Segment 2 to cutoff altitude. The controls in this segment :re caiculated to eliminate the R error with minimum control effort.

The minimum effort criterion is used in regions where the control of one parameter takes high priority over the other. In Segment 1, the objective of getting onto a desirable temperature profile takes priority over range considerations. Therefore, the quantity AR is computed as a scalar constant times the required A6 and the constant is determined to minimize the control change. For example, let the measure of control cbange be given by

where c is an arbitrary weighting constant. Assuming that range control is to be temporarily ignored, let

Then 9.12.3 Entry Guidance (contit d) where DET P is the determinant of P .

Substituting these expressions for Aa and A$ into J and setting aJ/aK = P results in

It is easily shown that this value of K represents a relative minimum of J . A similar result follows if ~4 is specified as a constant times AR.

It has been found in sl.mulation results that the minimum effort criterion to specify the "uncontrolled" parameter results in excellent targeting in Segment 3 where heating problems are no longer of consequence. Although extensive simulation verification has not yet resolved the proposition, it appears that Segment 1 may not be necessary. The advantage of Segment 2 cannot be overemphasized. In that segment, a desired heating rate profile (and therefore an approximate panel tl temperature profile) can be tracked while the guidance is simultaneous~ysolving the range problem.

Typically, Segment 2 covers from 5 to 10 minutes of trajectory time during which heating considerations are important. Neglect of direct range control for this length of time and at the high-energy end of the trajectory causes a considerable loss in targeting ability. Simultaneous control of range and heating rate in Segment 2 is overridden only in regions where the control saturates. These regions can be 9.1 2.3 Entry Guidance ( cont d) minimized or eliminated by choosing realistic control profiles for the prediction integrations. The result is that Segment 2 provides both path-type and terminal-type control and appears to increase substantially the guidance footprint areas over that obtained with a temperature-only control segment followed by a range-only control segment.

One of the principal advantages of integrated predictions lies in the fact that completely arbitrary control profiles can be assumed in the prediction. Currently the program uses a constant bank angle profile and a variable angle of attack profile of the form

= SO0 - ZOO sin ( ~2' (0.8 - 8)) 0.2 -< 5: -< 0.8

The guidance adjusts the constant b to increase or decrease the entire profile by the amount necessary to null the guidance errors. The a profile choice was made to allow the guidance to stabilize and still permit the pitchover maneuver necessary to leave the vehicle at a small angle of attack at guidance cutoff. The best choice of prediction profiles has not been studied to date but it is anticipatzd that such a study could produce improvements such as enlarged target 9.1 2.3 Entry Guidance ( cont ' d) areas, more nearly optima? trajectories, and reduced sensitivities to navigation errors. The possibility of using several parameters to specify the prediction control profiles and of using the guidance to adjust these parameters in flight is discussed briefly in references 3 and 6.

In the FTI guidance routine, both the prediction bank angle and the commanded bank angle are modified, if necessary, to provide trajectcry damping. It has been found that at lower angles of attack the delta-wing configurations have a tendency to show altitude oscillations that are undesirable. These oscillations can be overcome by using a simple flight path allgic feedback. Since low frequency flight path angle changes nust be permitted, a simple high-pass filter in the feedback loo$ is suggested. The bank angle command is used for damping. Tilo feedback loop has the structure

, + * ZERC- KCIS ORDER * 3Gr HOLD 9.12.3 Entry Guidance (conhld)

The transfer function from the sampled flight ~~thangle y* to the bank angle correction 64 must include the dynamics of the hold and is therefore given by

-aT where d = e 7 I' is the sample period, and Z represents the 2-transform. The inverse of G(Z) is

(K, for o u n - (3.16) a(nT) = jr, dnol(d - 1) ~OSn>l -

Using the convolution summation, the correcti~~6$(nT) is obtained as

The choice of an appropriate value for the filter break frequency, as based on the frequency of the undesirable altitude dynamics, results in a rapidly converging series. The guidance uses four terms of the series with approximately a 3% error due to truncation; i.e.,

+ y*(t - 2 At)g*(t - At) +y "(t - 3 At)g*(t) (3.18) 9.12.3 htry Guidance (contld)

This simple damping logic using three backpoints from previous guidance passes has nrovec very effective in smoothing the altitude-velocity profiles. Since the daztping is incorporated into the prediction and sensitivity calculations as well as the commands, no degradation of the targeting accuracy is produced. 3.12.3 Entry Guidance (contld)

REFERENCES (1) Curry, Donald M.: Local TPS Weight Estimation Methods- for Space Shuttle Orbiter Entry Trajectory Optimization Study: NASA MSC Memo ES32, June 21, 1971. (2) Vickery, S. A.: "Subroutine ARODYN with Spline Cubic Interpolation," LEC Tech Memo 67542G/118201, July 1, 1971. (3) Willoughby, J. K. and Rao, T. C.: A Study of Alterna- tive Guidance Concepts for Shuttle Reentry, LEC Tech Report 67542C/024502, September 1970. (4) Willoughby, 3. K.: "Detailed Documentation of Fast- Time Prediction Guidance Software," LEC Tech Memo 67542B/036303, December 28, 1970,

(5) Willoughby, J. K.: "FTP-4D Resntry Guidance," LEC Tech Memo 67542B/036201, December 30, 1970.

(6) Willoughby, J. K.: "In-Flight Optimization using FTI Guidance," LEC Tech Memo 675428/1228@3, August 16, 1971. (7) dilloughby, J. K.: "2-Contrci Variable FTI Guidance Viewgra2hs From Oral Documentation,..-. LELm/. Tech. Memo. 67542B/122804, August 26, 1971. 3.12.3 Zntm G-&dame \ cont d)

FUNCTIONAL >"LOWCH.AKC AND

LISTlNGS OF FTI GUIDANCE SOFTWARE 9.1 2.3 Entry Guidance (cont d)

SUBIOVTINE FTI FllNCTlOkAL FLOWCHART (7START

4 IUWGE-KUTfA STEPS BLEW TAIEN

DECELEMTlOll SU? LCImLY

INITIALIZE STATE VAIIABLES POI IN- TxqATIOw

SET COmOL YML

SUSITIVITItS SAW

SAVE A??IO?IIAIE

II:

'a!9 at 9;

$1fl

9.12.3 lEnt-g;-1 G danc (

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I I I I 11 I/

III I I I I i 31~IS g

"IfIll W," " 812 &::V,

Il I or: > : * 1 ' u. 'C* c 4 0"lm a a' Sf!

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SPACE SHUTTLE

GN&C SOFTWARE EQUATION SUBMITTAL

SoPtxare Equatioa Sec+uion Er~ii'yAutopilot Submittal No. 33

Fuiction Blended DFCS for Entry

Module No. OC4 Function No, 1.2.3.4 (MSC 03690 Rev. B)

Submitted by: 3. L. Zacharias Co. EG2

Cate: Octobsr 21, 1971

NASA Contact: W, H, Peters Organization EG2

Approved by Panel I11 1.J. @ Date (Chairman)

Summary Description: This submittal defines an entry DFCS which controls stability axis attitude uain~both the aerodmamic control surfaces and the

ACPS jets. The desim minimizes variations i.n airframe dynamics and uses u blended amroach for aerodgnamfc/~~~~cont-rol.

Shuttle Configuration: (vehicle, Aero Data, Sensor, Et Cetera)

NAR 161C (~ev.A')

Comments:

(Design Status)

(verification StaLus)

Pbnel Comments: 9.12.4 A PRELLMINARX DESIGN FOR A BLENDEG ENTRY DFCS

INTRODUCTION

This chapter presents a preliminary design for SSV attitude control during entry, using both the ACPS and ASS (cerodjmamic ccntrsl surfaoe) torques in an integrated or llblendedtl approach. In addition to providing a means of minimizing ACPS fuel expen- ditures (by blending with the ACS torques), E prime objective of the design approach is to jninimize variations in the closed-loop a%titude dynamics due to variatims in the open-locp airframe dynamics.

The mterial presented here is a summary ol the design synths- sis and gain comp*1-ta$ian documented in refwences 1 through 4.. Current changes to the latest documented dbsign (given in refer 3nce 1) flave been imp;emnted in this work.

This chapter is orbdzed ir+t~three sections: Section 1 describes the trajectory parmeters defining the entry operational environment of the NR 161C vehicle used for controller design; section 2 describes -the longitudinalcontrol channel; while section 3 describes the lateral control channel.

1. 'Tra.iectory Parameters

The trajectory paramstors prenented here were genwsted by the Statistical Analysis Sectton (EG~),using a point mss sbulat5on with pitch and bank angle modulation tc control heati:g, loads, and targeting. Given in Table I are the initial entry i;c\rditions for two NR 161C vehicle trnjectories: A law cross-mlge, clam-range entry (CR: 370 mi: DR 4003 mi), and a high crops-range, high dam-. range entq- CR U50 mi: DR: 6490 mi), herein designated as trrrjec- tories A and B respectively. (1xitia.l conditioils are idenijcal.) 9.12.4 Entry DFCS (contld)

Table I. - KWRY TRAJECTORY INITIlL CONDITIOXS

Parazster Value - - 24,405) ~t/sec 53 die -0.9 deg 395,052 ft 90 deg Lat 0 deg 81.53 deg

Showa in figures i through 5 are the pertinent entry trajectory parmeters, for both trajectories. Plotted agai;;st Mach number Y in the first three figmes are: Trim angle of attack a(T, Ir dynamic pressure , and flight p~thm.gle r6 . Dlotted against tircle from entry interface t in the last two figures are: Mch mmber M and total reiative ve10cityT)~. It should be noted that in addition to a large parametric variation alcng a parr.5cul.a trejectory, there is also E significant v=iaticn between 3rajec- tories.

TEs sactio~presents the control block diagrams =d associated gains fgr b~gitudinalcontrol, or equivdently, control of tha vehicle's angle of attack o(. The basic design procedure, described in reference 2, involvss a separation of the ACE and ACPS contra1 loop synthesis, *iththe addition of an interface logic to defin2 the operational region in which the two control torque systems operate simultaneouly. Further, the design of the ACS control loop is predicated on cloeed-loop dynamic insensitivity to variations ill the airfrave characteristics.

- 9.12.4 Entry DFCS (cant d)

Entry Dr'CS- (cont1~)

Section 2.1 and '2.2 present the block diagrams defining the aerodynRmic surf&:e (i.e., elevator) control logi.: and the ACPS (i.e., pitch jets) control logic, while Sections 2,,3 and 2.4 present the fixed and scheduled gain ptlrameters appopsiate to these controllers. Findly Section 2.5

2.1 Elevator Control

Shown in figure 6 is the block diagrm for elevator control, adaptedfroa reference 1. Basically, contro? consists of attack aagle error and rate feedback to appropria-i:-lyposition the elevetor actuator. Use is inade of both fixed and trajectory dependent gains for transient pLtch conti-01, in psrallel with a clamped integrator to assure a t~imcapability.

2.2 Pitch EACPS Control

Shcwn in figure 7 is the block diagram for pitch ACPS control, taken fron reference 1. As with the previous logic, attitude control is achieved through the use of pitch rate damping, and the appropriate torque signal is sent to the jet select logic.

The interface logic between the ACS ard ACPS s=lbsystems is also shown in figure 7. The appoach taken here is to inhibit firing of the pitch ACPS when there is "suff'.icient"pitch control acceleration available from the elevator. This determination of suffi- C ciency is obtained from the commanded elevatar deflection (4 ) end hence, is a closed-loop ifidex of elevator effectiveness.

2.3 Fixed Longitudinal Gains

Given below are values for the fixed longitudinal gain (and limit) psrameters, which, from present simulation efforts, result in reasonable closed-loop vehicle response throughout the entry flight envelope. 9.12.4 Entry DFCS (contfd) 9.12.4 Entry DFCS (contld)

(s') Wo&IUD Wtr# HWrn/$/$ :

Ngure 7 Pitch ACRS Control Block Diagram Table 11: Find Longitudinal Gain

It should b'-n-rjcd t;%t the above gains are applicable to the NR 161C vehicle.

As shown in figure 6, there are three variable gain psrameters A in the longitudinal control channel: f, , fa, and q . This section presents gain schedules for the first two parameters and a simple limiting logic for the third, As discuasd in reference 4, the gain parameters r, Rnd fa may be plotted ageinst Eaach number and angle of attack, respectively, By camparing the values for two different entry trajectories (described in section 1), a piecewise linear approxlmtlon may be made for each parameter, eo that trajectory independent gain schadulihgl ie possible. The ~esuliisare emin figures 8 and 9, with f, a function of Mach number andfca Atnction of angle of attack,

9.12.4 Ehtm DFCS (cont Id) 9-12.4 Entry DFCS (contld)

In ordez to avaid cc~pl~tationaloverflow problems due to div- h ision by the dynamic presswe q , a simple limiting logic is used to set a lower bound on this panmeter, and is . own below:

Limiting Logic for Dynam5c Pressure A In t5e above dia- '; is the dynamic pressure obtained from the .&LC air $ak empiter, wid-ct is lower limited to becoms the dymmic pressure (rq used in the zontroller logic of figne 6.

2.5 Songitlldirvh Channel, I~pute,Outputs, and Sample Rebs

The inputs for :he longitudinal controller fall into two cat

egories: ?\ose pertaining to the inner "controln loop, and those

pertaining to the outer "gaLntl loop. These two sets of inputs,

their comesponding origha, ere tabulated below : 9.12.4. Entry DFCS (contld)

The outputs f3r the longitudinal controller are commcuded elev~tor deflection,bc , and cmqarici 36 ,>itch ACPS aactlleration ,pi. To C obtein ele;on cdg,the elevator and aileron cmds (the latter fram the lateral logic) must be differenced in an elevon logic es shown in figure 10. In a similar manner, C-ed ACPS accelerations must mke use of an appropriate jet select logic, which wiL be the subject- of a future memoraxdum,

- Big. 10: Elevon Logic

There are twc sample ratsa presently in use for DFW simulation efforts: a high-frequency control loop rate of 8h2, anci a low- frequency gai.9 loop rate of O.&. It should be noted that this inq,liee gain updating every 20 control qdes, and may thus prove to be comervative.

3.0 Lateral Control

This section presents the control block diagrams and associated gains f~rlateral ccntrol, or, equivalently, coiltrol of the vehicles cideslip and bank ugles, AS with the longitudinal controller, $he basic desigr. procedura, daacribed in reference 2, bvolves a separation of ACS and ACPS control, with the addition of 9.12.4 Entry DFCS (cant13)

an interface logic. Further, the ACC ctoa*'Uer utilizes an analogous procedure rIf ,&?L zchedding to minimize sensitivity to open-loop .-?hlcls parameter ck-~ss.

Sections 3.1 an2 3.2 present the block diagram defining the aer-c s1xrface (i.e., rudder and aileron) control logic and the LCPS (i.e., pw and roll jets.) contrcl logic, while sections

3.3 ad 3.4 present the fad md schedule2 gain parameters appropriate to tlL=seCU~~~TQU~~S. Finally section 3.5 discusses the inputs, outputs and sample rates of the ItLte- control chmnels.

3.'- Rdder and A3eron Control

Shown in Cigure 11 is the block diagram for rudder and aileron cantrol, adapt€' from reference 1. Basically, control consists of sideslip and k?k angle attitde and rate feedback to approp- riately position the rudder and aileron actuators, with the gains chosen so as to minixize lat,r-?ral couplins and simultaneoilsly pro-dde ~dequate dynamic response with sufficient damping. The syxthesis procedure is described in reference 2; as can be seen, the design incorporates both fizd and scheduled gains for laterai control with the ACS.

3.2 Roll and Yaw ACPS C~ntrol

Shown in firowe 12 is the block diagrm for roll and yaw ACPS control, taken from reference 1. As with the previolu l~gic,at- titllde controi is ackieved through the use of sideslip and bank angle A.12.4 Entm DFCS (contfd) 9.12.4 Entry DFCS (contt.1) 9.12.4 Entry DFCS (contld)

4. rate damping, and the appropriate torque signals are sent to the jet select logic.

Q As discus*?e

Ire fj a,, 6i 4% 0+

Pigurel3 - Letera]. Mode Paranetera

3.3 Fixed Lateral Gains Gire~i1ri Table 4 are values for the fixed lateral gain (and limit) parameters, which, from present ahmilation efforts, result in recaonable vehicle response throughout the entry flight envelope. 9.12.4 Entry DFCS (cont'dj

Tublc 4 : Fixed lateral Gaine

Dimene ion ar8 *-I-

As before, it should be notsd that the a5ove gains are qplf@ie to the M 161C vehicle. 3.4 Scheduled Lataral Gains

As shown in figure U, there are sevm variable gain parameters in '!he lateral coatrol channel: gg though g1~(excluding ge) ,Q and Be This section presents gain schedules for the first six; the 9.12.4 Entry DFCS (cont'd) dynamic pressurs is limited in the same nanner as dicuased in section 2.4. As with the longitudinal gains, the lateral gains, obtained from reference 4, may be plotted against trim attack angle, and then fit in a piecewise.linear sense. The trajectory independent gain schedules are shown in figures 14 throwh 19 with all gains hct- ions of attack angle.

3.5 Lateral Channel Inputa. Outputs, ad Sample Rates A.s vith thelon@;itudinalcontroller, the inputs for the lateral controller fall into the two categories of control inputs and gain inpats. 2hese inputs and their corresponding origins are tabulated below :

Table 5: Lateral Inputs

The outputs for the lateral controller are cammded' rudder and C C aileron deflections, (; and $, , and commnded roll and yaw ACPS acoeleration~a~C and*. C . To obtain elevon commands the aileron comand mget be differenced with the elevator command as shown in figure 10. As with the longitudinal controller, the roll and yaw ACPS acceleration command8 must maks use of a jet select logic. The eample rates for the lateral controller are the same as fcr the lringitudind chauel: a ssmpling frequency of 8 hz for the control loop and 0.4 hz for the gain loop. r 9.12.4 pltrv DFCS (cont'd) 9.12.4 Entw DFCS (cont'd) 4 9.12.4 Entry DFCS (cont'd)

9.12.4 Entry DFCS (cont'd)

9.12.4 Entry DFCS (conttd)

References : 1. MSC Memorandum ES2-71-2; 8, "A Preliuhq Design for a Blended Entry DFCS (~ev. 11, November 10, l97l. 2. K'C Memorandum EG2-71-206, "A Prelimhary Design for a Blended Entrg DFCS,n October 19, 1971. 3. BCMemorandum EG2-71-207, :.iehicls Dgnamic Parameters DLring Entry," October 19, 1971. 4. BS Memorandum EG2-71-208, "Autopilot Gain Parameters for Entry, " October 19, 1471. TRANSITION

The transition phase starts st the end of the entry phase j:st prior to the pithhover from a high weof attack to the cruise angle of attack. This period of pitchover constitutes the transitiori phase. The transftion phase ends with the attainment of the nominal cruise qleof attack. lwo distinct functions are -performed during t~arisition:

1. Transitian from entry control which la ba~ically RCS attitude cmtrol to cruising flight control, which is basicnllr full aerodpadc control. 2. Transiticn from entyy angle of attack (high a) to cruising angle of attack (low a). The transition phase is character-zed by a transiti~nir_ contra1 modes and sm~form of flight path angle control to effect a mooth transition to a new equilibrium altitide. This suggests that SODS 2hanges to the guidance Logic will also occmr during this perf&.

In this Section it: presented the first cut at a Unified Mgital Autopilot. A basic structure ic provided for the purpoae of encourging commonized coding for all control system. A specific control law is included for only the Transition phase. Ths spproach is currently being extended to ot%er miasion phases, and tie Transi$ion autcpilot is bing upgraded as additional ikforkr mation becames available. The autopilot stmcture presented here was in- tentiorally made g3neral enough to coqasa all mt$cipated roqtrirements. ks specific autopilot designs mature for i;he various dssion phases, the re- quiremen"us f or certain aspects sf the coding presented here may not mteridi3e. For e-le, the bending state estimatio~is predicated on a reqdre-mnt for active control of several bending modes, a requirement that may not m.terialize. SPACE SAXmrTLE

GN&C SOFTWARE EQUAT IOE S UBMM'TG

Software Equation Section Transition Attit~l~ontrol Submittal Bo. 22

Function: ?Jnified Digital Ahtopilot with s2ecificA- reference to the Transitio~! phase.

$Mule No. W-4 Functior; NO. 2 (MSC 03690 :lev. A) Subsitted by: R. F. Stenael Co . KT No. 8-71 Date: 1 July 1971

NASA Contact: W. H. Peters Organization ECI:i Approved by Panel I11 a. Date (Chairman)

Summurg Description: Basic stawcture is presented for a Unified Dln,tal Autopilot. A preliminary tzsatment is provided for attitude control during the transition phase.

Shttle Configuration: (Vehicle, Aaro Data, Sensor, Et Cetera)

With the current generalized treatment, the software is basicallv independent of configuration.

-- (Design Status) - (Verification Status) - - Panel Comments : ).- 1. INTRODUCTXON-- The objective of the Unified Digital Autopilot Program is to prgovide rctationai and translational control of the space shuttle orbiter in all phases of flight, fram launch ascznt through orbit to entry and touchdown. The program provides a versatile autopilot structure while maintaining simplified communications with other programs, with sensors, and with cor;trol effectors by the use of an executive routine /fur,ctional subroutine format. The program reads all external variables at a single point, copying them into its dedicated storage, and ccnirols its major support subroutines to be synchronous with the autopilot cycle. As a result, the autopilot program is largely independent of other programs in the guidance computer and is equally insensitive to the characteristics of the processor configuration ;dedicated guidance computer vs. shared multi- ;~rocessor). The unified autopilot program makes provision for sampling rates which are integer multiples of a basic sampling rate, using counters to establish the synchrci,ous cycles. Extended computations carried out with a low repetition rate must be provide-: with pre-determined break points, in o~derthat the low rate - anci high rate - calculations can be inierieaved. This requires pro- grammer co~trol,but it has the advantage of precluding skipped or lost computation cycles (unless interrupting external programs of higher priority monopolize the computer's time). The sequence of autopilot subroutines is arranged to minimize transportation lag, the time interval 5etwee:l receiving a measurement and effecting a control fcrce. While this lag mby be largely duz to equipment external to the guidance computer, the time required for control computation can be significant. As a consequence, the state estimation computations are separated into two subroutines. State measurements are incorpcrated in the esfi- ma1 o t- )r filter in the early portion of the autopilot cycle, but the remaining state propagation or filter "push-down" does not occur ciltil the autopilot commands have been written in the control effector output channels. In order to discuss the Unified Digital Autopilot Program beyond the level of the functional flow diagram, it is necessary to make specific refere~~ceto the autopilot for a particular missior, phase. The transition from entry to cruising flight has been chosen for this purpose, as this phase makes use of all of the types of autopilot subroutines. The prototype transitlox autopilot described here can be considered an upper limit on the control system computational requirements, as it includes adaptive bending mode stabilization, high order state estimators and controllers, optimal state estimator gain computations, aerodynamic -and reaction jet control, inertial and aerodynamic parameter estimation, and sensor /effector failure detection. It is almost certain that simpiificationa can be found: however. it is equally likely that unexpected complexities will occur. It should be emphasized that this is not a final transition autopilot design. A Mode stabilization estimation matrix (diagonal) z 91 Element of ---A B Mode stabilization estimation matrix (diagonal only -- for unc~up!ed elastic modes) Element of B b~~ - -C Mode stabilization estimation matrix (diagonal) CI Roll moment effectiveness ratio 'm Pitch moment effectiveness ratio cn Yaw moment effectiveness ratio Element of C 11 - -D Mode stabilization estimation matrix (diagonal) Element of D 11 - -E Mode stabilization control matrix (diagonal only for uncoupled elastic modes) f Rigid-body control vectors -1, 2, 3 H Altitude =I Identity matrix Rigid-body estimator gain matrices 5, 2, 3, 4 k Ratio of specific heats

k1, 2 Dynamic pressure estimator gaine -M Rigid-body measurement transformation matrix (longittcdinal axis)

M Mach number

-N R igid-body measurement transformation matrix (lateral-directional axes) P Me~surementnoise covariunze matrix - (longitudinal axie) Stagnation pressure minus static pressure Roll rate (body axis) Measurement noise covariance matrix (lateral-directional axes) Dynamic pressure Covariance matrix of -x Universal gas constant Yaw rate (body axis) Covariance matrix of -v Mode stabilization sampling interval Air Temperature Velocity component along x-body axis (earth-relative, positive forward) Mode stabilization measurement vector Rigid -body disturbance input covariance matrix (lateral-directional axes) Velocity component along y-body axis (earth- relative, positive right) Magnitude of earth-relative velocity vector Perturbation state estimate vector (lateral-directional axes) Rigid-body distl1rbance input covariance matrix ( longitudi~alaxis)

Velocity component along g -body azI.3 (earth- relative, positive down) Perturbation state measurement vector (lateral-directional axes) Perturbation state estimate vector Mode stabilization estimate vector Variance estimate for .th component of y J- Perturbation atate measurement vector (longitudinal axis) Angle of attack Sideslip angle Control deflection vector Bending mode estimator damping ratio Pitch angle Air density Roll angle Yaw angle Transformed bending mode natural frequency

Bending mode natur a1 frequency

Aileron Control Autopilot output quantity DB Dead b and DLC Direct lift co~ltrol e Elevator Estimate Quantity estimated by -atopilot

Guid ar ce Input qusrtity from guidance program I Bending mode index i Current sample of subscripted quantity Measurement Measurement input to autopilot RCS Reaction control system Rudder

Speed brake Derivative with respect to control deflection 9-13.1 Autopilot (contld)

Special Notation

Derivative with respect to time

(-7 Mde stabilizati~ncontrol output ("1 State estimate before measurement update De-tuned bending mode estimation quantity

Transpose of mati-ix or vector FUNCTIONAL FLOW DIAGRAM

The sequence for a single autopilot cycle is illustrated in the functional flow diagram of Figure 1, The autopilot program is called on a periodic basis with a sampling frequent:? determined by the highest bandwidth control mode. which, in turn, is a function of the flight phase. Active bending mode stabilization will require the highest sampling rate; where this is not necessary, the sampling rate will be determined by rigid body control requirements. Initimli- zation branches r-re as~rnchronous, occurring only when the flight control mode changes or when there is 8 computer restart. All other branches are synchronous with the autopilot sampling rate, although their sampling intervais may be integer multiples of the basic sampling interval.

The basic subrcutines of the unified distal adopilot we the followir-g:

a) Sequence Pnd Input / Output Initialization Subroutine This subroutine establishes the address of a list of subroutine addresses according to the flight mode, determines the basic samoling interval and th2 integer multiples for medium and slow sampling rates. and initializes all indices b) -Read Subroutine This subroutine copies all inputs to the autopilot into dedicated temporary storage. The read list and sampling rate are functions of the flight control made. C) Filter and Parameter Initialiutinr,- Subroutine This subroutine initializes statt ud parameter estimates either at predetermined values or at the appropriate values read by (b) as required by the re,- or control mode change. d) -Bending Stabilization Subroutine This subroutine performs the minimum computations necessary to stabilize the bellding mode(s). It incorporates new measurements in the bnding coordinate estimates, computes control commands, and, if bending pamameter adaptation is performed, compctes the avei qes required by the parameter adjustment law. 1 .irameter adj*tstment, w.hich may Autopilot ( cont 1 d)

be carried out at a lower rate, is performed in (h). In the present scheme, this suSroutine does no rigid- body control. e) Perturbation State Estimation Subroutine - Part I Measurements and computed cmtrol outputs are incorporated in thc first part of the estimation subroutine. Perturbations from the flight profile generated by the guidance progrsm are estimated here for use in the control law which follows. Only those perturbatl~nstates which arc necessary for control or for display to the crew are estimated. This may include coordinates of bending or sloshing nlodes v 'lich are not sufficiently decollpled from the rigid- body modes for stabilization in (d). f) Rigid-bod: Control Subroutine This subroutine uses the outputs of (e) to derive control effector cornmancis, which are intended to null the error between the actual and desired states. For proportional control eifectors, e. g., engine gimkals or aerodynamic control surfaces, the control law may simply consist of scaling adcqordinate transformation. For RCS thrusters, 2hase plane se..ritching logic can be used. g) Perturbation State Estimation Subroutine - Part I1 The calculations performed hore prepare the estimator for the incoi-poration of measurements and control outputs on the next approprrate autopilot cycle. In the case af all estimator expressed as a constmt- coefficient digital filter, this consists of "pushing- down" the filter variables, i. e. , st~ringthe i- th value in the (i - 1% lacation , etc. For a time- varying filter expressed as a state-space estimator. the starc must be propagated to the next sampling instant, and revised g~nsmust be computed (it is possible that the latte- be $one at a rate which is slower that the propagation sampling rate). h) bend in^ Parameter E' tim mat ion Subroutine Should mcertainty or time vari a+.ionin the bending parameters be excessive. this subroutine will revise the parameter estimates, either by parameter scheduling or parameter tracking, as required. This subroutil~ecan oe executed at a slow rate. i) Ynertial Parameter Update Subroutine-- 'A 4ssubroutine will alter ma.rs, moment-of -inertia, and RCS specific control moment estimates at a slow rate as required for revision of estimator and control law constants. j) Aerodynamic Parameter Update Subroutine This subroutine will alter dynamic pressure, Mach number, state transition matrices, and aerodynamic specific control moments at a slow rate as required for revision of estimator and control law constants. The ca'culations madr in this subroutine are dependent ou the flight control mode. k) Failure Detection Subroutine This subroutine examines the variances in the state and sarameter estimates of the previocs sdbroutines for "reasonability", detecting failures in sensors or control effectors by compadng the computed results to thresholds for normal operation. The subroutine is an adjunct to the failure discretes issued outside the autopilot program; since it depends upon an averagh~gprocess, it can hz executed at a slow rate.

Although not explicitly shown in Figure 1, the option to branch to "Closeout" is availab.2 at each branch point. This precludes wasted testing when, for example, a bending stabilization computztion is the ~nlycalculation required on a given autopilot cycle. It is also implicit that lengthy subroutines contain break points, allowing internal branching on intermediate autopilot cycles. For example, an aerodynamic parameter update subroutine with e ampling interval 50 times longer than the bending stabilization sampling inte rv8l can be .entered at the higher rate, with computations proceeding from breakpoint to breakpoint on sequential passes. 9.13.1 Autopilot (conttd)

5'ENTRY

Iseque.-ce and 110 I

Yes

Filter and Parameter . Initialization 1 i

Yes

Figure la FUNCTIONAL FLOW DIAGRAM Rranch 4 to Part I of h- mEstimator

Branch to Part I1 of Estimator . Estimator EstimatorZ Estimator

Figure 1 b FUNCTIONAL FLOW DIAGRAM 9.13.1 Autopilot !corrttdj

Yes

Yes Update Mass, Inertia RCS ?/ Moment Update

Aem- Yes

q, M, Aero Control No Gain, ex, Update

gCloseout Figure lc FUNCTIONAL FLOW DIAGRAM 3. PROGRAM INPUT-OUTPUT The unified autopilot program will require inputs from inertial sensors, air data sensors, automatic guidance programs. manual controllers, failure monitor devices or programs, and the data management system's executive or control program. Control could be improved by inpdta from control effectors, e. g. . aerodynamic surface or engine gimbal deflection angles. and bending or slosh displacement sensors. Autopilat outputs will include control effector commands, crew displav variables, and parameters of value to guidance and service prc_s:ams. The input-output lists are dependent on the flight control mode; the lists which follow are based upon the transition autopilot prototype. For this case, it is further assumed that angular and translational state vectors are transforn~edto earth- relative. body-axis components before being read by the autopilot. that control effector sensors and elastic displacement sensors are not used. and that tht space shuttle vehicle is equipper! with conventional aircraft control surfaces as well as a reaction control system. The subject of what types of sensors are used to measure the vehicles state is not addressed. It is assumed that the transition maneuver is unpowered (no thrust input) and automatic (no manual input). Direct lift sad drag controls are accounted for in the estimator but are not specifically co-anded by the autopilot prototype. Mode and failure discrete8 are not specifically identified in these lists, nor are crew display variables. Input Variables

Desired altitude Measured altitude Stagnation pressure minus static pressure &sired roll rate Pguidmce Measured roll rate Prneasurement Desired yaw rate rguid ance Measured yaw ?ate r measurement T ( 11) Air Temperature Time Time-to-go

Desired velocity dong x-axis Measured velocity along x-axis Desired velocity alrri~gy-axis Measured velocity along y- axis 'measurement Desired velocity along z-axis Measured velocity along x-axis Nominal aileron deflection Desi~eddirect lift control setting 'DI.C guidance Measured direct lift control setting %LC Measurement Nominal elevator deflection guidance Non'linal r rldder deflection 'r guidance Desired speed brake setting %B guidance Measured speed brake setting 'SB measurement 8guidance Desired pitch attitude e measurement Measured pitch attitude 'guid ince Desired pitch rate Measured pitch ratz 'measurement d H) Air density DLsired roil attitude Measured roll attitude 'measurement D~siredyaw attitude bguid wce Measured yaw attitude

Output Variables RCS thruster identification (one per commanded thruster) RCS thruster on-time - roll axis RCS thruster on-time - pltch axis RCS thruster on-time - yaw axis Aileron deflection Elevator deflection Rudder deflection 9.13.1 Autopilot (conttd)

4. DESCRIPTION OF EQUATIONS The equations of this section are applicable to the control of an elastic vehicle in atmospheric flight, with particular reference to the transition phase of the shuttle's return from orbit. The transition phase actually consists of 2 transitions: sn angle- of attack transition and a control effector transition. The transition from high-to low-angle of attack is necessitated by the need to meet heating constraints early in the flight aid the requirement for inc. sased maneuverability toward the end of the flight. Similarly, reaction control thrusters provide attitude control during hypersonic flight, while aerodynamic control surfaces are used during the terminal portion of the flight. Eech type of transition causes major chmges in the dynamic characteristics of the system over a relatively short time interval. The transition autopilot prototype includes the followiag elements : a) Adaptive stabilization of 3 structural modes based upon a 11classical" resonance filter, b) Linear optimal estimation of the rigid-bady perturbation state. c) Gain- scheduled control comalands to 3 aerodynamic surfaces. d) Simplified phase-plane lcgic for backup control using the reaction control system, e) Inertial and aerodynamic parameter update. and f) Sensor and control effector failure detection. Bending Mode Stabilization It has not been determined that active bending stabilization will be necessary for the space shuttle; however, should this be the csse. a high oandwidth mode stabilization control loop will be required. Thi ; infers not only that sensors and control effecters have high bandwidth capat ility , but that the digital compenaatio~ibe executed at n kigh sampling rate. If rigid-body control and mod : stabilization are combined in a single estimator- control law, the resulting number of computations may be exeassive. As anrlternative, it is suggested that the computations be partttianed, with the rigid and elastic control equations executed at different rates. A simple mode stabilization law is then executed et a high 99 13.1 Autopilot (cont f d)

rate, wklile the more! complex rigid-body control occurs at a slower rate which is consist,ent with the frequencies of rigid-body motion.

The mode stabilization technique is divided into 3 parts: ident ificetion of the bending frequencies, estimation of the bending mode corrnponents in the state measurement, and control to oppose the bending deflection. The present design neg1ec:ts the transportation knd dynamic lags of the control loop but could be modified as these quantities are identified. It also assumes thuat inertial angle measurements are the only inputs for bending mode control.

The continuous-time resonant filter.

where < is a damping ratio, and wf is a radian frequency. has a frequency response of 1 when o = uf, while its frequeccy response at zero and infinite frequency is 0. The sharpness of the resonant peak is determined by c, and the filter's tuning is fixed by 'ut. A discrete-time realization of this filter is required for implementation in a digital systern.

The details of digital resonant arrd notch filters can be found in Ref. 1, where it is shown that the bilinear transformation,, s = (2-l)/(z+l), can be used to find the discrete-time version of eq. 1. This transformation eliminates the "folding" problems of the z-transform by mapping the entire e-plane into a horizontal segment with width f n/ T radlsec (where T is the sampling interval), i. e., it establishes the frequency relationship, 0 = tan uT/2, and provides the corresponding digital filter as 2 well . The recursive digital filter corresponding to eq. 1 is

where 9.13.1 Autopilot (cont Id)

Equation 2 has unity frequency response with zero phase lag when w = wf and has zero frequency response for o = 0 or WIT. Thus, equation 2 passes 1 sinusoid at frequency uf, without modification, while frequencies to either side are attenuated. If this resonant filter is tuned to the bending mode frequency, then yi is a sampled estimate of the bending displacement, and a control command of the form,

is in-phase with the bending oscillation. By proper choice of the magnitude and sign of e, commanding the appropriate control effect - or with 46i will oppose the oscillation. It will be recognized that this is a form of phase stabilization, and the lags mentioned earlier can not be neglected. This col~trollaw is proposed only for a csss in which passive - or p*.;n-stabilization is not sufficient. In the latter case, it would be sdfficient to use equation 2 to form a s~~btractivenotch filter1

to neglect explicit commands to the control efrectors for bending stabilization, and to us u{ in the rigid-body estimation and cont tbol.

The mechanism for the adaptation of the resonant filter is the tracking of a relative maximum in the power spectrum of the input signal. The variance of yi forms an estimate of the power spectral dsnsity at w = wf (with a bandwidth proportional t to wFj. A resonant filter tuned to uf = wf + Arrr yield^ an I estimate of the power spectral density at w = wf in the form of t the variance of yi. The greater varivnce i: assumed to lie closer to the spectral peak, indicating the direction for adaptation. Upon reaching the relative maximum, the frequency estimate will limit cycle about the proper value, a minor deficienc; which c~illdbe rectified at the expense of adding a third resonant filter. A recursive estimate for the variance of yi car. be found from where k is a constan? between 0 and 1, and a eimilar equation t can be applied to yi.

It may be necessery to stabilize more than one elaskic mode, and each mode may be present in more than one axis. In the worst case, it will be necessary to transform the measurements hitc normal coorri~testo perform the bending mod2 estimation on +he transformed coordinates, and to control each mode with more than ctle control effector. Then vector analogs of eq. 0, 3, and 5 must be formed:

In a.11 cases, -& - and Q- are diagonal matrices with elements dependent on the damping and frequency of the normal modes. Band &are diagonal only if y, -u, and Ab- have identical dimensions and if the ccrmpanents ~f -u are normal (in the bend- modes). If this is not the case,

is diagonal and has elemems 2tj q., and & transforms -u I tcr normal coordinates. & ecales y for proper control of the n~rmalmodes and transforms the result tc control effector coordinates. Equation 8 is actually n scalar eqwtione, as the components of y are indemndeat.

For the flow charts of Section 5, it is aeaumed that there are 3 elastic rnode~,3 awemeaslrrementt, and 3 control effectors. Autopilot (cont 1 d)

4.2 --fiigid- ---- bod^ ------.------Ferturbation State Estimation For control during the transition, it will be necessary to have an estimate of the crror between the desired state, as determined by the guidance program, and the actual st-ite, as inferred sy the state measurements. The error, or perturbation state, can be estimated usin3 a linear recursive filter whose general form is

Equation 10 propagztes the perturbation state according to the homogeneous equations of a physical model asin, the etate transition matrix, 9.- The effects of model errors and f~cingt~rrr s are adied in eq. 11. Equations 10 airi 11 provide a completely general formulation for linear estimation; it is the means of determining -9. El, and & which defines the filter as optlmal, near- c;t;mal, or iiJ &. The Lunar Module rate estimator is an example of an Lox. estimator which can 3 be expressed as a speclal case of eq. 1G and 11 .

For the transition phase an optimal estimator has been proposed, and the Section 5 flcw charts make additional assumptions . The transition estimator is partitioned according to aircraft convmtlor,, i. e., into a longitudinal set and a lateral- directional set. The estimator for each set incorporates all the variables which ;r r ;lccessarj to solve the linearized equations normally used for the study of stability and control. Keeping in mind that the autopilot is primarily responsible for attitude control, it may prove possible to eliminate from the autopilot estimator some or all oi the variables normally associated with "guidance", thus reducing the dimensions of each of the two estimators; however, this should not be d~newi+hout assurances that the integrity of guidance-control interaction is maintained. It is assumed that the measgrement variable3 have been transformed to the d2sil-ed body-axis coordinates before being read by the autopilot; hence, no additional transformations are necessary, and the &matrix of eq. 11 is an identity matrix with the dimension of the measurement, -z (which nted not be of the same dimension as -XI. The measurenlent vector of the longitudinal estimator is defined as

Guidance thus it includea axial v!elocity, normal velocity, acd height errors as well as ?he conventional pitch and pitch rate errors. The control vector,

includes direct lift coatrol and speed brake setting as well as elevator serting and pitch thruster rate, with the assumption that the guidance prohiides estimates of what these quantities should be (with the exception of reaction control rates), No assump.ion is made with regard to the source of the "control" quantities; they may be derived from autopilot and guidance commands or from control effector measurements. The latter is clearly d2sirable if accurate meassrements are available; however, there is preced~ntfor !.sing the former in the Apollo digitril autopilots. .- 9.13.1 Autopilot (cont'd)

The estimated perturbation state, -x, is

Estimate

The gains & and & will be described in a later paragraph. The angle of z.ttack estimate is derived from the total linear velocity estimates (summing perturbation estimates with nominal values) using the conventional formula

a = tan -1 (-w7- ) Estimate W - A Estimate = tan 7-u---:--- Est~rnate

Similarly, the lateral-directional estimator inclcdcs the measurement vector,

Guidmce

the control vector,

Control and the estimate vector

Estimate

The sideslip angle estimate akain uses a standard formula:

z sin-' (I' ) 1 Estimate

('~uid +vA Est T------+w )I1122--- - YW~uidA Est 1 The flow charts of Section 5 indicate that calculations of eq. 10 and 11 occur at different points in the autopilot sequence. In particular, eg. 11 occurs soon after the input is read, while propagation of the state (eq. 10) occurs after the control command has been issued. This is dme to minimize transportation lag between the computer input and output. Since eq. 10 is solved for the --next autopilot cycle, the indices are incremented by one, and the equation appears in the flow =hart as

A = px. 5+l -4

ALthough the longitudir 1 and lateral-directional estimators are each 5-dimensiont., it is likely that many of the off-diagonal elements of 9- will be negligible, allowing a reduction in the number of additims and multiplications necessary to s~lveeq. 10 and U. 9.13.1 Autopilot (cont'd)

Estimator gains for the transition autopilot prototype are computed in real-time and are the linear optima] gains associated with ~alrnan~and presented by Liebelt 5 . The gain calculation is based upon the estimation of state covariances, B,- which in this case also dzpends upon -\a ~iori--- knowledge of the disturbance input and measurement noise covariance~. The covariance propagation, covariance estimate, and gain computation equations are

Here the indices have been incremented by one, as the solutions apply to the next autopilot cycle.

It will be notes that the gain matrix has been partitioned. El is the gain matrix which operates on the measurement residuals; g2 operates on, the control inputs, which are represznted as estimated residuals in the gain comp.atations 6 . The measurement tranformation matrix, a, is augmented as nzcesssry to incorporate the control iilp11t.s (hence the subscript, A). The disturbance input covaritnce matrix, &, appears in eq. 21; in general, this term prevents the gain matrices from vanishing under the influence of the inverse of the measurement naise covariance, -2, in eq. 2.2. The ebove notation is used for the longitudina; estimator; in the lateral-directional estimator, -N, C& -S, and -V are substituted for &I,---2, R, and _W.- The state transition matrices are different in each case, being subscripted by x and v accordingly.

Although it may not be apparent from the equations, this formulation of the optimal gain is well-suited to incorporating data at differing rates. As an example, let us examine the longitudinal estimator, assuming that 6 is not measured and that only reaction control torques are present. Further assume that 0 is measwed on each autopilot cycle, that U and W are measured every tenth cycle, and that H ie measured every fiftieth cycle. The diagonal matrix is potentially fifth order; however, it is only fifth order when all measurements are taken simultaneously, i. e., on an autopilot cycle when U, W, H, and 6 are meascred simultaneous!y and when in non-zerc. When there is no control torque, - has a maximum dimension of four, but this Dccurs, at most, every fiftieth cycle. It is easy to see that measurements can be staggered so that the dimension of M is .?ever greater than 2 (asssming that the pitch attitutde meas~rement,8, is incorporated zn every cycle). This simplifies the estimator greatly, particularly as a result of the reduced dimension of the matrix inversion in eq. 22. The price paid for the reduced dimensionality on any single pass is the increased logic and storage required to account for the 5 measurement combinations (8 ~lcsU or W or H or bBRCS); however, the computation-time snving is considerable. This estimation scheme is demonstrated in Ref. 6.

Rigid- Body Aerodynamic Control

It is assumed for :he transition autopilot prototype that the shuttle vehicle is equipbed with three independent aerodynamic controls - aileron, rudder, and elevator. In fact, each control surface generates secondary torques, and for the delta- wing configuration. the elevator and ailerons are likely to be combined ia "elevons".

The postulated control law includes nominal aileron. elevator, and rudder commands obtained from the guidance program (where the commands may Le stored, computed, or arbitrarily set to zero) plus perturbations derived from linear feed back control. laws. The control gains may simply be stored functions of the time-tc-go, t however. the nonlinearity of 80' control effect. ' the aide range of angle of attack, dynamic pressure. and Mach number8- and the variaticm in "nomhl" conditions from one mission to another may impose a requirement Autopil3t ( cont 1 d)

for additional flexibility. This will be especially true if the guidance program is unable to provide nominal control setti.lgs.

It is proposed, therefore, that the control gains be comprised of two parts: 1) a set of feedback gains stored as a function of t and 2) a factor to ccrrect control surface effect- go iveness as a function of the estimated flight condition and the actual control setting. The gains dependent on t can be obtained 80 prior to the flight by minimizing quadratic costs on the state and control in the linearized model of perturbations along a n~minal flight path. lo The ccntrol effectiveness fnctors are stored tables or functions whickare dependent on the deviation of flight parameters from their nominal values. The control surface commands then take the form

and

a = (b + A ,,Ii a i a~uidance

= (8 + dr i rGu idance

He re. C,. CL,and Cn are not the converit ional non-dimensional aerodynamic coefficients; they are tbe control effectiveness factors. The vectors f 5.and5 are tke feedback gains which are stored as functions of t go' For the delta wing configuration, control moments about the three body ares will be supplied by the rudder* and a pair of elevons. The specific control moments due to rudder deflection (er). left elevon detection (de , and right elevon L ' Some configurations have dual vertical tails and, the refore, two rudders. deflection (6 ), will be e~

Expanding to first order,

Then the perturbation specific control moments due to feedback control can be expressed as and

6 = (6, +A6 1 e~ eR i i R~uidance

r = (ar + A6r)i I Guidance

The partials L6 , L6 , are equal only for identical e~ e~ mean deflections, as control effects are nonlinea-, iiarticularly at high angle of attack. This distinction is particularly irclportant as a result of the coupling of longitudinal and lateral -directional control actions indicated h eq. 35b. The separation of control gains into time-deper-dent and flight cond it ion-tiependent components is retained. in eq. 35b; however, it is clearly possible to evaluate the aerodynamic control partials for the nominal flight condition and con settings, making them functions of time as weil.

Above a certain angle of attack, the rudder effectiveness of most orbiter configurations will be negligible; thus, the 3rd column of the partial matrix in eq. 35 is effectively zero. While the elevons (or ailerons) could be used to control yaw, there are only 2 control szrfaces for 3 axes, and the control of each axis is no longer independent of the other axes. This coupling could be beneficial ("provers~"1 or detrimental ("adverse "l , 'n general, it will be necessary to supplement yaw control a'. high angles of attack using the reaction contrc! system. Auto~llot ( cont 1 d)

4.4 Rigid Body Reaction Jet Control The ceaction control system used for attitude control during orbital flight and high-angle entry will serve as a backup control system during the transition (as well as a primary system for yaw during the early transition phase). Consequently, it is sufficient to provide a rate dampicq and attitude limiting control law with wide deadbands fcr pitch ar?~roll (or sideslip), assuming that the aerodynamic control surfaces will exert precise control within the dead zones. A more precise parabolic-curve switching logic iS retained for high angle of attack yaw control. An important feature of the reaction control logic is that it not oppose the aerodynamic control inadvertently. Unless the lags in one system or the other are excessive, opposition will be re vented by using the same attitdde estimates for each set of control laws.

The control law for the pitch axis commands the appropriate control jets when 1 A 6 1 s iDBor when 1 A@ I .BDB- At high angles of attack, sideslip angle and yaw attitude are very nearly normal-mode components of the lateral-dircztional rnr!ion?' Thus it is appropriate to choose thess as control ares, firing roll and yaw jets simultant.ously when sideslip errors exceed their deadbands and firing yaw jets alone when yaw limits are exceeded. Sideslip rate ran be approximated by a combination of rcli and yaw rate errors, allowing the sideslip rate damping to command jets on when 4 ~4 cos a + A; sin ol > iDB.The sideslip limiting logic consists of commanding jets on when 1 $1 - BDB. Parabolic switch curves similar to the Lunar Modulet8 TJETLAW~or to those presented in Ref. 12 would be used for yaw control.

Oelow some angle of attack (to be determined) the sideslip control law degenerates into a redundant yaw contrc~ller, and tne rudder becomes effective as well. At this point, the sideslip control law should be replaced by a body-axis roll law, firing on 1 A; 1 > GDB or ( A@ ( > gDB- Slnce the rud,der becomes the pri3~1.yyaw control effector, simple d and 6 deadband logic then replaces the parabolic curves. 9.1 3.1 Auto~ild( cont 1 d)

The selection and timing logic for the control thrusters is similar to the Lunar Module logic and is not repeated here. The choice of selection logic is based on the number and positioning of control jets; should a highly redundant configuration be chosen, a linear programming approach could be considered as an alternative to the LM design. l3 Timing jet firings to the nearest millisecond, as in the LM-Alone autop~rot (rather than to the resolution of the sampling interval, as in the L?.Iil's CSM -Docked autopilot 1, is essential 1) when the reaction control system is the primary sjstem and 2) when the mode of motion most closely associated with a control axis is unstab~e (this car, occur for both longitudinal and lateral-directioiial modes). 14,15

4.5 Inertial and Aerodynamic Parameter Update Inertial and aerodynamic parameter updates are sepzrated in the Section 5 flow charts because it will not always be necessary to update both at the same time. Although the inert iai. update is included in the trans it ion autopilot prototwe, this subrout ne r-eed Sc done only when a main engine is firing and substantial changes in the vehicle mass are occuring (reaction controi pr*cspellant usage can be ignored). In this case, the mass estimate is decreased as a function of the average thrust during the last. autopilot tampling interval,

*n--- - nu--- ' A ~N-QS. (Thrust) .I.-.&--L 1-1 -. while moments of inertia are functions of the msss,

and reaction jet specific control moments ("jet accelerations") are functions of the moments of inertia. Both the moments of inertia and the specific control moments are reqvired, as these data are necessary for aerodynamic control as well a9 reaction control. The need to vary the relationships between masu and inertia as functions of cargo bay loading must be determined. It is aot anticqated that products of inertia will bt estimated; however, cargo bay loading could have a significant effect on the 'hose-up" product of inertia. Jxz.

The aeror',yr.aaic parameter sloroutine wtU update dynamic presiure, q, Mach number, M, aerodynamic cohtrol gains, and the estimator's state transition matt ices. The dynamic pressure ctin be derived from the difference between measured stagnation and static pressare; it also can be derived frcm the eathated total vebcity hgt.and the air density. p M). A 'best estimate" can be formed by combining the two using parametric optimization. Assuming static pryssure and air temperature are measured (or stored as a function of aititade 1.

where R is the universal gas constant, and

The weighting constants, kl and k2. are determined by the known variances in g and q2:

The Mach number is determined from the total velocity estimate and the measu~dair temperahire:

where k is th9 ratio of specific heats for air.

An alternative formulation for ql eliminates eq. 43 and uses eq. 47. It is The control effectiveness correction parameters of cq. 23-25 or the inverse matrix of partial derivatives in eq. 35b are next computed as functions of a, M, and control deflect~an. The optimal gain vectors il,i2, and& are computed as functions of t The prod~ctof cmtrol effectiveness correc- go' tions and the gain vectors is taken m the update subroutine in order to minimize computatior.s in the more frequently computed aerodynamic control subroutine. Finally. the estimator's state transition matrices are upciated as functions of a, q, M, Mass (or Inertia), and t using a ridapproach similar to that for PD control gain computation. As in tile case of the control gains, the purposr, behind the dual approach is to maximize reliability and flexibility by incorporating both expected matrix values with measured values in the state transition matrix update.

4.6 Failure Detection This subroutine ha15 not been examined in detail. The fsiiure detection algorithms will monitor estimator residuals ior abnormalities which would indicate failed sensors or control effectors. They wiU be tailored to the mostprobable failure modes of the monitored instruments. 5. Detuiled Flow Diapnn~s This section contains detailed flow diagrams for the Unified Digital Autopibt Progr- c4t). t~ecificreference to the transition flight control mode. External FLAG words

EE LINT

Yes .-+

Yes

t I Sequence & I/ 0 Initialization No . Establish the following according to Flight Mode: . Subroutine Address List . Fast, Medium, & Slow Samplmg Rates . Initialize Indices . Return to Executive i I

b'igure 2a DETAILEC FLOW DIAGRAM . Establish next DAP Entry

Branch to Appropriate R.ead Subroutine I Transition R ead Subroutine

(Read inputs according to Fast, Medium, and Slow sampling rate indices ) . Inputs: . Time Nominal Control Commanded State ( from Guidance ) "Time-to-Go", t go External Control Settings Failure Discretes Manual Commands Measured State I . Return to Executive

Figure 2b DETAILED ZLOW DlAGRAM Q

Yes ?,

1 L Filter & Parameter Initialization I . Initialize State and Parameter erti- I I mates according to Flig*t Mode . Return to Executive I

- NO 4 = %[,B (E~-E~-~ )+C-4-1+E~i-2 - 1

- ui --=&, subject to .F:]LA6r - deflection limits endi in^ - 4 = Elastic displacement ( 3 -vector 1

- A, C, and C diagonal matrix L = s - 3 and E diagonal only for Qn- couple^ elastic modes

Figure 2c DETAILED FLOW DIAGRAM 9.13.1 Autopilot (contld)

i Output Ahi 1 to Control- I Effectors

Mode Stabilization Parameter Estimation - Part I I

1 - - 2 l 1. j = 1.3

- "De -Tuned.' Elastic displacement - 7 12. = Running Estimate cf Ti:uiamesof J J Elastic Displacemed . Push Down Filters: - - - U 12 - 2 3-2 - -i- 1 = Yi Yi-lnj - $j = U - -i xi-2-xi-1 ,2yi-lnj=yinj Q-2 = Yi-1 G-l = Yi . Ret~,mto Executive . 7-Q. I 1

Figure 2d DETAILED FLOW DIAGRAM Branch to Appropriate Estimatio~r Subroutine

'r Transition lviocie lerturbalion State Estim.ator

Longitudinal.-

Control Guidance

AW - 1 'W~uid.- at i, = tan (- Est,) astimate

u Guid. + A %st.

Figure 2e DETAILED FLOW DIAGRAM I Estimator. Cont. I Lateral-Directional

'~eaeurem ent

Control Guidance

. v.=v+K(w,-N$)+K(~A I -1 -i ,3 -* r-i 4

I . Return to Executive

Figuru 2f IjETAILED FLOW DIAGRAM

90 13-41 9.13.1 Autopilot (contld)

Branch to Appropriate Control Transition Aerodynamic Control

Longitudinal- T Cm I-15 'R 'R igid

+ Abe Guidance Bending

+ hb, subject to deflection Rigid I limits Lateral-Directional

,subject to deflection + a~igidJ limits

0, Prior to Transition Jump r. v.,AfterJump -3 -1

. b =[6 r + A6 +ASr ri Guidance endin in^ Rigid 4 I 1

Figurs 2g DETAILED FLOW GXAGRAM .wControl Effectors elRE LINT

Transition Reaction Jet Control- -Pitch If 1 Ai >iDBor if 1 A@ 1 >eDB#command thrusters in appropriate direction

Sideslip ( Prior to Transition Jump Only) ~flo$ COS ai + sin ail >iDB#or If 1 >bBbcommand thrusters in appropriate direction

Yaw a) Prior to Jump: Parabolic switch curves with lo DEADRAND and ''FLAT"

, b) After Jump: If1 &dl >kB,of if 1 A# 1 > JDBbcommand thrusters in ap - propriate direction

-Roll ( After Transition Jump Only ) ~f(44 (>aB, Or if IA* command thrusters in appropriate direction

Figure 2h DETAILED FLOW DLAGRAM . r Jet Selection 1 and Timing Logic I CkIINHINT

rzYJThrusters

Return to

ABranch to uSubroutine I -Transition Mrde I Perturbation State Propxation

Figure 2i DETAILTD FLOW DIAGRAM Covariance, *timal Gains

= State Transition Matrices d' *v W, V = Input Covariance Matrices I

P,= Q= = Measurement Noise Covari- ance Matrices 5, -!,= Aagmeuted Measurement Transformation Matrices

Return to Executive

Figure 2j DETAILED FLOW DIAGRAM Estirnaticn - Part 11

Figure 2k DETAILED FLOW DIAGRAM

9.13- $6 Yes (Slow Rate) C,

No 9 . &asi = &asi- I - AMa8e ( thrust) . Moments - of Inertiai = fcn ( Massi ) . Reaction Jet Specific Control Moment = fcn (Inertia) . Return to Executive

Figure 21 DETAILED FLOW DIAGRAl11 -

-1/2

p ( H ) = Air density T( H ) = Air temperature A P = Stagnation pressure - Static pressure

- - .= fcn (a,q, M, tgo. Mass)

Cbseout Inc rernent Indices I

Figure 2m DETAILED FLOW DIAGRAM Supplementary Infomat ion The functional flow diagram of the Unified Digital Autopilot Program is largely independent of the mission phase and vehicle configuration; however, detailed flow diagrams depend on 111issionphase. The estimation and control z!gorithrns are further dependent on vehicle configuration, while the parameters for control may vary with vehicle Loading as weli as flight conditions. Algorithms and control parameters will be further developed as mission profiles and vehicle characteristics are defined.

In addition t~ standardizing functional flow, the Unified Digital Autopilot Program should allow sharing of sub - routines by autopilot logic developed for various mission phases. For example, the transition estimator could be useful during cruising flight and landing approach. It also can provide guidance system monitoring during atmospheric boost and on-line estimation during orbiter powered ascent. Failure detection subroutines will be dedicated to specific measurement and control sub5ystems; thus the sub~tii,,2 will be employed as the subsystem s are required and may be used during more than one mission phase. Inorder for the autopilot pr-ram to be truly "unified", it will be necessary to consider autopilot requirements for all mission phase, in a parallel fashion.

mqiPrrework will follow two specific paths. The unified autopilot concept will be rec;ned through simulation and further analysis; The autopilot requirements for specific mission phzses will be pursued in accordance with the assigned tasks of NAS9-? 0268, with particclar emphasis on t!!e requirements of high cross-range, delte -wing configurations. 9.13.1 Autopilot (conttd)

References

Stengel, R. F., ItDigital Resonant and Notch Filters, " MIT DL SAD Memo 16-68, Oct. , 1968. Kuo, 3.C. , --Analysl,: :.nd Synl'ihesis of Sampled-Data Control Systems, Prentice - A 'I Snglewood Cliffs, 1963. "Ciuidance Stste;;. ,-jp~ratior.sPlan for Manned LM Earth Orbital and Lunal* M~ssionsUsing Program LUMINARY ID, It

Section j, Digital Autopilot (Rev. 61, MIT CSDL R-567, Feb. ; 1971. . Kalman. R. E., 1t A New Approach to Linear Filtering and Prediction Problems, " ASME Journal of Basic Engineering, 82D, March 1960, pp. 35-45. Liebelt, P. B. , An Introduction to Optimal Estimation, Addison- Wesley, Reading, 1967.

Stengel, R. F. , "~ttitudeEstimation for a Highly Flexible Vehicle. " MIT DL AAP Memo 70-388M-1, Jan., 1970. Stengel, R.F., 11Aerodyliamic Trim Boundaries and Non- linear Elevator Effects for the NASA MSC April 1970 Baseline Orbiter. " MIT CSDL SSV Memo 70-23C-16, Nov., 1970.

Stengel, R. F. , "Optimal Transition fiom Entry to Cruising

Flight, " MIT CSDL E- 2522 (also AIAA Paper 70- 1018). July 1970.

Stengel. R. F. , "Space Shuttle Transition to Cruis kgFlight, " MIT CSDL. E-2539, Sept. 1970.

Bryson, A. E. , Jr. Ho, Y, C., Appled Optimal Control, Rlaisdell, Waltham, 1969. Goss, R. D. , ''Normal Modes fc'r Latera!! Directional

Motions of the Space Shuttle Vehicle During btry, " MIT CSDL SSV Memo 70-23$-14, Sept. 1970.

Cox, K. J. , "orbital operations rotational DAP for the

redundar t flight control systems sinlulator, " NASA MSC internal memo, Feb. 1971. C rawford, B. S. , "operation and Design of Multi - Jet Space - craft Cor~t~olSystems, " MIT DL T-509, Sept. 1968. 14. Basile, P. S. "Handling Qualities Parameters for the North

American Rockwell Delta-wing Orbiter 134C, I' MIT CSDL SSV Memo (to be published).

15. Freeman, D. C. , "LOW-Sdbsonic Aerodynamic Characteristics of a Space Sh~ttle-OrbiterConcept with a Blended Delta

Wing-Body, " NASA TM X-2209, Jan., 1971. 9.14 CRUISE AND FE%E CRUISE

The eruiee of the shuttle mission applies to the period of atmospheric flight between transition and approach. The leer-7 Cruiee pnase refers to pawered flight betweem airporte. These phase8 include law altitude earth-relative na@-gation, guidance and aeroeurface contrd. The Software i'unctione required ir thia mis~lionphaae ctre the follwiug:

1. Powemid flight navigation augmented by external d~tato aaintain esrth-relatin position. 2. Powered flight @dance resultiq in thrust 1-91 contzol (for F=;rry only) and autopilot (attitaide) cnmmais req&ed to achieve desired intereection with the terdml approach path for landing. 3. Autcpilot n.omputatione to meult in paper aer-mic surface control and trim settings to mnintaiu desjred heading ad flight path.

9.14.1 Naviaatian TBD

9.14.3 Cruise Autopilot SPACE SHU'lTLE

GNK SOF?TJARt EQUATION SUBMlTTAL

Software Equation Section cr?l;ae- .Submittal No. 36

Function Pro- t cQ

Mcdule No. 3C-6 Function No. ,3 (WC 036%)

Submitted for: FT,~ Co . (Name )

Date: 21 October 1971

NASA Contact: - W. H. Peters Organizaticn EG2 (Name)

Approved by Panel I11 .T- Date- j0/* I / 9 4 (Chairman) Summary Description: T& su-n-u: -

associeted with the manual control emlosed duriru verifica~ion

testing of the Approach Guidance equa+Yians.

------Snuttle Configuration: (vehicle, Aero Data, Sensor, 6t ~etera)

Coefficients associated with NR 161C orbiter.

Comments : - (~esign Status

' (verification status)

Panel Comments: TBbecontrol aystem for the delta wing orbiter (as implemented by the Control RPquirements Branch, GDC, & their Orulse and Landing Simulator) provide. the following modes of operation: 1) Direct Manual (CM) 2) Rate Command (RC) (3)I Rate ~~'~ttitudeHold (RCAH) (4) Automatic Guidance (AUTO) (5) Yaw ileunper (YD) Figures 1 through 3 present the comp1e:e control ayatems implemented for #MI, roll and yaw, respectively. The systems presentad include certain modifications over the previously imple- rnented control systems (for the straight wing arbiter.) For the pitch and roll spstems, the RC and RCAH control loops are no longer separate and a logic elant has been included to preclude twitching to attitude hold with large vehicle rates. In the pitch system,the tittitide hold function is ~otenga&d unless the selected mode ia RCAII, the hand controller ia in datent (QIN) , and the vebiclo pitch rate (q) minus the thcoordinatcr pit& rate (b)is -dthin 2 .0175 rad/wc (w). Swar conditiG8 are also req-a to engage the roll attitakfle hold function excppt for the *n coordhite that ia not required in the roll channel. The first parts of Figurea 1 and 3 are presented to show the turn coordinator for pitch in the RCAH mode and for yaw in the RCAH mode wit1h the yaw damper die- engaged. The turn coordinator aa implemented provides improved orbtter reqponse during banked maniivers.

In Figure 3, a seed feedback loop (fa addition to the yaw damper) ie shown in the pw coatrol system. It has been rnnluded for ctudiee to evaluate the ef- fectiveneas of lateral acceleratian feedback during cruise and landing. For baseline purposes, horever, the loop gain (R3) is zero and the loop may be dbregarded. Table 1 pre~sntathe gaina implemn%ed for all three control system. Table 2 shows the logic expressions for controlling the nrmarous switching functiod used in the control eystems. (The witch deeiptions represent logical conditions, not individual switches; and the aams suitch is employed in various locatione). Integrators controlled the logical ewitches are considered in reset, or tern- porary reset (t~0.01 sec .) , when the switch is closed. Attitude and trim ocmruands are input to the integrator initid ctmdition tomhala. The integrat.or gain is assumed to be plus one. 3.14.3.1 Manual Modes (contld) 9.14.3.2 Manual Modeog (COLA*a ..,0\ Lo 9.14.3.1 ManW Modes (contld) 3 4

'I- 9.14.3.1 lhmal Modes (cont'd) ,a TABLE 2

5t\l1rcrt I. Locllc CO~)P!T~OF)SFez I

1 l?C+KCAh + AUTO 0 ~fr/ AUTO 9.14.3,2 Cruise DFCS

SPACE SHUTTLE

GN&C SOFTWARE EQUATION SUBMITTAL

S~ft~wareEquationSection Cd.seAutopilot Submittal No, 40

# Fuction: Aerodsric cruise Matal Fli~htControl System (DFCS)

Module Function Rev. B)

Submitted by: F. Elm Co. EC2

Date :

NASA Coutackc Organization EC2 (NW) Approved by Panel I11 g-r. Date 10/+4 / 9 (Chairman)

Sumary Description: Orbiter DFCS for horizontal uerodsnamic fliaht phase of miasioa includiw horizontal take-off.noat-entry cruise, amroach / and lendiw, The DFCS receives commands fram the Guidance modules or pilots and sends cmnmRnds to the aerodynamic controlceurface, '*A.

Shuttle Cmfiguration: (~ehfcle,Aero Data, Sensor, EX Cetera)

Delta-winn Orbiter: NRl61C aero or LYSC O40A aero,

Cammsnta:

(Design Statue)

(Verification Status) Version 1IB verified at MT and at MSC (ZRALS) with NR161C aero data,

Panel Commnts: Dirtital Might Control System

INTRODUCTION

The principal objective of the DFCS, horizontal aerodynamic flight phase, is to prcvide rotational control and speed brake con- to1 of the Orbiter during those phases of the mission where the Orbiter flight resembles conventional aircraft. These mission phases are the post entry aerodynamic flight, cruise, and landing, and also the horizontal takeoff (without ~ooster). The aerodynamic DFCS contains an auto mode, direct manual, stability augmentation system (SAS) manual, and a rate command attitude hold RCAH mode. The horizontal aerodynamic flight ph~seof the DFCS is in a state of growth itself, even without regard to the incorporation of other mission phases. Modifications presently planned include additional tasks, such as anti-skid, brake control, nose-wheel l, steering, landing gear extend, throttle, a DFCS self-contained terminal guidance system, and flexible body and fuel slosh control.

This version of the DFCS provides the embrionic structure for the ultimate unified DFCS (see MIT Rep030 belaw) which wiY. be used for both rotational and translational co~trolof the Space Shuttle Orbiter and Orbiter/~oostercombined in all phases of flight, from launch ascent through orbit to entry and t~uchd~.The DFCS will evolve into the unified DFCS by sequential incorporation of the presently separate DFCS's for the other mission phases. Thus, the present DFCS contains routines iabelcd such as:

Transition Mode

Entry Mode

Orbit TVC Mode

Orbit RCS Mode

Insertion TVC

Booster TVC and such routines, while presertly empty, will contain those functions in the unified version.

The WCS provides a versatile autopilot etruct~trewhile.&- taining rimplifled c-cat-ions with other progmm, with 8emor8, and with control effectors by the use of an exlecutive-and-subroutine format. (However, +,he present version of the DFGS temporarily has de- moted theme sub-routines, for convenience, to mere routines. ) The DFCS reads all external variables (comrmands, ssmors, and lrupplied data) at a single time point, copping them into dedicated storage,and 9.14.3.2 DFCS (conttd)

controls its major support-- . aubroutines (presently routines) to be synchronous with the autopilot cycle. As a result, the autopilot program is largely independent of other programs in the guidance computer and ia equally insensitive to the characteristics of the processor configuration (dedicated guidance canputer versus shared multi-procesaor ).

The sequence of autopilot functional computations is arranged to minimize transportation lag, the time interval between receiving a measurement and effecting a control force. While this lag may be largely due to equipnent external to the guidance canputer, the time required for control canputation can be significant. As a consequence, the filter compukations are separated into two aectians, one being performed between the ltreadlt and "write," that is, Just prior to the control equations, he second filter section, including filter "punh down,'' is performed after writing camnands to the control 8Urface8, therefore does not contribute to the transport lag. The DFCS is written in a basic Fortran version (IV) without using features peculiar to a particular computer installation in order to minimize canversion problems by other investigators. Flight versions or special teet beds may require reprogramming into machine language to minimize canputation time, at the expense,of course, of engineering readability.

The baseline equations for the DFCS for the horizontal aer9- dynamic flight phases of the Orbiter are presented herein as a Fortran listing, v%?rsion 4~.The listing contains a definition of the alpha- numerics, cament cards, and a compilation.crosa reference printout, An autefluw chart ia 8180 presented, which was made from the exact listing shown. The listing and auto-flaw chart constitute version 4~ of the DFCS. Other explanatory diagrams herein, the six-page block diagrams of the control modes (version 4~),and the DFCS interface diagram (veraicm 4~),are intended only to provide understanding for the more official listing (version 4~).

MIT Reports

The DFCS was developed by the Draper Laboratory of MIT for MSC. The MIT project leader ie Dr. Robert F, Stengel. Additional information describing the DFCS can be found in:

a. Space Shuttle GN&C EE&i~m Document No. 8-71 raper Labora- tory), "Unified Digital Autopilot With Specific Reference to the Transition Phase," by R. F. Stengel, March 1971. (Sec. 9.13.1 of thio Report. ) -DFCS (cont Id)

1;. SSV M.emorandun No. 71-23~-4 r raper ~aboratory),"Cruise Phase Autopilots for the Straight Wing Orbiter vehicle," by A. Penchuk and R. W. Schlundt, May 1971. The first of these reports ctefines the intended approach for combining all the DFCS from the several mission phases into a unified DFCS, and is written in the context of modern control theory. The second report (memorandum) debcribes the servo design procedure and results whereby the analog/raot-locus selection of servo loops feedback signals, gains, and compensation were selected. The conversion from analog servo-loops to digital se~vo-loopsusing the difference equaticn approach is also detailed. The control equations for the delta wing orbiter in the present DFCS are based on this report, not- withstanding the nomenclature "straight wing" in the report kitle.

The C.Ruise Ud Landing herodynamic Simulator (CRALS) at MSC presently contains - the DFCS (version 4~)with minor modifications as required for the machine dependent interface signals. Copies of this variatioq can be obtained by request, both in list form, and as card decks. DFCS Interf'acka

Figure 1 (which is largely self-explanatory) shms the interface signals between the DFCS and other units. The signals actively used in the present version are shm as solid lines. The dotted Unes represent signals contained in the read and write statement# of version 4~ but which are not currently uaed due to zero gaim loaded in their signal flow paths.

Investigators who 'mtend to uee the DFCS need not provide the "dotted line" group of interface signals, but ii these interface sig- nais are not provided, they should also be dtted from the read statements to prevent program aborts.

The guidance system is shown in Figure 1 as two separate syrrterns; one for commands to the DFCS, and the other for computed information utilized by the DFCS. The camputed information source need not be the guidance computer, but could be other sources such as the air data computer, or navigation system, or sensors. Of the latter set, speed, angle of attack, and altitude enable the DFCS to update control gains and filter constants. Speed and "range" (range to go until touchdown) enable the DFCS to control the speed brake during landing approach.

One recurring interface problem traditionally is the arbitrary definitions for cmtrol surface poeition. Within the DlFCS and at the interfaces, surface positions of elevator, aileron, and rudder are defined such a6 to cause poeitive pitch, roll, and yaw mameuts. Thia is opponite to'some camn0nl.y uaed sign convemtlons fop elevator and 9.14.3.2 DFCS (contfd)

aileron. Elevon position polarity ia positive for trailing edge upward. A right rudder pedal push will cause a positive rudder by DFCS definition, which is the same as pilot language for right rudder. The elevators and rudder follow the left hand rule, for thumb of left hand in direction of plua y or plue z direction. The purpose of this selection of signs wae to simplify the verification cf proper eigne eince positive gains remtlt for the airplane tranr "er function. A more cwling reason for the si aelection was that in ditching from RCAH to Direct - * Mode, stick back rusing standard signr) calla for plw pi%ch rate in RCAH but nenative elevator poaitinn in Direct Mode. Using etandard signe, numerow sign ctaages w~.-ld confusingly appear aud disappear with mode switching. The speed brake angle magnitude is defined in the DFCS as one-half of the included angle between the two eurfaces. Interface simals are of two types, discretes and proportional variables. Figure 1 identifies the discretes and the values each can have. All others are proportional variables, The maximum and minimum permissible values of the interface signals have not been defined.

The "restart" discrete is considered to be generated external to the DFCS. After re-initializing, the DFCS will reset the "restart" signal to zero, wnich informs all other programs that the DFCS information is trustworthy @ricemore.

The DFCS computes -9 TNEXT and informs the main computer when the next lFCS cycle is to be called. Control Modes The DFCS (horizontal aerodynamic flight phase) provides control at thia stage of development fcrs the elevons, rudder, speed brake, and landing gear extend. The major modes are (1) Manual, and (2) Automatic, The Manual mode cont-ains three aubmodes : (1) Direct, (2) Stability augmentation system (SAS) - a form of rate cammand, and (3) Wte Om- mand Attitude Hold (RCAH). The SAS mode has been retained because of historical pilot familiarization with it and for pwposes of evalu- ati~~gcmparative flight handling qualities.

The manual modes receive commands froan the pilot's hand controller and rudder pedal. In the Direct manual mode, the hand controller sig - nale are considered elevator and aileron position commands. lh SAS and RCAd manual modes, these eame pilot's hand controller signals are considered as attitude rate commands, pitch rate and roll rate. The rudder pedals ccllnnand rudder position in direct mode, and sideelip in RW. The Automatic mode receives Cammands only from the guidance system. Provision is included for many other guidance command signals which may be utilized in later versions if required by guidance. Verrion 4~ "reads" all the guidance cammanda, but the DFCS internal gainrt are set at zero for those signals not currently used. 9.14.3.2 DFCS (cont'd)

A yaw attitide or rate command to the WCS is not used (at present) Because it would contradict the sideslip feedback for coordinated tms. Later vereiona may use yaw commands to avoid crabbing dirhg gusts at landing. A control option, vhich may be termed a mode, is Nautomaticflspaed brake cont~ol.and the elwator dtitbde trh ccfitrol availabll only in the RCAH mode. Later versions will provide the auto speed brake ~pti~n in all manual modes. It is sblectable froin the pilot control panel using FWG 5. A trajectory profile of speed versus distance to touchdown and altitude versus distance, stored in core memory, is used together with externally provided infomation on speed, altitude, and range-to-go, to compute the speed brake commands and eldvator trim canmranda.

More details on this mode are contained below in'Lthe section entitled lvFortrsaListing" near the end of that section (see the heading "Landing Approach Trajectory for Manual ~odes~'). Control Equatione Sheets 1 - 6 contain block diagrams, in servo-loop format, of the digitized equations for the Auto mode, and the RCAH mode, for each of three channels: elevator, aileron, and rudcer, Each. calculation block ' is a separate Fortran card, except where several blocks have been en- closed in a larger, dotted-line block on the diagram, which indicatee one card.

The 20' calculation blocks are achieved in the D'CS progrmming by the relative time sequence of cards, wMch permits the DFCS cycle time lq to occur at the pobt so designated. No lortran cards appear for the 2-1 blocks. The filters are also shun in Sheets 1 - 6, dtinough located in the DFCS under headings called "Filter-ln and "Filter-2," instead of in the "control lawmroutine. The filters are generalized eecond order digital. filters, but at present, most of the filter gains are zero which results in first-order filters.

The filter network folluwing the summing junction of comnrand and feedback is an integrator, and a first order laad. Thie function is called (in alternative language) a "proportional plue integraln function. Washout filters are so labeled on the diagram and correspond to the analog TS/TS~, which is high pass filter with unity gain at high frequencies, The wamhout filter is wed now only in the yaw rate feedback path for rudder control. It permits the yaw rate feedback to damp the Dutch Roll mode, but not to oppose a steady yaw rate turn. A pitch rate washout filter may be used in later version6 to keep the vehicle nose up during banking manemra, ~CAH/~levatorChannel (gee &eat No. 4) .- The presently active part of this made/channel hae:

a. Pilot's hand controller longitudinal canmand of pitch rate.

b. Pilot's staticn trim b.eeper witch is a discrete integrated within the DFCS. This trims the pi'3h rn?, thus off setting - null biases in the hand controller, rate gyro, or any other source. In direct nodc, the trim button provides attitude trim,

Pitch Rate Gyro,- This signal is differenced with the hand controller ccramand and the trim camand to provide an error signal. The pitch rate gyro signal is also "gainedw and f edback to tin inner loop to provide semc dszpfq.

The "attitude holdn aspect of the RMmode results only from the fact that with a zero x-.,te c-ded, the attitude cumnand is "held." No switching-in of an attitude gyro occurs at stick detent to ensure attitude hold, Thie has the advantage of permitting tkc RCAH mode to f'uncticn evea though all attitude references have been lost. Any drifting of attitude due to gusts can be corrected by pilot iqp~t.

Additional integration in the servo loope are being considered to improve the attitude hold features of RGAH,

The normal acceleration feedback is not curreltr~lyused and there is a zero gain in the siepal p&th, This feedback will be used in later versions to provide so-caned C-ntar cantrol during landbg where the pllot's controller camands a cabination of pitch rate and vertical acceleration.

The ~onualacceleraneter is not used in the Automatic mode.

The elevator camand produced by the RCAH longitudinal channel is sumaed or differenced with the aileron caanand frau the RCAH lateral directional channel to result in individual elevon conmaMs.

The cmveraian of elevator and aileron signal to elevm eigaal ia acccmplished internal to the DFCS to permit wage of non-linear effectiveness g~in8of the elevona in future versioa~,

In order to avoid ataiz-step motion of the control surfaces at the DFCS cycle period, rreveral fixes have been proposed which utilize either local filtering at the actuatm or rate camanda without poaiticm cMmands or 8- canbination.

Prefilter* doqe locally at the ratd gyro has bern promncrl t;l filter body bending without increa: q t',~ 2-le ir~q~11Cy. During bank angles (i.e., d.zirq +mas), the pitch rate gp?o picks up body pitch rate and the RCAH gives a nose down output. To correct this, a wasi~outfilter in the pitch rate gyro path can be employed, or a more direct cross feed fram the lateral RCAH could be added. The DFCS present listing contains the pitch rate wa~hout filter in anticipation of this purpose, but the signal iu temporarily deadended, as shown in Sheet no. 4. ~~~~/~ileronChannel (sheet 5 ) and RCAH/RU~~~~Channel (Sheet 6 ) .- Together, the rudder and aileron channelrr canatitute the lkteral- diree%ional RCAH control. The rudder channel is coeeidered an inner loop for the aileron channel. The loop closure sequence is:

a. Yaw rate gyro feedback to rudder, with gain and washout filter,

b. Sideslip feedback to rudder with gain. The "filter" at present is inactive as such,

c. Roll rate feedback with gain (aileron channel) for damping.

d. Roll rate feedback (aileran channel) differenced with pilot's nand coritr~llerto prod-ace the RCAH roll rate error.

e. Two feedbacks sham are presently inactive. Future versions may use yaw rate feedksck for crosa feed into aileron, and roll rate cross feed into rudder.

The forward path, fran roll rate crnrmand error to aileron, contains a gain, an intewator, and a first order lead.

As discussed above, the pilot's hand controller provides roll rate canmands, and the rudder pedals provide sideslip cumnand.

Manual trim ia provided separately .for roll rate and sideslip in the RCAH mode.

Future versions may substitute lateral accele~ationfor the sideslip feedback, due to possible difficulties with sideslip sensors, with corresponding changes in cappensation.

Auto Mode (sheet8 1, 2, and 3).- Letis detailed discussion of the Auto mode will be required since it is essentially a position loop closure around the RCAH mode.

Camparisms of the Auto mode and RCAH aide control equatimrr can be made by viewing the corresponding diagrams together; i.e., Sheets 1 and 4 for elevator, Steta 2 and 5 9or aileron, and Sheets 3 and 6 for rudder. Auto/~levator vs. ~C!AH/~levator(sheets 1 and 4). - The Auto cc md is pitch attitude from the guidance system. The forward path cc .,bains a gain, integration, and first order lead, all of which operate on the pitch error signal. Damping by the pitch rate gyr' ia provided. Inactive in the present version are the guidance camnanda and feedback for angle-of-attack, and guidance crmmand for pitch rate. Manual trim is not provided in the auto mode since the function is accanplished internal to the guidance system.

~uto/Aileronvs. aileron (Sheets 2 and 5).- Similar remarks to those contained in the precediq paragraph apply to the aileron channel (with an appropriate change in axis nauenclature). The guidance system coumands for.roll rate, yaw rate, and yaw attitude are currently inactive in the auto mode. The yaw rate gyro cross feed into the aileron channel is also currently inactive. Auto/Fbdder vs. ~~/Rudder(sheets 3 and 6). - Presently inactive for the Auto/rudder channel are the guidance camnands for yaw, sideslip, yaw rate, and roll rate. The follm-ing cross-feeds are also inactive: Roll rate gyro and yaw attitude gyro feedback. .

list-. - The sections of the prow in sequence are:

1 Entry point (for all cycles).

103 "Pad Loadn~itialization.

If flagword ITURN = 1, this hdicates an initial turn on Conatants will be loaded ffau some external source by "readn statements.

104 Begin standard cycle. External flagwords are read which indicate restart, modes, gain update option, and autanatic speedbrake. Read clock and compute n& DFCS cycle start time. 24 mic test to determbif DFCS needs re-initialization.

If there has been indication of a restart, or a mode change, the DFCS must be re-Initialized, -DFCS (cont'd)

20 Sequence and 110 Initialization.

Reset the restart flags, change to the new modes, and set an internal flag (ISTART)to indicate that this DFCS pass is an initialization cycle. At the end of the entire DFCS cycle, this flag will be set back to normal.

33 Establish Sampling 5es

The DFCS has three different cycles. The control laws and filters are performed on each fast cycle, naw set at .10 seconds. The speed brake canmands are calculated on each medium cycle. The gains are updated on each slaw cycle. A .table look-up sets the three cycle times as f'unctions of the DFCS node and mission phase.

The half-time TF2 for a fast cycle is used in the digital filter gains.

The ratfos of tihe three cycle periods are canputed so that countdowns can be used to determine which fast pass cojlncides with s medium or slm pass. The Modulo function is used for the coating at the very end of the program. The initial count for the medium and slow passes are offset by one cycle to avoid having a medium and slawpaSS occur simultaneously,

2001 For the initial pass, the gains are set equal to the 2002 basic gaine in table KFIX, and filter constants are set to the basic GFM canatants. Subsequent passes will update the gains and constants as functions of speed, altitude, etc., which are stored in other tables. 99 Initialize indices.

These are the indices for the Modulo functions which count passes to identify medium and slow cycles.

52 Branch to read, based on mode. Each mode will result in reading a different set of canmands, sensors, and other data.

All "reads" are located below in a read subroutine at statement 300. After reading, the program returns tothe executive section for the next branching test, 7DFCS (cont 'd)

22 Branch to filter and parameter initialization.

A logic test is made to determine if initialization should be bypassed. Otherwise, a branching is made on mode, initialization is made, and control is pasaed to the next branching.

Whenever a branch teat is made on mode, and the result is Manual mode, a second branch test is made on Manual mode, to determine which manual submode.

Similar branching and returning to executive control is made for: 56 Branch to state filter - part 1 (filter update). 57 Branch to control law. 59 Branch to state filters - part 2 (filter pushdown). 60 Branch to parameter estimation.

This branch depends on mode, and also if Flag 4 has requested parameter estimation. ?!he parameter estimation routines are located below at statemsat 7051. These are filters for external information for angle-of-attack, velocity, air density, and dyn8mic pressure.

Afterward, table lookup is performed to obtain the wte for the control law gaina. - 80 Wench for closeout.

A different closeout is ueed for the intial pass.

Thia canpletea the branch- section in the executive program. The 'tsub-rautineen follow. In this veraion, ae stated above, the subroutines are routines.

Cmneuts will. be made only to eupplement reading of the lieting.

2000 Initialization Routines.

87 Pullup and flare constants for manual approach. The strategy is to let the DFCS ccmpute these control 8yatem conatante to avoid human calculation errors when tradectory changes are made. -DFCS (cont~d)

400 Filter Routines - part 1.

All possible filter calculations are done in Filters part 2 fcllowing the control law calculations to avoid transport lag.

Filters ?art 1 is performed immediately after "read" and prior to "control laws. It

The filter equations and identification of constants by symbol can be seen on Sheets 1 to 6 of the block diagrams,

5000 Control Routines.

The control la,ws for Auto mode and RCAH are shown in tile block diagrams Sheets 1 to 6.

Multi-Rate Speed Brake Control.- An automatic speed brake control mode is available (only in RCAH) to assist in landing approach. A reference trajectory is ztored in the DFCS based on altitude and velocity versus range to go to touchdown. Error signals of velocity and altitude are simply "gained" (without integration or canpensation) and added to the pilot's manual speed brake camand. The altitude gain is set at zero. Additional information on this subject is below in the routine "Landing Approach Trajectory for Manual Modes" at statement 702,

514512 Elevator Trim for Landing Approach Trajectory.- DECH and DECU are the delta elevator comands due to altitude and velocity, respectively, fram the a an ding Approach Trajectory," for RCAH only. The altitude and velocity errors are "gained" (without integration or campensation) and added to the otherwise total RCAH elevator canmand. 1%~velocity gain is zero at present. The altitude error produces a low gain, slow loop elevator trim which tends to keep the vehicle on the glide slope. The loop is so slow that pilot commands to the RCAH are much faster. Hence, the pilot and not this automatic feature produce the pullup maneuver and landing flare. More information on this subject is belaw in the routine "Landing Approach Trajectory for Manual ~odes"at statement 305. 6000 Filter Routines - Part 2.- This routine contain^ aU. the filter calculation that can be done before the "read" on the next cycle, Also included is the "push down" of the digital filter where the quantity at becanes the same quantity at tn-1 for the next cycle.

The filter equations for the RCAH and auto modes are shown in the block diagrams, Sheeta 1 - 6. -DFCS (contr d)

611 Medium Cycle, filter for X-velocity. -Slow Cycle, filter for altitudes. 762 Landing Approach Trajectory for Manual Modes.- The reference trajectory is used only in RCAH mode, but must be maintained in all modes in case of switchover to RCAH. Two trajectory curves are stored, velocity versus range, and altitude versus range. The velocity trajectory assist8 in speed brake control of vslocity. The altitude trajectory aruista in elevator control of altitude. The range-to-go is broken into four segments. Trajecto:*y information is stored at the endpoints of each segment for velocity, altitude, and altitude slope (slope with respect to range). IR is the index 1 to 4 for each segment of range, with 1 nearest touchdown and 4 at high altitudes.

For altitude, the segments are: Landing flare = 1 (ending in touchdown with a sink rate), straight line glide slope = 2, approach pullup = 3, and steeper glide slope straight line = 4. The glideslopeand pullup segments for altitude are algebraic quadratics (a + bx + cx2 + dx3) such that the slope and position of the curve coincide with the adjacent straight line segments. Coefficients for these interpolaticma are canputed in the DFCS In the initialization routine "~eneratePullup and Flare Conatants for Manual Approach," located near statement 2010. The velocity segments of the reference landing trajectory are straight lines for the three nearest touchduwn. The fourth segment is exponential and results in a linear US (indicated airspeed) versus range.

RGO is the range-to-go (to touchdown) and Is navigation type data supplied to the DFCS by landing navigation aids or by the guidance system. RLAND (I) is the range-to-go (reference trajectory) at the endpoints of each range eegment. RGO segment number IR= 1 is bounded by endpoints I = 1 and I = 2. Segment IR = 2 is bounded by endpoints I = 2 and 3. The program determines IR by comparing RGO - RLANI)(I) until it goes negative - then IR = I - 1. Having found IR, the program proceeds with the interpolation formulas. First, however, each sement of range has its own measure ~f reference length RL, which,as the list- ~uggesta, RL = RGO - RLAND(IR). 9.14.3.2 DFCS (cont'd)

The results of the interpolation equations are UG and HG, a velocity command and altitude commad. These commands are used in the control routines (descrihed above), to provide speed brake and elevator ccmmands.

The next version, or soon thereafter, will contain a Mach- trim featua at altitudes above 45,000 ft to provide a steady-state angle-of-attack along a reference t-*ajectory in the RCAH mo?e. 81 Closeout Routine .- ISTART is the flag which indicates if this pass- was an initialization Pass for the DFCS. If this was a "first" pass, the executive program will begin the closeout routine at statement 81 and set IS'PART = 0.

For the first pass, both the count indices for medium 8::d slow are 0. IS = IS + 1 offsets the slow cycle index from the medium cycle index 80 that the mediurumd slow cycles will not occur on the same paaa.

82 Increment Indices. - Each fast pass increments the counting indices for the medium and slow cycles. The Modulo function is a comparison function used in countdowns such that if the index exceeds or equals the second argument, the first argument (index) is set to zero. For example, MoOulo 5 would count 1, 2, 3, 4,0 and repeat.

When IM = 0, the DFCS will perform the medium pass operations. in additic- to the fast pass operations, and similar results occur for the slaw pass when IS = 0.

Autof low Chart

The autoflow chart is a flow diagram made automatically by computer program. Hand notations in ink have been made on the first page of the diagrams to explain the autoflow symbols. The computer mainstream of flow does not always emphasize the same mainstream that the human designer had in mind, so the results are sometimes confusing. However, the mtcaflow chart is a useful tool.

Pad Load and Constants The constants have beec verified for the NR 161C. Now constants are being determined for the MSC O4OA Orbiter, These constants have no% been included because they are changing, but are available upon request. A CTUATOILS

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W* + C c* I I z ul u-l I *3+ C.1 1 Z It' ---* - t --- I I A C 1x1 I *L* ILUI 1 -I I I I *U* I I I lln* I I * I I *** I I .-----I I I 9.15 APPROACH AND LANDING Approach carmnsnces with the vehicle in the viciniity of the landing site and includes the manuevere performed in the process of achldving the final approach trajectory in the final approach plane, Finai Agproach termbates at touchdm on the mm&y. Landing begins at touchdown and continues until the craft reaches ground taxi speed. The GN&C software functions to be performsd during this phase are: 1, Approach navigation using msasurementa frm the IMU and the ground transponders. Both the shuttle state and the landing site stab mey be estimated. 2. Approach and lAnding guidance resulting in crntnwnrls to the autopilot (attitude), thrust throttle ems,braking and/or lift flap c-s* 3. Autopilot computations to computa control surface comads in order to achieve the cnmPnRna attitude.

SWttals are inclded herein for Approach Guidance and Final Asroach Guidance. Lading Guidance requiramenta have not yet been defined . SPACE SHUTTLE

GN&C SOETdAH3 EQUATION SUBI4lTTA.L

Software Equation Section Approach Guidance Subczdttal No. 35

Functian: Terminal Area Guidance with variable mint of entry in final

Module No, OG-6 Function No. 1.2.L.7 (MSC 03690 Rev, A)

Submitted for: T. Em Moore Co, EG6 (~C-05121) Date October 21. 1971

NASA Cozlt act: J. Suddath Organization EG-2 (wame)

Approved by Panel I11 ll .T. 4 Date 'o/s, /3 1 (Chairmen)

Summarg Description: Near opt- amroach for ~utinnvehicle satisfactorils on final amroach nlme Pram ambearing and heading within footmint of capability, Rr3-k. amroach with nominal L/D fliaht path. Alternate approaches for borderline initial conditions include three=%- ap~roachand LID wv fliaht paths. Shuttle Configuration: (Vehicle, Aero Data, Sensor, Et ~etera)

NR-161C delta wing orbiter with fU&t control characteristics described in Sec, 9, 74.3.1

(verification Status) Considerable tesi data : 6W[P H~bridand All Mpital Panel Coments: 9.15.2,1 uproach Guidance SUMMARY

A teohnique Is presented for guiding aa aimraft in ruboonio flight (with or without power) from any bearing and heading with respect to a runway to a reference trajectoq in the final approach plane (FAP), that contains the runway. This technique produoes three phreot an initial turn toward the FAP, wings-level flight to the FAP, end a final turn into the FAP, Each phase is flown with a nearly oonotant angle- of-attack and indicated airspeed. The guidance selects the moat sfPi-. cient aet out of four possible sets of turn direction combinations; i.e., left initial turn with right final turn, etc. The energy management parameter is the range of the FAP entry point from the runway. The in?tial condition requirements or the end condition conatmints imposed on the supersonic flight phase are that the vehicle be within the footprint of capability (of the order of 20-30 n mi radiu8 from the landing site), and be at an energy state which will nrin subsopic during the initial terminal area turn which L made at amxinun L/D and 45 degrees bank. (The heading angle at this point need not be con- atreined .) Thia guidance technique has been uuccesafully flown on a six- degrees-of -f reedom hybrid simulation for a straight-wing orbiter. Results from an all-digital program for both a straight and delta-wing orbiter are presented. INTRODUCTION

The Shuttle Orbiter'is presumed to have reantered the atmosphere. ., and received a navigation update following the communications bhokout period. A llpost-blackout~nguidance technique which is the subject of a subsequent study will have ateered the vehicle to a subsonic state (figuse 1) which is considered the beginning of the texminal area mission phaae. Since the Orbiter, in its operational configuration, will not have a cmise capability, it is necessary to provide a terminal area guidance techniquo which makes most effective use of the available energy. Also required in this mlseion phase is the neoesaity to operate in instnunent weather oonditions. Because of this requirement, the guidance murt be designed for ease of pilot mnitorlng and/or control when viaual pilotage cues are not available. The guidanoe technique presented brain will guide either the powered or unpowered vehicle from a high arbronio energy state in the moat efficient arnner (vithln the constmintr imposed) from any podtion and heading with reference to a runway that io within the vehicle foot- 9.15.2.1 Approach Guidance (cont'd) 2 print of capability, to a reference trajectory in final approach plane. From that state, the Orbiter can complete an unpowered landing. The design includes logic which makes it compatible with good air- oratft instrument flight procedure and reaults in maximising the periods of wingo-level flight at nearly constant airspeed and angle-of-attack. The objective of tnis internal note is to present the derivation of guidance equations. To demonstrate this guidance, some results of an all-digital program are preeented for both a straight and delta-wing orbiter.

DISCUSSION

To guide an aircraft from any state relative to a runway to a linear reference trajectory in the FAP containing the runway, a twa- tun maneuver is determined as shown on figure 2a. A constant and equal radius ie used for both the initial turn toward the FAP and the final turn into the FAP. There are four possible turn direction combinations of two-turn Mneuvers (figure 2b). At any guidance computation cycle, the guidance selects from theee four sets %hat which dl1 place the vehicle in the FAP with the greatest energy. The FAP entry point is then adjusted until this energg is the amount required to intercept the FAP reference trajectory once the vehicle is in FAP. The two main parts of the guidance are determining the reference trajectory to the FAP, which is continually computed, and the attitude and attitude-rate commanda to guide to thie reference trajectory. Attitude commnnda might be processed more often than the reference trajectory determinaalon equations. Simulations to date have used equal computation time intervals of two seconds. Determine Reference Trajectory Determine around tracks. - With the initial and the final turn maneuvers of the aame radiua, it ie a fairly simple problem of geometry to solve for the four poasible ground tracke of figure 2b.' The vector equations to be aolved are shown in appendix A. The anewers required are the angles of the initial and of the final tuna and the distances between turns for each of the four possible turn combinations.

If either of the opposite turn combinations (lee., left initial, right final tun) has overlapping turn circlea, then that particular oombination is eliminated aa a candidate for the reference trajectory. 9.15.2.1 Approach Guidance (cont'd)

Detenniae altitude ~rofilsq.- In pbmning the flight to the F@, some margin of flight path aontrollability should be maintained for control against errora; 1,e. , wind, aero assumptions, eto, This requires a noainal angle-of-attaok ( a) lesa than that for ~h.To mrnintain this control margin would require the noaalnll a to be constant. The guidanoe plans each segment for a spooified constant a, and assumes the vehicle will achiev~a ateady-atate flight path ( Y~~). Examples of aumbers used with the rtraight-wing orbiter am:

Justificatlan of this aaaunrption and equations that determine mgni- tudea of for data load Into guidanae computer are prorented in appendix Ba Equation four, which specifies the velooity required for u to be constant, and equation seven, which prodicta the trajectory with tiny velocity magnitude, are utiliaed in the guidnnce. For the initial turn, the ground plane distance X = (Tuzn RadFur Initial Turn Angle). The predicted trajectory would be

The incremented shlft in predicted altitude (H) account8 for the general case wherein the exlstlng vehicle energy state 18 not exactly that required to fly at the new angls-ofattaok for the next segment, The guidance predicts an appropriate ahift in altitude for an assumed constant 7 segment, The aotual trajectory, of oourse, approsohe8 the predicted tnjrctorg moothly and re ache,^ the anme end conditionrr, very closely. Equations four and sovan arv reproceased rith the prediotec? end oonditions of each phaae to predict the entire altitude profile; 9.15 -2.1 Approach Guidance (contld)

Present Altitude

Proj8cted Initial Alti - ,ude Turn Error (DH)~ fl .I - I ma..-? m..- level 1

FA? I Min &try Pt. FAP Etltrg Pt

The minimum entrg pint $8 a point in FAP which is a specified erbitrary minimum time; Lee., 60 sec, before touchdown on runway. Select most efficient maneuvers. - Out of the four possible sets of tun combinations, the set that produces the highest projocted altitude, at a given location of FAP entry point, is selected as the ma-L,siffi- cient. The projected altitude eTor of this set is then used to compute a new FAP entry point. If the FAP entry point does not require adjustment, then this selected set will determine the turn direction commands. Adjust FAP entry mint. - If the most efficient projected altitude emr is within a deadband range (+I00 ft has been used), the entry point will not be adjusted. Otherwise, the adjustment is made according to the guidance equations derived in appendix C. The 10'3 control logic shown on the guidance flow diagram of figure 3 will prevent infinite looping in the guidance. Convergence failure. - The guidance could fail to compute a aatis- factory reference trajectory as shown in the logic flow of figure 3, for two reasono, If the vehicle were outside the footprint of capability with nominal flight paths, a landing might still be possible by flying the most effictent trajectory with 4/Dmx rather than nominal values. Another type of failure can occur if the vehicle were too high 9.15.2.1 Approach Guidance (?ontld)

to fly directly to the minimum entry point without diving (7 > 15~-20'), and too low to fly any other two-tun maneuvers. A three-turn solution, ae sketch34 oa figure 2d, 1s aahhved bg oonmrandlng an inithl turn opposite in direction to that of the most efficient trajectory to the minLmum entry point, until a two-turn solution 1s achieved. Reference trajectory. - The reference trajectory is basically the met efficient altitude profile previously defined. More specifically though, the idance output at thir point is merely the altitude (Hc) and rate (&y commands for the present instant of time. During the initial turn, Hc = R + SHIFT

Hc = -V Sin lag

where 2 v2 - v C SHIFT = P b.e., the e:lergy difference between present 2E3 and desired conditions expressed as an altitude shift and where Vc is the Yc of equation (4), appendix a.

The initial turn is mde at mu L/D (although this is not a constraint) to coneerve altitude during turn and, therefore, there is no control margin to remove rrsidual altitude error (that emrnot removed by entry point adjustment, DH), but after the initial turn,

The Lateral part of the reference trajectorg ie the ground track that goes with the moat efficient altitude profile. The lateral command is by definition the actual position of the vehicle, becauee the ground track is defined from the preeent vehicle position. For the initial tun, it ie necessary o~ly-to fly a constant radius turn ir1 the commanded direction in order to maintain the oame projected ground track, and for the flight between turns to fly In the com~randed lirection towad the final turn. There is an exception, though, for the final tun, during which time 3s entry point is no longer computed; lee., remains f ixsd. The lateral position is then colrmwnded to be a fixed radiue from the center of the turn. Initial turn: The lateral axis definition of the reference trajectory is chosen as the perpendicular to the true airsped (u). 9.15.2.1 Ap3roach Guidance (uont Id)

In a following section, m acceleration commrrnd, Yc will be computed independent of Y a~df to hold a ons st ant radius turn. Flight between turns: The late~alaxis definition of the reference tmjectory ie chosen ae tha pr3rpendicular to the selected mat efficient flight directlon vector (FD) as computed in appe~dixA (i.e., a = AC, or AD, etc.) .

rrhere is the local vsrtical and U( ) means the unit of the vector within the parenthesis.

Final turn: The fiaal turn can be flown in the same semi- open-loop manner as the initial turn. But for more precise guidance in the presence of arrors, the lateral axis directlon la chosen along tne vector between the present vehicle position (RP) and the presiint 1oc.i- tion of the center of the air turn circls (TTCNCNT)-. of radius R. During the final tun, TRNCNT is a fixed vector 0219 if the apriori wind is sero (discussed in later wection).

Phase control. - Definition of the reference trajectory and vehicle poaitinr relative to it has just been shown to be phaee dependent, initial turn (IT), between turns (FD, flight direction), or final turn (FT). Ar, eetimate of phase time is necessry for phase contral. From the geometry (defined in appencix A) of .&he moat efficient ground track eelected by guidance, the ground plane distances for each phase can be computed. In the procesa of predicting (using appendix R) the trajectory, airspeeds (horizontal component) at each phase change point have been computed. 9-15 .2.1 Ap~oschGuidance (cont 1 d)

The gufdmse trajectory determination aesumes hotantaneaua attitude respccse at phase change points; i.e., fl = 35-0. To cornpenrate for attitude response time delay, the orvuvers are led. The phase (PH) control logic with emplea for lead times are:

At first processing of Cuid, PH = IT

At aukaeqiant processing,

If PtI = IT and TGO(IT) < 3, then PH = FD

If PH = adTGO(IT) > 5, then PH = IT L" PH = FD and TGO(FD! < 3, then PH = FI'

If PA = FT and TGO(FT) < 3, then EXIT Tern Area Guid; i. e., PH = Fb~lApproach Cuid. Wind considerations. - The guidance will compensate for wind errors in two simultaneous manners. With em=. sompenuation networks (to be dlacussd), the angle-of-attack will be adjusted in order to hold the reference trajectory. Also, the FAP entry point will madjuat during IT or FD phaeea if the vehicle is blown off the predicted course.

The performance of the guidance in the presence of wind is greatly enhaEced by pmviding the guidance vitn howledge of the wind (apriori vind magnitude and direction versus altitude). The reference traj ec- tcry can be adjusted for wind in order to maintain ndmlangle-of- attack, in which case, a- margin is allotted for wind uncertainty of apriori profile rathsr than on full magnitude of wine-. In addition to apriori vind profile, s routhe is desirakie w;iich will compute the average wind over two specified verisble levels of altitude.

To incorporate this wind in the guidance, appendix A requires modi- f ication of final turn circle (S) as shown on figure 2c. To keep the turn bank angles nominal, the fim1 turn circle center is first rotated so that ground speed at end of final turn is in FAP, and second, trans- lated againat the wind by the sum cr' the average wind of each of three maneuvers times the time of each maneuver.

Guide to the Ref eronce Trajecfa~~.

Each time the reference trajectory equations of the.previoua s~ction ax processed, vehicle state counBnndr :hc, $, Vc, and Y,) are pnerated 3.15.2.1 Approach Guidance (contld)

and present vehicle state components (h, 6, Y and ?) are defined. The task- is now to guide to the conminded state. The guidance equations of thia section are derived in detail and presented in appendix D. A functional description of the guidance output commands (two component8 of Euler attitude and three body rates), and guidance-autopilot interface follows. Attitude commands. - Fitch (ec) and roll (gC) attitude commands of the standard aircraft Euler attitude sequence, $ , 8, @, sre generated. An azimuth command, $c, ia not generated. The control requirement on is that sideslip be zero relative to actual, not navigated airspeed,

To control the vehicle state, a aecoud-orter control law is u,ed,

which corresponds to 8 system of the form ahown:

where Q = is either h or Y

Wn = natural frequency of desired response (of the order of 10 times slower than vehicle attitude responae)

= damping ratio of deafred response .. - Qee - dQc = ateady state acceleration required to maintain the two error signale at zero. For example, thia term for the LBteral axis during a turn would be the centripetal accelerat%on.

0. The acceleration commands He and Yc are converted respectively to angle-of-attack a, and bank angle @,,, commands. Pitch 8, and roll gc commaads are computed from these two mgies and the navigated airapsed; i .e, , J& = -:'S(NRV gnd aped) + mJ (apriori wind).

b • btfitade rate coaanands. - The state vector acceleration corpmands (Qc) are by definition variable. The vehicle can be codedto linearly vsryfng acceleration state by qpmputing body attitude ratea u.'.icS vl11 produce the co-ded jerk (Q), where an expresdon for Jerk cfmmarci is obtain& by differentiating c,

Body rate commands, PC, ~c,and rc, as f-uctions of jerk aommmd are obtained tr diffsrentiatGg (aa done in appendix D) nc and GC, -Error cornteneation. - Acceleration errors can exist from emrs'in the aem coefficient aasumptiona, navigation, wind, attitude reaponse time delaya, etc. Any of them error8 that edat i~ a form of a bias can be detected by conparing the present vehicle r~tatewith the state that should edst had the acceleration and jerk comds of the prev- iox conputation been flown, A biae error term is obtainod by weighting and aceum~latingthis measured error, compenasted for expected acceleration error due to ettitude taae dehy. This bias Is then fed back Into the axeleration command so that the actual acceleretio~will cr8?lverge on the command acceleration ir t\% presence of any bias enors. Guidance-Autopilot ittsrface. - The guidance can operate at a mla- ti~relylarge computatioo cycle the auch aa 2 sec or probably even larger, There are autopilot interface equations that mast be pmceaaed more often as shown OD figurn 4. If the sequence of attitude of the Inertial measurement unit (M) fa not standd aircraft relative to landing site, then the three anglee mat be converted to the required 8 and f8, Attitude error is then converted to body axss amr. Coordi- nated tun rate commnnds must also be added to the guidance rate commands. The autopilot is ahown on the figure simply as e aecondarder system merely to show that the guidance comra~ndaon the autopilot am attitude ramps in body axe8 pitch and roll. Body dspau control to a rate and also for sideslip B = 0. 6 could be replaced with either an integral of accelerometer measurement or merely a aim1 pm- portional to bank angle. Selec ,Lon of Turn Radiua

With rrapsct to altitude lost per unit of turn angle, a 45' bank turn is most efficient. Uith respec'; to comfort though, L 30° bank turn ia more desirable, A constant radius turn tendo to eatisfy both, For example, a 9200 ft radius for the straight-wing orbiter requires Approach Guidance (contld)

45' bank for m initial turn at 20,000 ft altitude with max L/D, acd a 30' bank for a final turn if at 4000 ft altitude with L/D < L/D,. This same aituetion exiets for the delta-wing orbiter with a 12,000 ft radius of turn. These numbers were used for the results that follow in another aection. At initial turn altitudes greater than 20,000 ft, the bank codwas limited to 450. This reaults in a minor adjustment of entry point in FAP because the actual is greater tbn guided turn radius. The actual converges to the guided trajectory at either the aoqletion of initial turn or altitude less than 20,000 ft, whicherer occurs first.

Turn radius could be selected so that it would be flyable with 45' bank at the madmu altitude for termins1 area guidance; lee., about 4O,W ft for delta-wing. But this two to three time3 larger radius would give mi inefficient final turn which would require of the order of 15' bank.

Description of SWation

The results presented were made on a six4egrees-of-freedom 1108 computer program, This program contains aerodynamic forces as a function of mgle-of-attack for a Mach number of -25. In place of aero- dynaaic momenta, an autopilot is assumed which drives the vehicle to the cannmnd attitude and rate with a second-order response, where the natural frequency is 1 rad/sec with -707 damping. The results of this program, though, are representative of results obtained on a more detailed real-time hybrid simulation.

Guidanca reference trajectory computations and attitude conxnands are processed every 2 sec. The autopilot and environment equations are processed every 1/16 see. The natural frequency of the guidance commands for driving to the ~eferencetrajectory is selected to be 1/10 that of attitude msponae, or .I rad/sec with .707 damping.

Phase (IT, FD, or IT) control is monitored in the fast time loop so that phase change ufll occur within 1/16 sec of the time computed in the slow time loop. The guidance equations are processed immediately at phase change.

This report presents only the guidance to FAF. The end condition energy atate should be such that the reference trajectory in FAP will be intersected after entAry into FAP. The sianhntion contains a complete guidance to touchdown, and the results show part of the FAP guidance in order to demonstrate the intersection with the reference teajectory. Simulation data appliceble to all memade la shown on table I. 9.75.2.1 Approach G;lidance (contfd)

Results

Resulta of runs are presented to demonstrate8 For atraiaht-ulna orblter. - (I) Groud :racks from various initial position relative to runway, (2) Eff ecte of wind error8 on trajectory and control parameters. (3) Effects of very high winds with guidence knowledge of ouch, on trajectory and control parametera. (4 Altitude convergence to reference trajectory. For delta-ulna orbiter. -

(Ij A nominal ground :track from a maxlmum energy state initial condition for terminal area guidance. (2) Sor as (1) except with a guidance modification for a nuximum entry point. Isitial position. - Run 1 on figure 5, which consists of two right- t~rnmaneuvers to an entry point at 50,W ft range from mway, Lo the nominal run that is used in tho next sections. Run 2 demonstrates a left turn-right turn maneuver. For nm 3, which is already h the FA,, the altitude high error at MEP wuld be graater than 100 ft if the vehicle were to proceed di-ectly to MEP vith nominal angle~f-attack. 8ut also, the energg state is too low for any other two-turn eolution to MEP; i.e., a 360 initial turn. The guidanoe aets the flag IOPOST to 1 when It detect8 this condition, and the vehfgle is commanded to meke an opposite turn; Lee, initial turn direction opporite in gimc- tion to the moat efficient path to MEP. After approhtely 110 of turn, a tvo-turn (right turn-left turn) eolution is achieved, and the flag is then set to sero. For t!ie above case, a possibility under study exiets to modulate speed 5rakea and thu6 increaee the flight path angle. Thia technique could also provide a aatisfactorg two-fit-% solution and minhize the necesalty for a non-standard procedure,

The hithl szergy s+ats '2r rcn 4 f8 too low for ho~Inalangles- of -attack flight to MEP (IOPOST = -1 ). The vehicle is then conmanded along the best path, but at nx L/D. At a lakt point, the vehicle intersects the reference tra ectory, at which point nominal angles-of- attack are flow (IOPOST = 03 . wind errors, - 1 (no vind) ir mplctted on figure 6 810- with -+a 'perrors (mro wind assumed). Thiu wind is 45 relative to the runway. Entry point varied between 46,000 and 52,000 ft. Alti- tude la shown to converge on the reference trajectorg in FAP. 9.1 5.2.1 Approach Guidance (contfd)

Control parameter variation is shown on figure 6b for the nominal and one wind error case. Angle-of-ettack holds very near the reference values for each phase (see table I for comparison). Apriori wind. - With guidance computer knowledge of the high winds, a euccesaful descent was made as shown on figure 7. Note the altitude climbed during the initial turn, the reason being that thia run started a8 run 1 with same ground speed, and in effect, it instantaneously encountered the wind which then increased the initial airspeed by the wind velocity. Note also the change of final turn direction from run 1. This change of direction was nct one which occurred after initiation, but was computed as the best during the firet pass through the guidance, The turns no longer appaar circular because the plot is relative to the ground. Relative to the movlng air mass, the turns should remain as circles.

One thing the guidance does with its knowledge of wind is adjust the reference trajectory slope in FAP in order to maintain the nominalM for that phase. Thia slope adjustment is shown on figure ?P.. The altitude ia shown to converge on the reference trajectory in FAP. Control parameter variation is shown on figure 7b. Angle-of-attack converges very near the reference values for each phase (compare with figure 6b). Altitude converaence. - The guidance computes altitude command as a function of the potential energy equivalent of the kinetic energy difference between present vehicle state and that required to hold the reference flight path with nominal angle-of-attack. At phase changes then, there can be a discontinuity Ln Hc 89 shown on figure 8a for run 1. Note, though, for the nearly constant a (see figure 6bj, B converges to Hc (figure 8a). The discontinuity at other phase change points is emall because of the choice of targeting conditions, but this discontinuity la not required to be small. The same type plot la shown on figure 8b for the apriori wind run. Here there are discontPnuities at each phase change, but, still, tihe trajectory is shorn to converge smoothly to the reference. The reason for these discontinuities an figure 8b and not on figure 8a is that the nomlnal final turn angle-of-a%tack is replaced with the higher initial turn a. The guidance automatically makes thia targeting change whenever it estimates the altitude of the final turn to be greater than 15,000 ft (13,000 ft for delta-wing). This keeps bank angle required from exceeding the mximum in order to hold tun radius. 9.1 5.2.1 kprnoch Guidance (cont d)

ahel delta-wing orbiter. - For a aonrtmlnt of Maah L .9 during the Eitial turn with = 7.5', there ir a mulmum energy state from which the initial turn san be started. The rune on figwe 9 are approx- bnte1.y from this maxhm energy sfiete, Note that even though the 12,000 ft turn radius cannot be flown at h = 41,000 ft, a smooth convergence to a aolution is achieved. The entry point with the nominal guidance is 88,000 ft from the landing sib.

There should not be any fear that the entry point is too far from the runway, because there is aonsiderabla margin in controUbility against error8 once in the FAP. For example, at the 80,000 ft point for the nominll trajectory, the landing gear pes down and 8psedbrakes at one-half mxbm drag. And even if thir were not enough control margin, then the reference trajectory slop to could be mnde nt,oeper--ma were mde with the same s'iope to and from MEP. But, to demoastrste that entry point can be limited, the dashed xw on figure 9 activated the opposite turn logic whenever entry point greater than 60,OCO ft,

A gutdance technique ie derived which will guide an unpowsred aircraft in a nearly opthmanner from any bearing and headkg with respect to a mway to a reference trajeatorg in the final approach plane from which a landing can be made, The entxy point into this plsne is computed so that the aircraft cea fly at nearly constant, spacif ied angles+f attaak, Constant twn radii are utiliaed. Simulations of both straight and delta-wing orbiters demonstrate the ability of the technique to guid~in the prsssacs of large known winds and of wind errors.

Subsequent study will be concerned with proaodural variations within the guidance which migbt he desirable for use under different weather and wind environments. 9.15.2.1 Approach Guidance (cont'd) 9.1 5.2.1 Approach Guidance ( cont d)

Air speed Vehicle position @5g MEP: Minimum entry pint in FAP

FA P f Entry pintp (a) Two turn maneuvers.

(b) Select best maneuvers out of four possible sets.

(cl Displace ' orget circle by function of known wing.

Best turn7, -\

(dl Three turn maneuver capability. Figure 2. . Sketches demonstrating ground tracks considered by guidance. 9.75-77 9.15.2.1 Approach Guidance (cont Id)

I if final turn in progres t Yes No b II- ? Compute angie between If initial iurn in progress air speed vector and .' at end of turn No Yes

7 Decrement time to Decrement time of final turn by initial turn by eiapsed time elapsed time i t b If time to final turn < min time to compute final turn point * 1 Ies

1 4 a a I 4 + Set entry Pt Compute new Select most efficient of entry point in FAP four possible maneuvers in final approach L to minimum plane (FAPI - . 1 Yes No . f r 1 If 9th computation of entry If /h error (at min entry pt)/ pt this comp cycle 5 boundary limits 1 No Yes No I J If r 3rd failure this cornp cycle

I I Yes No -> If entry ptLl minimum . 4If vehicle high h error I Yes No

t v 1 T Command initial turn direction ~lymaximum ' opposite that computed above L/D for all ) maneuvers I t i"" Figure 3.-Flow diagram of guidance to final approach plane. 9.15.2.1 Approach Guidance (cont d) 80x 10'

Initial conditions h = 20 000 ft v = 562 ft/sec v=7*

IdPOST= 0 40

Figure 5 .- Terminal area guidance of straight wing vehicla frcm various positions relative to runway. 9.15.2.1 Approach Guidmce (cont~d) 9.1,5.2.1 Approach Guidance (cont'd)

Initial Directed Final Final I turn I flight I turn I approach

Elapsed time, sec Fiyre 6b: Termiqal area guida~ceof straight wing vehicle, nominal and with wind error. Trajectory con'crol parameters. 9.15 b2.1 Approach Guidance (cantld) 9.15.2.1 Approach Gddance (contld)

I IT I FD I FT I Final approach

Elapsed tine, sec

Figure 76 .- Terminal z, 3 guidance of straight wing vehicle with apriori wind equal actual wind: Trajectory control parameters. 9.15-24 4 9.15.2.1 bproach Guidance (contld)

Ei8.psed t ime , sec Figure 8a .- Terminal area guidance of straight wing vehicle, nominal - altitude and command. 9.15.2.1 Approach Guidance (cont'd)

- Elapsed time, sec

Figure 8b. - Teminql r ma guidance of etraight-wing vehicle with apriori wind equal actual wind - altitude and command 9.15.2.1- Approach Guidance (cont Id) -9.15.2.1 Approach Guidance (conttd) 9.15.2.1 Acsroach Guidance (conttd)

Ground Track Vector Equations

U_ ( ) = Unit Vector -i = e (x) -j = (Y) -k = p (2) yuJ =-k = Unit Inca1 Vertical 9.15 .Z.1 Approach Guidance (contf d)

9 = A3IK ( ID 2R- A! ) -AD = (1- 1- 2 R SIN a) ( ) + (2 R COS a) • -u ((D - A) x 3))

If Ig - -A 14 2R, seouf hi >o eliminate this turn comb.

b = ASIN(-- 1s - q1 BC = (1~- El- 2 R SIN b) (C - 8) + (2 R COS b)

If 1s - -rB 2R, set flag to eliminate this tun comb. Initial Turn Angles - Solve for + angle (0 to 360') between V_ and vector between turns. Final Turn Angles - Solve for + angle (0 to 360') between vector between turns and &. 9d5.2.1 Approach Guidance (contld)

APPENDIX B 9.15.2.1 Approach G7ddance (cont f ci)

Trajectory Predict ion of Airoraft Flying Constant Angle-of -Attack and Turn Radiue

Steady state flight wth andle. - The equations presented hsre are not (except equations (4 and 7))a direct part of the guidance, but are equations to be externally proceased for data load in the flight plan portion of the onboard guidance. The guidance makes eimple uae of the fact that the steady state flight path angle la nearly conatant for constant anqlo-of-attack. The approximation 1 ) le not eatiefactory. (7 = a- To hold a constant turn radius (R), the centripetal accelsrat!on, n *Y= (v ccs 7)' R - = sin but lift,

2M (1) Sin $ = COB' 7 RSLS F.

and by differentiating (1 ) ; #=--a P Tan Standard atmoephere air density, 1 (2) P = .~)237g m ?a(l - 6.875 . 10-6 . h)

by differentiating (2) P 6.875 10-6 v sin 7 (?) - = P .; jg (I - 6.875 b)

If there is a steady value of 7 , then L- 7=0='4 * COB 7 - M- cos fl SIGN CONVENTION --v- '). (t) for Descent or 6 COO 7 ' aoa $

froet this .rd the lift eqation veloaity ia constrained,

I2 E! cos 7 (4) y'I/c L * s d- The rate of change of velocity by decinition;

Also, for a steady 7 ,

The flight path that produce8 ;* = 0 is then, D+b n sins ii 1 i *-sin r Tan v= - . =I +yg crS5 Sin 7 g C08 M Cos $ ti Cos fl

by reamnging and collecting Tan 7 terme, thia equation becornea

3.1 itarctlve proceaaing rf equations (1 te 6) provides the state of ~e';~.*.by and flight path that must -xist for the first and second derivative of flight path to be zerc at any altitude, radius of turn, snd 9.15.2.1 Approach Guidance (cont ld)

angle-of-attack. Two questions to be answered empirically are: a. Is thew correlation between the predicted 7 of equation (6) and actual ? ?

b. Is there a steady state value for 7 ?

Results of equations (1 - 6) for three conditions of n and R are shown as a function of altitude on figure El. The aero-c~efficien~ used are those of a straight-wing orbiter. The wings-level case (infinite radius) corresponds to within the resolution of the plot with an actual flight. A ateady state value of Y is not achieyed. but for practical guidmce purposes, the variation is sufficiently &ll so thet a constmt 7 can be assumed. For tu~sunder 20,000 ft altitude, if a and R are selected so that bank 5 45 , the Y holds fairly steady at 8'. The simplified astimte of

is ahown to be greatly in error.

Turns starting at higher altitudes and with turn radii so thet max- imurr banks are 46.5 degrees are ahor, on figure B-2, along with actual results for c.,e case. More variation is seen here for 7 , but still, for practical guidance purposes, a steady state 7 can be assumed. For ersmpl.s, at 50,000 ft altitude, a 180' turn would lose 8000 ft altitude wit" a resultant Y from 4.4 to 5.75. The guidance can estimate altitude at end of maneuver and Y (5.75) for that h can be aseumed. The angle-of-attack required to hold this aaaumed 7 for o(= '7.5 will be 5 7.5. This is a conservative approach because the klnetic energy et end of maneuver must be 2 ahcondition of gui0ance. Trajectary prediction. - At any altitude with a velocity as given by equation (4), the future flight path can be predicted and it ia auf- f iciently constant so that c linear trajectory ( Y can 5e assumed. The remainkg problem, though, is to predict the trajectory from a state with V # equation (4). X solution !e to shut the linear trajectory the potential energy equivalent of the kinetic energy difference of vehicies present state and thst of equation (4); 9.1 5.2.1. A~proachGuidance ( csr!tt1d)

V = V ol equation (4) C

the predicted reference tnjeotory for aonstant a flight

(v2 vc2) '-j =h+ - - -c 28 - X Tan fu.

Some results of thir assumption are show on figure B-3. A to, of ".76 was selected from figure B-1 for m altitude of 10,000 ft. The three actual trajectoziea of figure B-3 were started at h = 20,000 ft, Y 6.8, md V = 579.3 (from equation 4), 632.4 md 989.5 cor:e¶pnding to 0, 1000, and 10,000 ft equivalent potsntial enerw-diffamnce. The ft case steadies out on the ~ferencetra!ectov, but the shift for the 10,000 ft ca8e is 'only about 50 percent of predicted. hero ia disarpated during flight hoauss of drag force (D).

The tmjeckrg prediction asmmee no additional mere dirriprtion over thi8 nominal diesipation, but actually, +,here is additional drag with a gnator veloc?ty, and therafom,

It 1s possible to ~redictthis additional energy 1088 to better prediut the trajectory but an Iterrtion roluticm would be required. Also, thir better solution indicatos that the 1000 ft oms ir only 25 ft in error, md 1000 ft is about the msxh value encountered with the guidance system presented in thir report, and therefore, the simpler prediction (7) is wlid* 9.15.2.1 Approach Guidance (cont 'd)

d=O

Turn radius = 9200 ft =7.5

10 20 Altitude, ft

Figure 8-1 .- Predicied flight path for constant angle of attack Flight. 0.15.2.1 Approach Guidance (coxlt f d)

Altitude, ft Figure 6-2 :predicted flight path fw constant angle of attack W, and turn :adius (R). 9-15.2.1 Ap~roschGuidance - (contfdj

30 x lo3

\ Potential enegry I \ equiv.ofexcess kinetic enegry C

Reference trajectory 20 -

.4 Q: -aJ aJ . D 3 - .-4 4 -u

=40 CL= .5167 Cd =.0726 -- - - Actual trajectory

Range, X ,ieet

Figure 0-3.- Predicted trajectory for constant angle of attack flight.

4.15-38 APPENDIX C 9.75.2.1 Approach Guidance (conttd)

Compute New FAP Entry Faint

Gi~sn: 1. A vector DDA from exit point of initial turn to entry point of final turn.

2. Exit point of final turn (R6X = FAP entry point). 3. T.4N of flight path angles; K1 to FAP and K2 in FAP. 4. Projected vehicle hi h altitude ermr (DH) at minim FAP entry point (R5X k .

M IN. R6x EPJTP1'

Assumptions: 1. A nev solution for a new R6XN will have th3 same DDAY component. 2. The sum of both the initial and final turn angle remain constant with variation of R6X, and therefore, altitude losb of turns is approxhtely independcct of R6X.

KOTE: Theae are better aeeumptions for tuns with same direction (lee., lef'c ir 't la1 and final turns) than for oppoeite tuns --thir shodd merely mean that convergence on proper 36X will be faster if vehicle is in position fcr alike tuns.

Bemuse 5f the ase;unptiors, the prcoblt~becomes on9 of determining !ntersection(s) of two straight lines--trajectory to FAP and in FAP. 3.15.2.1 k?:roach Guidance (cont'd)

Q, = R5X - RbX + DDAX

Tho oonstant altitude difference between pint A and the desired eltitude @ R5 fe.

The objective of the new R6I$ 1. t. hea zero DH, therefore,

rearranging equation

where By squaring equation (1 )

vhich is of quadr~ticfonn 2 A DDAXN + B DDBX + C = 0

where

the eolution of which ie

thia equation presents a problem thaugh, when A = 0, which ie likely for a no-wind condition; therefore, s better fonn ie

before ueing equation (3), some cones,iraints must be applfod.

The roots cf (3) must be real, 0,,15.?.1 &protich Guidance (csnttd)

There are at mat two real rootr of equation (3), and there can k eight sete of two real ruots depending on the sign& of the coefficieata (A, B, & C). Fobs of there sets vi~ereB is positive, although reel for equation (3) am not real for the phy~icalproblemj i l , squation (1 ) . These am be avoided with constraint

TVQ other sets of mota where A I8 negative oontain tu* real root8 for equation (3), but only one ir valid for equation (1). The valid one io obtained by uring the positive eign in equation (3). The mmainfng two aets are salid for both eqiitions, but the more negative root (F@ entx-y rt greatest dirtance from RSP~ is desired, and It also r3quires positive sign in equcltioa (3), and therefore, if no constra4~t violated,

If any constraint was violated, then FAF entry point aet to minimum, 9~15.2.1 Apb; ~achGuidance - ( cont d )

APPENDIX D * 9.15.2.1 Approach Guidance (cont'd)

The rriere~net.3: eete~~(E~, Bg, Lo i,) and actual vehicle rbte (A, i,Y, ?) have ken def hod fur vertioal aad lateral ilrectlone. The guidance equations are derived that produce guida.noe outplt corn- vnds of 8,, go of standard aircraft roquence $, 8, @ and bodl rate comerids PC, upr,. A compilation of jurt the guidance oquationr ia aumm%risadat tb end of thie appandix. General Pbeical Ehuationa Utilisd Airspeed

1 = V_ (1~11relative Cjr ground) - (apriori wind)

Lift coefficient

Lift

(2 L=CLS~

Afrspsd ~czeleration 1 A (V - v0j/4t where At is anpitation cyalo the (i,e., 2 aec)

and 8, Is airaped at pmious ompatatLon the.

Flight path Note: 7 + DOWN Total vertical aaceleration L D (4) I+=~Coa~Cos?+~SinY-g

a component of vertical acceler~tiondefined as

.. e. (6) H = HT + + Sin T

angle of attack from (1, 2, 5, and 6)

by differentiating (7)

alw, rate of change of angle-ofattack

(9) cl =VCo. gv + q uharo q is body pitch rate. 9.7 5 2.1 A7proach Guidance (cont '8)

rate of ahwe of flight path

Bank angle from (5, 6, and 8)

- c0a2& # *# (13) av - (7-Tan gV (A +41an7 (*+ g Coar )

Vertical axir ddance. - To guide the vehicle altitude to the aom- mnd reference trajeotory with specified ma nee charaateristics of natural frequency (VW) end damping ratio ( r a second-order acceleration 00- 10 gbne~8ted

The laat term of thla equation ir the otmdy state aaaeleration required to hold the error signals of the first two t9m at sera. But, if thlr acc~lerationir applied to equation (I),the V ten will aanael, and therefom, just the following component of the oownd need be generated. 9.15.2.1 Approach Guidance (cont'd)

Quation (7) will give the ireu1tin.g aCfor this accel commd,

where GCIwhich is discussed later, met be generated first for use fa this equation.

Given Y , a,, and # , the local vertioal component of a unit vactor along the coradISd dlrectlon of the fuselage is,

(16) UXBLV = sin% l ~oskc l COOT - COO% l Sin?

The pftch component of this vector for the standard aircraft sequence of $ 8 @ is,

The ameleration comu~Pld (14) is a variable, the slop of which at a given tlme,

a sin t (as defined for reference trajectory ) dt = 4 ,, Substituting thia into eqution (8) and neglecting the last two tbm of (8) , uhich ie an imperically datemined good appmximation,

Prom (9 and lo), the pitch rate oonmend,

Hc $08 gvc (20 Qc = v Soa v + a~

If these carm~andauers perfectly n_s?-iprl; then the total vertical acceleration wuld be,

Assume, though, that there are bias type errors present reaulA*ng fmw errors in eem c~efficients,navigation, vicd, etc., the actual scceleration,

Th!a error can be computed by conparing the altitude rate from one 30mp~tmtioncycle to the next with the rate that should exist, At P 9.15.2.1 Approach Guidance- (cont'd)

The objective ie to remove bias errors, but not tranaientI error euch as aaused attitude response time delays. For ~tepchange of attitude oommnd, the instantaneous error would be,

As that system reeponde to the command, the error will reduce, so that the net expected error over At sec will be some fraction (1.e.. .A) of H: . The error to be compensated should then be reduced by the elrpect,ed error,

By accumulating this error through a gain, i.e., .8,

and feeding back a corrected command into (15) only

the bias will bs removed and the actual acceleration will converge on the desired level of (14).

Lateral Axis Guidance. - To guide the vehicle lateral position tc the comund reference tra ectorg with specified response characteristics nf natural frequency (Wn 3 and damping ratio ( f ), a second order acceleration commend fa generated,

The last term of this equation is the ateady state acceleration requird. to hold the error algnals of the first two terms at zero. This last term erCsts only for turn maneuvers and Ls the centripetal force, 9.1 2.Approach Gvldacce (contta;

The nferenoe trajectory seotion of tho guidance has selected the P-aria dLm?tion ao that t,he poritl~nand rate oommanda Y, and ic are nem, .*.

The number of tarma of this equation that are utilized is phase dependent, The full equation is used 3or the final turn, but only the Past +.ern for i~itialturn and only eemnd term for flight between turns. The acceleration and je~kconpatetion phase dependency is shown Xn detail at the end of this appendix, but just the final turn phage dl1 be discuassd here.

The bank a~ le caammnd is obtained by aubatituti~gcommand vafuea into equation 4 12),

Given Y and 6 ,, the 10-1 vertical component of a unlt vector along the co-xed direction of the wings La,

The roll coaponent of thia vector for the standard aircraft aequsnas of' + 8 # ir,

The rate of chsnga of i which i~ referenced to a mtatf.ng axis system, 9.15.2.1 Approach Guidance (a)ntld)

The rate of change of the acceleration coa~mand

Substituting this into equation (13) and neglecting the negligible last tom,

Projecting thio on body axea,

rc = Bvc Sin a,

As done with the vertical axis, a bias acceleration error can be meaaured and compensated with feedback through the acceleration command,

where the gain of h is empirically determined for stable removal of error8

* 1 (36) Y, = Y, (of (27)) - ?BIAS

Th's cam enoat.& value of acceleration command la used only in equation (28P . The g~idanceto the reference trajectory equations end logic are now aul~marizedfor each RX~I. H, and 8, from mferenoe tzmjeotory motion of Guidance 1 -7 la p = .002378 .235 (1 - 6.875 10-6 H) i=& Fliaht Path Sinn Conv. (t) Down i = (V - vo)/4t, where ~t is comp ayole time; iar., 2 sec

If (iT ie< O), then =Oa t &e

If (Not at a phu ahoy, and a ,< ac- 1, then, RBUS = HBIA3 + .8 4 e

Nokr Compute gVc from lat. guidance first for uae here. 9.1 5.2.1 Approach Guidmce (cont'd)

If (~Ughtdlnotor phm between turn8 and mu~/b discrete from rder~nortrajectory ssction of g~ldance), thou a = acmxe

UXECZ = -Sin a, Coos gVc Coos 7 + COO% l Sin 7

*4* HCO C~aAc t *EM - . -1. qc v Coa v Pcu Coa kcS q C0%Y 9.21 Approach Guidmce (cont'd)

I,, Y, i,, and i from rrfannor trajrotor :.ro*.lon of guidanor

Limit Y to 22000 it

a b ~t (hitgal or final turn), thm I,, ' (V COO y I2ht

.a# e b .*a Ya = -2 Tun 'I, + Y,,

.b *. % c Yo = Y, + Y,, u (final or in FAP, / Y /<~OOO it) 9.1 5.2.1 Approach Guiianc :contld)

J b 0 *@b b * %b8n, y, I-I, d I, ' - yc

V (initial trum and .a opporlt. tun aoamnd for thrae-turn weuver),

, = I @rec~/~os6,) Note r Compute 8, first , ther. use here. 9.15.2.1 Approach Guidams (cant 1 a)

TABm 1. - SIMTJATION INRlT DATA FOR DWONSTRATICN RUNS

DELTA WING ORBITER

Condl- VG . 562 ft/sec tions y 7 deg 6 deg

.I954 + 4.60257

which & ?ioO~~Oft for

- t-- --- SPACX SilUrTLE

GN&C SOFTWARE EQUATION SUBMITTAL

Software Equation Section Final Approach Guidance Submittal No. 29

F- -&ion: Lateral and Lonpitudinal Autoland Guidance

Module No. OG? Function No. 1, unpowered (MSC 03690 Rev. B)

Submitted by: C. Dyer Co. EG2 (~ame) Date: Awt24 and October 21, 1971

NASA Contact: J. Suddath Organization EG2 (Nape ) Approve? by Panel I11 V.X. b)c Date '"/w 19 f

Summary Description: Pitch rete and speed-brake commands are computed and zlsed to control in-plane approach. Lateral position error and its internal plus heading-ang$e error are used to form vehicle roll command,

Shuttle Configuration: (Vehicle, Aero Data, Sensor, EX cetera)

NR161C orbiter aero - data Comments:

(~esignstatus)

(verification Status) . .

Panel Cclments: 9.1 5.2.2 Final Approach Guidance

These equations are submitted as candidates to fulfill the unpowered Final Approach Guidance requirements for the space-shuttle Crbiter. They include Autoland lateral and longitudinal guidance squations. The echeme is all-inertid; navigatioc aids are used only to update the navigated vehicle state. Pitch rate and speed- brake commands are computed and issued to contaol in-plane approach. Lateral position error and i5s intepal plus heading-angle error are used to form the vehicle roll command. (There is no decrab or wings Level manuever; the assumption is made that the gear is designed to accoinmodate the stress for crahbed landings in design winds. ) 2. Pmctiord Diagram

A general description of Autoland Guidance is contained in Ref, 1. Figure 1 is functional diagram. Fig. 2 is a block diagram. (For generai iniormation, the autopiloig 5eirg use6 in simulation runs are included in Fig. 2. )

Inputs to the Guidance module (OC-7) are from the Final Approach and Guidance Navigation module (ON+) ; the inputs are the navigated sta~~ein the Earth-fixed landing coordinate system. From this are pdculated the range to tovchdown target, altitude, inertial velocity magnitude, inertial flight-path angle, lateral position and heading angle. Outputs are pgtc? rate c-d, speed-brake position

C& and vehicle roll codto the autopilot. The guidance roll sammand drives a roll-rate aileron-autcpilot inner loop with roll attitude outer loop, Roll rste command is interconnected to a rate cnmmRnrl rudder autopilot with turn coordination and normal acceleration inputs. The acceleration and heading-angle signals are instrumental in holding the orbirer to the final approach plane in 33098ldIld~. 3.1 5.2.2 Final Approach Guidance (cont 1 d)

RE;AU vE.3lCZ STATE IN LANDING COORDINATE SYSTEM

PLAN TRAJECTnRY TNITIALIZE

2 L I

CALCULATE PITCH I RATE COW33

I CALCULATE SPEED

I-.+.--CALCULATE ROLL _I

t 9 ISSUE CCMMMDS FIGURE I TO ATJTOPILOT FUNCTIONAL DIAGRAM I 9.1 5.2.2 Final Amroach Guidance ( cont d)

Figure 2a Block Die&alp, LongitudJ.nal ' Figure 2b Block Diagram, Lateral 9.15.2.2 _Final ~pproachGuidance (contld)

3, Coordinate Syotem

The autoland guidance uses vehicie position and velocity re- lutive to a runway coordinate systcy,as shown in Five 3. Figure 3 also indicates longitudinal sign convention for the aquations. The "altitude of the IMUv at touchdown is represented in the equations as c.g. dtitude,

4. huatio~.sand Flm 4.1 The longitudinal guidmca equations are presented in Figure ?+. The guidance routine (as currently implmented) is entered four times per second. his frequency is to be verified by planmid guidance/autc9ilot interaction and wind gust response studies.) Stability of the guid.anco equatiorm and minimization of the ve-Ucle rotational mottons set the minimum rate. There are no switching requirements in the scheme. The vehicle's state is in a landing coordinate system. On the initial pass, the target sink rate, touchdown ground speed, and shallow flight path angle are used to cmpute reference tra- jeldaory constants. The reference trajectorg subroutine is entered with :he targeted range at pullup completion, and flare and touchdown constants, to find the reference altitude at pullup completion. At TARGET, a steep flight. path angle is cquted which wiu carry the vehicle frm its current altitude through pullup onto the shallow slqpe. This capability may also be used to reylan tho I reference trajectory during the steep phase to mhhizle transients from large navigation updates or to replan when forced by emergency cnnditions. A liuear reference velocity is defined to camy the vehicle from its current velocity to its targeted value at the campletion of the yUup. 9.1 5.2.2 Final Approach Guidance (cnnt d)

Figure 3. Runway Coordinate Sys tein mli~r- s,,rlt - -I iPoO.ITIMC CLII LOCKHEED ELECTRONICS COMPANY I Pfe~ored A L3 ~p. NOU8lOfl A1101P&:C 8VBvIYI DIVI8ION FIL~Lj Q* Cbcked Mo&i GdTDAcJCE UpJS (L) AOgf~d. R.oort No. *.MI TtlC LOCKHEED ELECTRONICS COMPANY HOUSTCJN AfIOSCACt SVSTCYS OIVISION Itroored ;=. 2- Paga

Ch~kd Model GLII~WC;. ~23'; (2) . Lwprovd Repart L

C%?$ .

A 4 MAS0 055 6901Y 1

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maw8 OATI LOCKHEEO ELECTRONICS COMPAdY YOUSTOm ACaObCaCZ IvLT&YS 01bIS10M Gi 7 I - VITLE f, y 4 Ckbd Model I EETE~ELXETPASQ:TOCI wds -Aporowa a Report No.

9.15.2.2 Final Approach Guidance (conttd)

On a nodcall, after the vehicle state is determined, if phase is steep the rderence trtfectory is defined through pullup. When the puilup-complete renge has been reached, pizase is set to shallow tirid a new reference velocity profile is defined to decele- rate the vehicle to its targeted touchdown vdocity. The two velocity dopes approximate the expected vehicle dsleleration along the steep and shallow glide paths with gear down 2nd half speed brakes. The switch to shallow is not critical since tL4 two portions of the reference trajectory overlap smoothly.

At LOOPS, velocity dependent gains are computed. A pitch rate co.mnmd is formed add limited. A speed brake command is formed such tkit zero error gets half brakes and both commds are issued to the autopilot. The reference trajectory subroiztine is entered with one of two sets of targets; pullup over and touchdawn. Calling arguments are as follows: V - Current vehicle velocity, ~sedfor f . R - Range to gc to end of current maneuver. Pullup, R-Rb,and touchdown, R. p - Constant which sqts maneuver curvature, normal acceleration level. pr , pf . m - Negative of difference between flight path angles eutering and leaving the maneuver. Steep minus shallow and shallow minus touchd~wn. L Q- &.gative of flight path angle leaving the maneuver. Shallow glide and touchdown glide slope. hb- Altitude at which maneuver ig cmplete and vehicle

flfing 9% . Altitude at pullup complete md cg height at touchdawn. 9.15.2.2 Final Ap??oach GuJ.dance (cont Id)

h, - Reference altitude Vr - 3eference flight path angle vr - Reference flight path angle rate

ERF is an approldmation to the error function devised in Ref. 2. Its use is illustrated in Fig. 4.

Linear approximations of the eystem transfer functions are presented in Fig. 4.

4.2 The lateral guidance equations are presentad in Fig. 5. On the initial pass, the roll gain, crossrange integral gain, and the heading gain are stored. On a normal pass the crossrange gain, Kr, is calculated as a functio~OF velocity. When altitude becomes less tbU 50 ft, the roll comnand gain is decreased from 1 to .5 over a 2,-second periad. The roll command is the sum of a crossrange, integral of crossrange, and velocity heading angle term. It is limited and issued to +.ha autopilot.

Figure 6 summarizes variables and constants. Precision and quantization requiremnts have not been finalized. Figure 7 describes the principal variables. Figure 8 lists typical input values.

6. Coding

The equations have been coded in FORTRAN for simulation cn -;;he SSFS (Space Skuttle ~ctionalSimulator).

7. Simulation Status

The scheme is operation on the SSFS, Figure 5 Lateral Guidance Equations

9.1 5.2.2 Final Approach Guidance (contld)

- - Y 73.- CR ft CAswS f x -GYcR rr d/#r HEDrn& rfi '4 GKHt'O rad/d PW IC ra d P#~;L~ GKP I ,

Figure 6c Constants/Variable Sumary *.Ma MI@ LOCKHtKO ELECTRONIC@ COMPANY YU~TOW AKROOCACI IV~TKYI OIVIOION

?r?LK f\6, 7& =kdrl, :Wl I VAU~A~LE~)KCIUPT\CW II) LOCKWEtD ELECTRONlCl COMPANY WOUITOW AEMOCACR IVOTIUI OIVIOlbk

~ITU ~\b7A , uwz i,+,i,~t'Q&C~~ST (a) 9.15.2.2 Final Approach Guidance (cont d)

Vehicle altitude, ft. Vehicle lateral displacement from ru-lway center line, ft. Vehicle velocity, fps . Velocity heading angle 1 I

Lateral displacement integral threshold, f t. Roll command, rad. Roll command limi\, rad.

Guidance gains, rad/ft, l/sec, rad/rad.

Figure 70 Variable Description 9.15.2.2 Final Apxosch Guiciance (cont d)

T t I.U. - OfiTS LOCKMEED ELECTRONICS COMPANY kma4 *OU.TON .#M.CAC# -*V*TIY. DIVI~IO~ poo. rltLr ,=\b 8 ctmK4.d Meh: 7 i - ~JDM~LAC TOhr. I Awro*.rd 1 Repon No

I I

w nUb ocs .to)( 1 A touchdown dispersicn study his been perfomed. Son6 results =e showr, i2 Figure 3. FG~zests beginning at 17s ft. zltit,ude aid 15,OC)Z ft. range, crossrange diapersisn in +- 10 ft. and era.;- r, r=ge rcte disprsion ia i-gfps, Vehicle yaw at. toilchdown is do- tedne6 eu~en5iallybJ- the crosswind, A 20 -knot wind results

'1 . Lateral guidance is Casially ar, all-inertial version of Ref. 5.

NR l6iC delta wing aero and mass propertie2 (~ef.4). 'u'npoversd lariding Error Nodela (per 94. 3) .

The iritegral-of-crossrange tern in tk lateral guidance linita steardy state errors. Wortunatsly, it also rekds response to dynamic errors. Simdation. 7. rms iadicatc that inproved performame I - say redt f~mfreezing(clampir4) the inbegral at some point before touchdcwn. vXRENCES

1. "IIigh Crossrange Shuttle Autoland Guidance, LEC Memo 675L+2~/123503, K. Alder.

2. !!An Analytical Approldmation for erf (t)," -%C Memo EG2- 7&?45, J. He Scddath.

Touchdown Performance, EG2 and Sperry Shuttle Autoland Note (in preparation), D. A.

4. "Qelta-Wing Orbiter Vehicle Model for CRALS," LEC Msmo SA3071-0020, J. Vanelli.

5. "Spucs Shuttle Data Flight Systems, Part I1 Orbiter," MIX: 20334, 30 June 1971.