The Pennsylvania State University
The Graduate School
Department of Aerospace Engineering
SIMULATION AND CONTROL OF
A HELICOPTER OPERATING IN A SHIP AIRWAKE
A Thesis in Aerospace Engineering by Dooyong Lee
c 2005 Dooyong Lee
Submitted in Partial Fulfillment of the Requirements for the Degree of
Doctor of Philosophy
August 2005 The thesis of Dooyong Lee has been reviewed and approved* by the following:
Joseph F. Horn Assistant Professor of Aerospace Engineering Thesis Adviser, Chair of Committee
Lyle N. Long Professor of Aerospace Engineering
Edward C. Smith Professor of Aerospace Engineering
Qian Wang Assistant Professor of Mechanical Engineering
George Lesieutre Professor of Aerospace Engineering Head of the Department of Aerospace Engineering
*Signatures are on file in the Graduate School. Abstract
This thesis describes a study in simulation and control of a helicopter operating in proximity to a ship. The helicopter/ship combination used in the study is a UH-60A helicopter operating off an LHA class ship. This represents the same aircraft ship combination used in the JSHIP program. The flight dynamics model is based on the GENHEL software and this
flight dynamics model has been updated to include high-order dynamic inflow model and gust penetration effects of the ship airwake. To simulate the pilot control inputs for typical shipboard operations, an optimal control model of the human pilot is developed. The pilot model can be tuned to achieve different tracking performances based on a desired crossover frequency in each control axis and is designed to operate over a range of airspeeds using a simple gain scheduling algorithm. The pilot model is then used to predict pilot workload for shipboard operations in two different wind-over-deck conditions.
Validation studies are conducted using both time and frequency domain analyses to understand the impact of a time-varying ship airwake on the pilot control activity for the approach and departure operations. The pilot control input autospectra predicted from the simulation model are compared to those of flight test data from the JSHIP program. It is found that the control activities are similar in low frequency range but underestimate
iii in magnitude in the high frequency range (over 1.5 Hz). There is clear evidence that the human pilot is continually moving cyclic stick in the maneuver. At this stage of the study no attempt has been made to optimize the parameters of the human pilot model.
The paper also discusses the application of a stochastic airwake model for more efficient simulation. This new airwake model is derived from the simulation with the full CFD airwake by extracting an equivalent six-dimensional gust vector. The spectral properties of the gust components are then analyzed, and shaping filters are designed to simulate the gusts when driven by white noise. It is proposed that the stochastic gust model can be used to optimize the automatic flight control system in order to improve disturbance rejection properties of the aircraft.
A stability augmentation system (SAS) is optimized for a UH-60 helicopter operating in the turbulent ship airwake. For disturbance rejection, a new performance specification is designed based on the power spectral density of the transfer function from the gust inputs to aircraft rate responses. The baseline limited authority SAS is modified and optimized using
CONDUIT (Control Designer’s Unified Interface) in order to improve handling-qualities and stability, and to minimize a weighted objective of gust responses. In addition, a H∞
controller is designed to provide an alternative SAS configuration. The optimized SAS and
H∞ SAS are then tested using the non-linear simulation model with time-varying airwake.
Time domain and frequency domain analyses of the simulation show that the modified SAS
results in significant reduction of pilot workload.
iv Contents
List of Figures viii
List of Tables xiv
Acknowledgments xv
1 Introduction 1
1.1 Modeling of Helicopter/Ship Dynamic Interface ...... 4
1.1.1 HelicopterFlightDynamicModel...... 4
1.1.2 ModelingofRotorAerodynamics ...... 7
1.1.3 ShipAirwakeModel ...... 11
1.1.4 FlightControlModel...... 13
1.2 Simulation of Helicopter/Ship Dynamic Interface ...... 16
1.3 Problem Statement and Research Objectives ...... 18
2 Helicopter Flight Dynamics Model 20
2.1 OverviewoftheGENHELSimulationModel ...... 20
2.2 MATLABImplementation...... 23
v 2.3 Peters-HeInflowModel ...... 24
2.3.1 Background...... 24
2.3.2 Basic Equations of Peters-He Inflow Model ...... 25
2.4 GustPenetrationModel ...... 29
3 Pilot Modeling 34
3.1 Optimal Control Model of the Human Pilot ...... 35
3.2 Nonlinear Elements of the Human Pilot ...... 41
3.2.1 Hysteresis...... 41
3.2.2 Deadband...... 42
4 Numerical Examples 44
4.1 Overview ...... 44
4.1.1 ShipboardDepartureTrajectory ...... 45
4.1.2 Shipboard Approach Trajectory ...... 46
4.2 EffectsofShipAirwakeModel...... 48
4.3 EffectsofDifferentTrackingPerformance ...... 65
4.4 ValidationwithFlightTestData ...... 70
4.4.1 FrequencyDomainAnalysis ...... 81
5 Task-Tailored Control Design 85
5.1 Overview ...... 85
5.2 StochasticAirwakeModeling ...... 88
5.3 Optimization of a Stability Augmentation System ...... 110
vi 5.4 H∞ ControlofaHelicopterSAS ...... 128
5.4.1 Review of H∞ Control Design Method ...... 129
5.4.2 Design of H∞ Controller for a Helicopter SAS ...... 135
6 Conclusions and Future Works 154
6.1 Conclusions ...... 154
6.2 Recommendations for Future Work ...... 157
Bibliography 160
vii List of Figures
1.1 TypicalWODenvelope(Ref. [2]) ...... 2
1.2 The modeling components of a helicopter (Ref. [3]) ...... 4
1.3 Momentum theory flow model for axial flight (Ref. [3]) ...... 8
1.4 Block diagram of coupled rotor and induced flow dynamics (Ref. [14]) . . . 9
1.5 Schematic of helicopter control system ...... 14
2.1 Block diagram of GENHEL flight simulation model (Ref. [11]) ...... 21
2.2 Overall structure of MATLAB based simulation program ...... 23
2.3 Comparisonsofinflowratio ...... 29
2.4 Vorticity magnitude iso-surface at t = 40 sec (Ref. [39]) ...... 31
2.5 Gustpenetrationmodel ...... 32
2.6 The approach of the overlapped time history of airwake ...... 33
3.1 Optimal control model of the human pilot ...... 35
3.2 Augmented plant model in longitudinal axis ...... 37
3.3 Effect of a sine wave passing through a hysteresis ...... 42
3.4 Effect of a sine wave passing through a deadband ...... 43
4.1 TopviewofanLHAclassship ...... 45
viii 4.2 Shipboard approach operation procedures ...... 47
4.3 Helicopter position w.r.t. ship coordinate system - Departure task . . . . . 50
4.4 Helicopter velocity [ft/sec] - Departure task (30 knot, 0 degree WOD condition) 51
4.5 Helicopter attitude angles [deg] in the DI mesh - Departure task (30 knot, 0
degreeWODcondition) ...... 52
4.6 Pilot inputs [%] in the DI mesh - Departure task (30 knot, 0 degree WOD
condition)...... 53
4.7 Helicopter velocity [ft/sec] - Departure task (30 knot, 30 degree WOD con-
dition)...... 54
4.8 Helicopter attitude angles [deg] in the DI mesh - Departure task (30 knot,
30degreeWODcondition) ...... 55
4.9 Pilot inputs [%] in the DI mesh - Departure task (30 knot, 30 degree WOD
condition)...... 56
4.10 Helicopter position w.r.t. ship coordinate system - Approach task ...... 58
4.11 Helicopter velocity [ft/sec] - Approach task (30 knot, 0 degree WOD condition) 59
4.12 Helicopter attitude angles [deg] in the DI mesh - Approach task (30 knot, 0
degreeWODcondition) ...... 60
4.13 Pilot inputs [%] in the DI mesh - Approach task (30 knot, 0 degree WOD
condition)...... 61
4.14 Helicopter velocity [ft/sec] - Approach task (30 knot, 30 degree WOD condition) 62
4.15 Helicopter attitude angles [deg] in the DI mesh - Approach task (30 knot, 30
degreeWODcondition) ...... 63
ix 4.16 Pilot inputs [%] in the DI mesh - Approach task (30 knot, 30 degree WOD
condition)...... 64
4.17 Helicopter position error [ft] - 30 knot, 0 degree WOD condition ...... 66
4.18 Pilot control input [%] - 30 knot, 0 degree WOD condition ...... 67
4.19 Helicopter position error [ft] - 30 knot, 30 degree WOD condition ...... 68
4.20 Pilot control input [%] - 30 knot, 30 degree WOD condition...... 69
4.21 Helicopter airspeed [knot] - 30 knot, 0 degree WOD condition...... 73
4.22 Helicopter altitude [ft] - 30knot, 0 degree WOD condition ...... 74
4.23 Angular rate [deg/sec] - 30knot, 0 degree WOD condition ...... 75
4.24 Pilot stick inputs [%] - 30 knot, 0 degree WOD condition ...... 76
4.25 Helicopter airspeed [knot] - 30 knot, 30 degree WOD condition ...... 77
4.26 Helicopter altitude [ft] - 30 knot, 30 degree WOD condition ...... 78
4.27 Angular rate [deg/sec] - 30knot, 30 degree WOD condition...... 79
4.28 Pilot stick inputs [%] - 30 knot, 30 degree WOD condition ...... 80
4.29 Pilot input autospectrum [dB] - 30 knot, 0 degree WOD condition . . . . . 83
4.30 Pilot input autospectrum [dB] - 30 knot, 30 degree WOD condition . . . . . 84
5.1 Task-tailored control system design scheme ...... 87
5.2 Derivation of stochastic airwake disturbances ...... 91
5.3 Comparisons of aircraft angular rates [dB] (time-varying airwake vs. equiv-
alentairwake)-0degreeWODcondition ...... 93
5.4 Comparisons of aircraft angular rates [dB] (time-varying airwake vs. equiv-
alentairwake)-30degreeWODcondition ...... 94
x 5.5 Comparisons of pilot inputs [dB] (time-varying airwake vs. equivalent air-
wake)-0degreeWODcondition ...... 95
5.6 Comparisons of pilot inputs [dB] (time-varying airwake vs. equivalent air-
wake)-30degreeWODcondition ...... 96
5.7 Power spectral density for vertical airwake disturbance component . . . . . 98
5.8 Power spectral density of longitudinal airwake disturbance component . . . 99
5.9 Power spectral density of lateral airwake disturbance component ...... 100
5.10 Power spectral density of vertical airwake disturbance component ...... 101
5.11 Power spectral density of roll airwake disturbance component ...... 102
5.12 Power spectral density of pitch airwake disturbance component ...... 103
5.13 Power spectral density of yaw airwake disturbance component ...... 104
5.14 Comparisons of aircraft angular rates [dB] (time-varying airwake vs. equiv-
alent airwake vs. stochastic airwake) - 30 knot, 0 degree WOD condition . . 106
5.15 Comparisons of aircraft angular rates [dB] (time-varying airwake vs. equiv-
alent airwake vs. stochastic airwake) - 30 knot, 30 degree WOD condition . 107
5.16 Comparisons of pilot inputs [dB] (time-varying airwake vs. equivalent air-
wake vs. stochastic airwake) - 30 knot, 0 degree WOD condition ...... 108
5.17 Comparisons of pilot inputs [dB] (time-varying airwake vs. equivalent air-
wake vs. stochastic airwake) - 30 knot, 30 degree WOD condition ...... 109
5.18 Augmented plant model for a SAS optimization ...... 112
5.19 ModifiedSASconfiguration ...... 113
5.20 A new disturbance rejection spec design (ex. pitch axis) ...... 115
5.21 HQ windows for the original SAS configuration - 30 knot, 30 degree WOD . 116
xi 5.22 HQ windows for the optimized SAS configuration - 30 knot, 30 degree WOD 117
5.23 Aircraft angular rate responses [deg/sec] - 30 knot, 0 degreeWOD . . . . . 120
5.24 Pilot control stick inputs [%] - 30 knot, 0 degree WOD ...... 121
5.25 SAS outputs [%] - 30 knot, 0 degree WOD ...... 122
5.26 Aircraft angular rate responses [deg/sec] - 30 knot, 30 degree WOD . . . . . 123
5.27 Pilot control stick inputs [%] - 30 knot, 30 degree WOD ...... 124
5.28 SAS outputs [%] - 30 knot, 30 degree WOD ...... 125
5.29 Control stick input autospectra [dB] - 30 knot, 0 degree WOD...... 126
5.30 Control stick input autospectra [dB] - 30 knot, 30 degreeWOD ...... 127
5.31 Standard compensator configuration ...... 131
5.32 Additiveperturbation ...... 132
5.33 Disturbance rejection at the plant output ...... 132
5.34 General block diagram of the mixed sensitivity problem ...... 134
5.35 Augmented system for airwake disturbance rejection ...... 136
5.36 Magnitude of weighting functions We and Wu ...... 139
5.37 Singular values of controller K∞ ...... 140
5.38 Aircraft position w.r.t. the spot 8 [ft] - 30 knot, 0 degreeWOD ...... 142
5.39 Aircraft angular rate responses [deg/sec] - 30 knot, 0 degreeWOD . . . . . 143
5.40 Aircraft attitude responses [degree] - 30 knot, 0 degreeWOD ...... 144
5.41 Pilot control stick inputs [%] - 30 knot, 0 degree WOD ...... 145
5.42 SAS outputs [%] - 30 knot, 0 degree WOD ...... 146
5.43 Aircraft position w.r.t. the spot 8 [ft] - 30 knot, 30 degreeWOD ...... 147
5.44 Aircraft angular rate responses [deg/sec] - 30 knot, 30 degree WOD . . . . . 148
xii 5.45 Aircraft attitude responses [degree] - 30 knot, 30 degreeWOD...... 149
5.46 Pilot control stick inputs [%] - 30 knot, 30 degree WOD ...... 150
5.47 SAS outputs [%] - 30 knot, 30 degree WOD ...... 151
5.48 Control stick input autospectra [dB] - 30 knot, 0 degree WOD...... 152
5.49 Control stick input autospectra [dB] - 30 knot, 30 degreeWOD ...... 153
xiii List of Tables
4.1 Initial profile parameters for the departure task ...... 46
4.2 Initial profile parameters for the approach task ...... 48
4.3 Crossover frequencies for different tracking performance (rad/sec) ...... 65
4.4 Initial profile parameters for the approach tasks from JSHIP program . . . 70
5.1 Gust shaping filters for 0 degree and 30 degree WOD conditions ...... 105
xiv Acknowledgments
I would first like to express my deepest appreciation to all the committee members for participating on the examination committee. Many thanks go to Professor Lyle N. Long and fellow graduate student Nilay Sezer-Uzol for sharing their experiences and support of ship airwake data. Especially, I gratefully thank Professor Joseph F. Horn, my advisor, for his time, guidance, and patience, which have been uniquely instrumental in the successful completion of this thesis.
I would also like to thank CDR Kevin J. Delamer, USN and Colin Wilkinson for their support with regard to the JHSIP flight test data. Dr. Mark B. Tischler, US Army/NASA
Rotorcraft Division, was deeply appreciated for providing the CIFER and CONDUIT soft- ware. Fellow graduate students Jun-Sik Kim, Nilesh Sahani, Derek Brigdes, Brian Geiger,
Youngtae Ahn, are thanked for their friendship and technical advice.
I am deeply indebted to my family for all the years of support and encouragement that led to the completion of this thesis. Endless thanks to my parents, my parents-in-law, my sister and the family of my brother. Finally, I dedicated this thesis to my wife, Kyoungsun
Moon, whose love and support gave me the strength of mind to complete this work on time.
To my daughters, Michelle and Jennifer, I hope this thesis makes you proud.
xv Chapter 1
Introduction
Many military and commercial helicopters need to be launched and recovered from a ship at sea. There are several distinctive problems associated with ship-based helicopters that can limit their operational capability. For example, the pilot has to takeoff and land the he- licopter from a moving flight deck within the turbulent airwake of the ship’s superstructure.
Since these environments increase the difficulty of the helicopter shipboard operations, the shipboard operation is one of the most challenging, training intensive and dangerous of all helicopter flight operations. To assure the compatibility of any helicopter/ship combination, a set of limits must be established to define the envelopes which safe launch and recovery can take place. Currently, those limits are determined by conducting flight tests at sea using particular helicopter and ship combination.
The so called “Helicopter/Ship Dynamic Interface Testing” is a comprehensive term referring to investigation of all aspects relating to the effect of ship presence on embarked helicopter shipboard operations [1]. Typically, the dynamic interface tests include analysis and quantification of the approach, hover, and departure operations under various shipboard
1 CHAPTER 1. INTRODUCTION 2
flight conditions. For example, during hover and landing, the objectives are to investigate the effects of turbulence and the ship motion and recovery assist system. The dynamic interface tests are also used to evaluate the adequacy and safety of shipboard aviation facilities and procedures.
An important issue of the dynamic interface testing is to establish the wind-over-deck
(WOD) flight envelope. The WOD flight envelope depends highly on extent of the winds encountered. Low winds result in a small envelope, even if the real envelope may be much larger. Before a WOD envelope is established, a very restricted ‘general envelope’, which results in a reduction in helicopter/ship operational capability, is used to determine safe operating conditions [2]. Figure 1.1 shows the general envelope and a typical envelope expanded by dynamic interface testing.
Currently the only method for determining the WOD flight envelope for U.S. military is
45 10 40 330 20 35
301 320 25 Expanded envelope 2 3 20 through DI testing 310 4 3A 15
5 45 10 6 5 60 General envelope
7 270 90
8 9
Figure 1.1: Typical WOD envelope (Ref. [2]) CHAPTER 1. INTRODUCTION 3 by actual flight test. This method of flight envelope definition requires a significant amount of time, expense, resources, and is limited by the weather and sea conditions. Thus, the need has arisen to use better simulation tools for analyzing shipboard operations to reduce the flight test time and cost to establish safe operating envelopes.
Over the last few years, numerous efforts have been devoted to develop helicopter/ship dynamic interface simulation tools. Such a simulation tool can be used to estimate the best approach and departure paths, provide improved real-time training simulator for pilots, and ultimately be used in the design or acceptance testing of future helicopter. Modeling and simulation of the helicopter/ship dynamic interface is a challenging technical problem.
Rotorcraft themselves are complex and highly nonlinear dynamic systems, but shipboard operations present further complexity. There are several considerations when modeling the shipboard launch and recovery flight tasks:
1. Modeling the helicopter flight dynamics.
2. Defining the trajectory of the helicopter.
3. Modeling the pilot feedback loop required to fly this trajectory.
4. Modeling the influence of ship airwake on the helicopter.
5. Modeling the effect of atmospheric turbulence on the helicopter.
6. Modeling the motion of the ship for the given sea state and its influence on the
helicopter and the pilot.
7. Modeling the visual, aural, and motion cues for DI testing.
In this study, the first four of these considerations will be addressed. CHAPTER 1. INTRODUCTION 4
1.1 Modeling of Helicopter/Ship Dynamic Interface
1.1.1 Helicopter Flight Dynamic Model
The simulation models that are required to describe the flight behavior of the helicopter include kinematics, dynamics, and aerodynamics of the helicopter subsystems (main rotor, fuselage, empennage, tail rotor, power plant, and primary flight control system). Since the dynamics of a helicopter is highly complex and nonlinear (Figure 1.2), obtaining an accurate mathematical model is a very challenging task.
In general, the equations governing the dynamics of these components can be developed from the application of physical laws, e.g., Newton’s laws of motion, conservation of energy, to the individual components. The basic formulation can be found in various textbooks
[3, 4, 5].
For the special case where only the six rigid body degrees of freedom (DOF) are considered, the state variables compromise the three translational velocity components
(uf , vf , wf ), the three rotational velocity components (pf , qf , rf ), and the three Eu-
Main rotor flap, lag, pitch, and wake
Rotor downwash On Empennage and Tail rotor Rotor Downwash On Fuselage
Fuselage Wake On Empennage
Figure 1.2: The modeling components of a helicopter (Ref. [3]) CHAPTER 1. INTRODUCTION 5 ler angles (φ, θ, ψ). The resulting equations of motions are :
X u˙ f = qf wf + rf vf g sin θ Mh − − Y v˙f = rf uf + pf wf + g cos θ sin φ (1.1) Mh − Z w˙ f = pf vf + qf uf + g cos θ cos φ Mh − where X, Y, Z are the external forces acting on the center of mass, g is the gravitational
acceleration, and Mh is the total mass of the helicopter.
L Iy Iz Ixz p˙f = + − qf rf + (˙rf + pf qf ) Ix Ix Ix
M Iz Ix Ixz 2 2 q˙f = + − pf rf + (rf pf ) (1.2) Iy Iy Iy − N Ix Iy Ixz r˙f = + − pf qf + (˙pf rf qf ) Iz Iz Iz −
where L, M, N are the external moments about the center of mass, Ix, Iy, Iz, Ixz are the
moments and product of inertia respectively.
The Euler attitude angles add to the equations of motion through the kinematic rela-
tionship between the fuselage angular rates and the rates of change of the Euler angles.
Using 3-2-1 sequence (yaw-pitch-roll), the kinematic relations are
p = φ˙ ψ˙ sin θ f −
qf = θ˙ cos φ + ψ˙ sin φ cos θ (1.3)
r = θ˙ sin φ + ψ˙ cos φ cos θ f − CHAPTER 1. INTRODUCTION 6
It is important to note that this six DOF model, while itself complex and widely used, is still an approximation to the helicopter behavior. All higher degrees of freedom, associated with the main rotor, powerplant/transmission, control system and the disturbed airflow, are all represented in a common quasi-steady manner in the equations, having lost their own individual dynamics and independence in the model reduction. However, this process is a common feature of flight dynamics, in the search for simplicity to enhance physical understanding and ease the computational load.
Typically, the reduced dynamic model is widely used in the field of controller design. For example, a six degree of freedom linear model of the Bell 205 helicopter was used to describe a typical steady hover condition [6]. Postlethwaite et al validated linear model of the Bell
205 helicopter against flight test with integration of uncertainty in the specific frequency range [7]. Frost et al [8] used 6 DOF and 10 DOF linear models of the unaugmented UH-60 at a variety of flight conditions. These models had been previously identified from flight test data using the Comprehensive Identification from Frequency Response (CIFER) software.
A more complex linear model was applied by Takahashi [9]. The total 23 states linear model represented the helicopter as a six DOF rigid fuselage with rigid rotor blades each with a flap and lag DOF. Lead-lag damper models were also included. Rotor RPM DOF and engine-governor dynamics were not included in this model. Linear two dimensional quasi-steady theory was used to model the rotor blade aerodynamic forces and a three state
Pitt-Peters dynamic inflow model was used to describe the unsteady wake effects.
A 40 states linear model was used as the basic helicopter dynamic model by Ingle et al [10]. In this analysis, basic model consists of fuselage rigid body modes, flap and lag dynamics, a simplified representation of blade torsion, first harmonic dynamic inflow for the CHAPTER 1. INTRODUCTION 7 main rotor, tail rotor dynamic inflow, and an approximation for the delay of the downwash effects on the tail rotor and empennage. The rotor speed was assumed constant and the quasi-steady blade element aerodynamics included the effects of compressibility and stall.
Finally, a 32 state model was augmented with an 8-state model of the actuator dynamics.
Several nonlinear helicopter dynamic models have been developed and can be found in public domain. Perhaps one that is most widely used in dynamic interface simulation is the
GENHEL (General Helicopter) flight dynamics simulation code. The GENHEL provides operational and verified engineering simulation of the UH-60 Black Hawk helicopter [11].
This work was originally developed by Sikorsky Aircraft and documented under contract from NASA. The solution in terms of helicopter motion is obtained iteratively by summing the forces and moments acting at the helicopter center of gravity and subsequently obtaining the accelerations. The helicopter model is divided into components for the purpose of modeling the aerodynamics(the main rotor, fuselage, empennage, tail rotor). The detailed definitions of each component are given in Reference [11].
1.1.2 Modeling of Rotor Aerodynamics
The unique problem for helicopter flight simulation is the main rotor unsteady aerodynam- ics. The presence of compressibility effects and an unsteady rotor flow field, even when the helicopter is moving with uniform speed, makes the analysis of helicopter motion very complex. Typical issues on rotor aerodynamics include the rotor wake and the ground effect.
The simplest representation of the rotor wake is based on the momentum theory, utilizing the conservation laws of mass, momentum and energy. The rotor inflow is assumed to be steady, inviscid and incompressible with a well defined slipstream between the flow field CHAPTER 1. INTRODUCTION 8 generated by the actuator disc and the external flow (Figure 1.3). Further assumptions are discussed in detail by Johnson [4] and Bramwell [5].
The early representations of unsteady rotor aerodynamics reduced the main rotor’s flow
field to two dimensions. The classic 2D unsteady approximations are the Theodorsen and
Sears functions [4]. The Theodorsen function describes an airfoil oscillation in pitch and plunge. The Sears function describes an airfoil with a transverse harmonic gust. These func- tions were derived from a non-rotating reference frame. However, they provide a convenient reference for rotating flows.
While changing to rotational coordinates creates some confusion as to how boundary conditions are referenced and measured, Johnson [12] showed the proper derivation of the boundary conditions. Loewy developed a 2D representation of a rotating rotor’s unsteady
flow field with harmonically occurring blade passages [13]. The lift deficiency function resembles the Theodorsen function. For high inflow rates, the Loewy function is approaching the Theodorsen results. The most important result from Loewy is that the wake geometry and phasing is the primary cause of unsteady rotor loading.
v = 0 v = Vc v = V - 2vd i
v = V - vd i
v = vi v = V + vc i
v = V + 2vc i v = Vd v = 2vi
(a) Hover (b) Climb (c) Descent
Figure 1.3: Momentum theory flow model for axial flight (Ref. [3]) CHAPTER 1. INTRODUCTION 9
Miller proposed a three dimensional rotating rotor wake theory [4]. The theory rep- resents the wake as a cylindrical shell of shed vorticity. Johnson discusses some of the implications of Miller’s results [4]. While the Miller’s theory represents a three dimensional rotor wake, it can not predict unsteady rotor performance with forward motion.
Numerous people suggested improvements to the Miller’s method based on harmonic theory. Pitt and Peters showed a model based on coupled inflow and harmonic blade theories
[14, 15]. The Pitt-Peters model stands out as a premier dynamic inflow model within the conceptual framework of a global approximation (Figure 1.4). It has been verified on the basis of flap response data. It can be easily adapted in nonlinear version for use in time history solutions.
In the most recent work, Peters and He have extended the modeling to an unsteady three- dimensional finite-state wake [16, 17, 18], that holds the traditional theories of Theodorsen and Loewy. The Peters-He finite-state dynamic inflow theory, also called the generalized dynamic wake theory, is characterized as representation of induced inflow as dynamic degrees of freedom in a system of first order differential equations in the time domain. Due to
INDUCED Inflow FLOW THEORY
+ + Angle of Attack LIFTING Circulation and Loads THEORY +
Blade Motions BLADE DYNAMICS
BODY DYNAMICS
Figure 1.4: Block diagram of coupled rotor and induced flow dynamics (Ref. [14]) CHAPTER 1. INTRODUCTION 10 its dynamic nature and computational efficiency, the Peters-He model is finding a wide application in flight dynamics and aeroelasticity analyses of helicopter. Especially, it has been implemented in major flight simulation programs currently used in helicopter industry, such as GENHEL, FLIGHTLAB, etc. In addition, this finite-state inflow model has been updated using parameter estimation technique by Kr¨amer and Gimonet [19]. The finite- state wake model was validated using measured flight test data for BO105 helicopter by
Hamers and Basset [20].
Operating helicopters close to a ship deck introduces a range of special characteristics in the flight dynamics behavior since the downwash field is strongly altered in order to meet the non-penetration boundary condition at the solid surface. The most significant is the effect on the induced velocity at the rotor and hence, the rotor thrust, hub moments and power required. In general, a helicopter rotor within proximity to ship deck can be subject to various kinds of ground effect, such as inclined ground effect, partial ground effect, and dynamic ground effect. These ground effects have been examined using both empirical methods and analytical method of mirror-image rotors [4].
Recently, Zhang, Prasad and Peters used an image method to develop a finite-state dynamic inflow model for the in-ground-effect of inclined surface [21, 22]. A simple ground effect model for implementation in real time simulations as was extracted from the analysis of the aerodynamic interaction results obtained from a computationally intensive method using spline curve fitting method [23]. Xin and Prasad developed the dynamic ground effect model [24]. The partial ground effect was been examined using finite-state dynamic inflow model by Xin [25]. Xin, He and Lee introduced the panel ship deck model for partial ground effect [26]. CHAPTER 1. INTRODUCTION 11
1.1.3 Ship Airwake Model
The simulation of the helicopter in itself is a challenge. The response of helicopter to tur- bulence in particular is more complex. Helicopters always operate in the lowest part of the atmosphere, where the turbulence length scale is relatively small, and due to the fact that the lifting surface moves through the local atmosphere, the effects of the disturbances are critical. Because of this, the modeling of the ship airwake and its effect on helicopter be- havior is considered one of the most significant technical challenges. General characteristics of ship airwake flow field are unsteadiness, vorticity, large regions of separated flow, and low Mach number.
For many years, numerous studies have been focused on investigation of the ship airwake.
In general, there are three ways to investigate the ship airwake, numerical simulation, model-scale testing, and full-scale testing. Since all the relevant aerodynamic qualities of the atmosphere and geometric qualities of the ship are measured, full-scale testing is most accurate approach. However, this approach is limited by cost and environmental testing condition. Model-scale testing is more affordable and offers a controlled testing environment, but both accurate simulation of the atmosphere and geometric characteristics of the ship are difficult due to environmental and scale errors. A brief history of those experimental testing is presented in References [27, 28, 29].
In past years, many researchers have studied numerous methods for the ship airwake
CFD modeling with different classes of ships. Tai and Carico calculated the ship airwake about a simplified DD class ship using a thin-layer Navier-Stokes method [30]. The airwake around an LHD class ship was also calculated with the same Navier-Stokes method by Tai CHAPTER 1. INTRODUCTION 12
[31]. Modi et al calculated the airwake around the general ship shape using the parallel
unstructured flow solver PUMA [32]. To describe the unsteady flow field around the ship,
turbulent velocity model has been developed and combined with steady CFD solutions
[27, 33, 34, 35]. Modeling of the turbulent airwake velocity component is achieved by
passing independent white noise processes through spectral filters whose transfer functions
yield the desired forms of power spectral density of experimental data. While this approach
provides good approximation for the characteristics of unsteady airwake, it is still involving
the experimental test.
Latest advances in the field of CFD make it possible to simulate the full scale flow
field with unsteady turbulence around the ship. Recently, time-accurate computational
CFD were performed at the Naval Air Warfare Center/Aircraft Division to characterize the
unsteady nature of the airwake produced by a LHA class ship [36, 37]. In these works,
the parallel unstructured flow solver COBALT was used to calculate the full-scale flow
field with different numerical methods. It was shown that the full-scale solutions could
predict the dominant frequencies in the unsteady flow field. The airwake around the same
LHA class ship was calculated using the PUMA2 [38, 39]. It was integrated with a finite
volume formulation of the Euler/Navier-Stokes equations for 3D, internal and external,
non-reacting, compressible, steady/unsteady solutions for complex geometries.
However, these CFD simulations produced a large amount of data. For example, with
three velocity components, 40 seconds of data sampled every 0.1 second, for 55890 points
in the region around the ship, the total number of values stored for a single relative wind
condition was 67,068,000 [39]. Thus, data storage requirements are extensive, making real-
time implementation somewhat difficult. A number of recent studies have shown that CHAPTER 1. INTRODUCTION 13 an equivalent disturbance model (e.g. stochastic gust model) can be used to investigate the helicopter gust response [33, 34, 40]. These studies paid attention to understanding the aircraft responses with turbulence models more representative of helicopter operating environments (e.g. nap-of-the-earth and helicopter/ship DI testing). In fact, pilot comments indicated that there was no significant difference between the complex CFD models and the simple stochastic models, thus the stochastic gust model is good enough to provide a reasonably accurate aircraft gust response [34]. The implication of this observation is that simple airwake representation can be used for real-time application. Furthermore, a simplified model that incorporates the statistical characteristics of the turbulent airwake may provide some insight to the effects of the airwake and assist in the design of future
flight control systems.
1.1.4 Flight Control Model
A brief history of helicopter control systems is presented in Reference[41]. The control problem of helicopters is a challenging task because the helicopter dynamics are highly nonlinear, inherently unstable, fully coupled, and subject to parametric uncertainties. The control of a helicopter is a truly multivariable problem in which one usually considers four inputs and four outputs with significant interaxis coupling. True multivariable analysis and design for helicopter control system can possibly provide improved performance in the on-axis loops while offering good decoupling behavior. Moreover, the use of modern multi- variable control analysis tools allows a more rigorous analysis and, consequently, improves stability robustness of the closed-loop system.
In past decade, numerous efforts have been focused on multivariable design of helicopter CHAPTER 1. INTRODUCTION 14
flight control systems for robustness. Manness et al used the eigenstructure assignment method to meet response-type and dynamic response requirement described by the handling quality criteria [42].
Rotor-state feedback technique was investigated by Takahashi [9]. It was focused on high-gain feedback in roll and pitch axes of helicopter in hovering condition. It was shown that roll and pitch dynamics have second-order behavior. Hess applied quantitative feedback theory (QFT) to the design of the longitudinal flight control system for a linear model of the BO-105C helicopter [43]. This work points out the fact that the inclusion of rotor and actuator dynamics, while obviously essential to a practical design, does not alter the basic design procedure of QFT.
Bogdanov et al introduced the model predictive neural control design [44]. In this work, model predictive control was integrated with neural network feedback controller in combi- nation of linear quadratic controller. Recently, autonomous adaptive flight control systems have been developed for an unmanned helicopter by Hovakimyan et al[45], Corban[46],
Johnson[47], and Krupadanam[48]. These approaches show that adaptive controller can provide a stable, robust, and significant improvement in performance over other control designs.
Helicopter Reference Controller Dynamic Model
Estimator
Figure 1.5: Schematic of helicopter control system CHAPTER 1. INTRODUCTION 15
The inverse simulation problem has been discussed for a possible solution to determine the control inputs which enable to complete some specified maneuver [49, 50, 51]. The integration based inverse simulation method in Reference [50] involves a numerical differ- entiation of the output vector with respect to the input vector for calculating the Jacobian matrix. Since this approach requires Newton iterations at each time step, the computational expense increases exponentially when the helicopter model becomes more complex.
Avanzini et al proposed two-timescale inverse simulation technique [51]. In this work, the timescale was divided into slow timescale (collective) and fast timescale (cyclic and pedal). While this approach significantly reduces computational time, it is not appropriate for long time duration due to accumulation of error. Alternatively, Xin et al [49] developed the combined technique for inverse simulation by modifying and combining the integration and differentiation based inverse simulation methods in such a way that the numerical dif- ferentiation and Newton iterations were only performed at selected points instead of at each time step. In addition, inverse simulation method was integrated with on-line compensator to eliminate steady-state error. But inverse simulation can be still time consuming and difficult to implement computationally.
Another issue on helicopter flight controller design is modeling of the human pilot. The development of a pilot model as a dynamic control element that can replace the pilot-in-the- loop simulations for workload investigations and handling qualities offers various important advantages, such as cost and test time. Moreover, any analysis can be done without the ambiguities and variations in piloted simulation or flight tests.
Early research on the human pilot model was devoted to understanding the characteris- tics of the human as a controller of single input, single output linear time-invariant systems. CHAPTER 1. INTRODUCTION 16
McRuer et al used a set of quasi-linear models that are adept at predicting human behavior.
The quasi-linear model, so-called crossover model, is very useful for analyzing closed-loop
compensatory tracking or state regulation tasks in which human operator attempts to min-
imize some displayed system error [52]. Alternatively, Bradley and Turner have developed
a general pilot model called SyCos (Synthesis through Constrained Simulation) for Lynx
MK3 helicopter [53, 54]. SyCos model includes the liner time-invariant inverse model and
crossover model. The inverse model represents the pilot’s adaptation to the helicopter’s
dynamics. In the crossover model, the pilot adjusts his behavior to compensate for the
perceived dynamics of the system being controlled. Heffley et al [55] and Lee et al [56]
have developed a pilot model using classical control techniques. These studies shows that
the pilot control inputs can be determined using forward simulation in conjunction with a
feedback controller for a given desired trajectories.
1.2 Simulation of Helicopter/Ship Dynamic Interface
Computer simulation of the dynamic interface provides an alternative to the current heli-
copter/ship system development and testing scenario, predictions of system performance.
Flight envelopes can be also estimated through simulation. All environmental conditions
can be specified, including sea state, and winds. In urgent operational scenarios, an enve-
lope estimated through simulation provides good approximation to support operating ships
and aircraft in previously untested conditions or combinations.
Over the past years, there is a wide range of activities associated with simulation of
helicopter/ship dynamic interface problem. Mello et al provided a brief insight into the CHAPTER 1. INTRODUCTION 17 relevant helicopter/ship aerodynamic interaction phenomena such as ship ground effect, airwake effect on trimmed control positions [57]. Bradely and Turner have investigated the pilot control activity with SyCos pilot model [53], [54]. ART (Advanced Rotorcraft Tech- nology Inc.) has developed a simulation tool for helicopter/ship dynamic interface testing
[28], [49]. The trajectory generation tool was developed for ship deck landing operations of a VTOL by Avanzini et al [51]. Benefits of a pilot assisted landing system was demonstrated by Perrins and Howitt [58]. Colwell provided the effects of flight deck motion in high seas on the hovering helicopter with Fourier and correlation analysis [59]. Lee et al have developed a simulation program for helicopter/ship dynamic interface testing [38], [39].
The Joint Shipboard Helicopter Integration Process (JSHIP) has been applied to in- crease the interoperability of joint shipboard helicopter operations for helicopters that are not specifically designed to go aboard Navy ships [2], [60], [61]. As a part of JSHIP, the
Dynamic Interface Modeling and Simulation System (DIMSS) was established to define and evaluate a process for developing WOD flight envelopes. Using the DIMSS, the fidelity stan- dards for the shipboard launch and recovery tasks have been discussed for combination of an
LHA class ship and the UH-60. The goal of this simulation tool is to prove the process for determining wind-over-deck launch and recovery envelopes using piloted flight simulation.
In order to validate the fidelity of this simulated dynamic interface, experimental trials have been conducted.
Although numerous studies have focused on simulation of dynamic interface testing, much additional work is required to provide a high fidelity simulation program. CHAPTER 1. INTRODUCTION 18
1.3 Problem Statement and Research Objectives
Considerable work has done on the helicopter/ship dynamic interface simulation tool devel- opment during past decades. However, there is relatively little work to provide an accurate pilot workload analysis tool without pilot-in-the-loop testing for the shipboard operations.
Moreover, little work has been focused on how to optimize the pilot model for the helicopter shipboard tasks. For example, the inverse simulation method is widely used to estimate the pilot control activity. Although a number of schemes have been examined to improve the inverse simulation method by combining with crossover model or on-line compensation, these pilot control inputs achieved in inverse simulation methods are far from the required control authority predicted for an accurate pilot workload analysis. Thus, the human pi- lot model remains a critical limit in practical implementation of helicopter/ship dynamic interface simulation tool for a pilot workload analysis.
Therefore, the primary objective of the present research is to develop an advanced helicopter/ship dynamic interface simulation tool that can help both to understand the potential of helicopter simulation, and to investigate the pilot workload issues in the dynamic interface. In addition, an automatic control system is developed to reduce the high pilot workloads that typically result in the flight safety limitations associated with shipboard operations.
In this new study, through utilizing the optimal control model as a human pilot model, a tunable human pilot model is designed to observe the relative behavior for different levels of tracking precision and is designed to operate over a range of airspeeds using a simple gain scheduling algorithm. This pilot model is then used to calculate the required control inputs CHAPTER 1. INTRODUCTION 19 for the specified trajectories for shipboard operations in two different WOD conditions.
Then the simulation model is validated with JSHIP flight test data.
Once the feasibility and potential of this helicopter/ship dynamic interface simulation model is established, a stability augmentation system is optimized for a UH-60 helicopter operating in a turbulent ship airwake. To do this, a new airwake model is derived from the simulation with the full CFD airwake by extracting an equivalent six-dimensional gust vector. The spectral properties of the gust components are then analyzed, and shaping
filters are designed to simulate the gusts when driven by white noise.
For disturbance rejection, a new performance specification is designed based on the power spectrum density of the transfer function between the gust inputs and aircraft rate responses. The baseline limited authority SAS is modified and optimized using CONDUIT in order to improve handling-qualities and stability, and to minimize a weighted objective of gust responses. In addition, a H∞ controller is designed to provide an alternative SAS
configuration. The optimized SAS and H∞ SAS are then tested using the non-linear simu-
lation model with time-varying airwake. A series of comparisons are also made to provide
a sound validation of the new SAS models. Chapter 2
Helicopter Flight Dynamics Model
A helicopter/ship dynamic interface simulation model of a UH-60A operating off an LHA class ship is developed. The helicopter flight dynamics model is based on the GENHEL simulation model. The simulation model is then converted to MATLAB/SIMULINK based simulation model to facilitate model improvement and controller design. A higher order
Peters-He inflow model is employed for the main rotor inflow. The gust penetration model is used to model the effects of a ship airwake on the helicopter flight dynamics.
2.1 Overview of the GENHEL Simulation Model
The GENHEL was originally developed by Sikorsky Aircraft and documented under con- tract from NASA. This model is a total systems definition of the Black Hawk helicopter and provides handling qualities analysis tool for the Black Hawk helicopter which can even- tually be extended to a real time pilot-in-the-loop simulation. The mathematical model is generalized analytical representation of a total helicopter system. It normally operates in
20 CHAPTER 2. HELICOPTER FLIGHT DYNAMICS MODEL 21 the time domain and allows the simulation of any steady or maneuvering flight condition which can be experienced by a pilot [11]. The overall block diagram of the GENHEL is presented on Figure 2.1.
The basic model is a total force, nonlinear, large angle representation in six rigid body degrees of freedom. In addition, main rotor rigid blade flapping, lagging and hub rotational
DOF are represented. The hub rotational degree of freedom is coupled to the engine and fuel control. Motion in the lag degree of freedom is resisted by a nonlinear lag damper model.
The main rotor model is developed using a blade element approach with five equal- annuli segments on each of the four blades. In the air mass degree of freedom, a uniform
Main Rotor Positions, Main Rotor Velocities, Attitudes, … EngineEngine
FuselageFuselage + Equations of Servo Model + + Equations of Servo Model MotionMotion HorizontalHorizontal Tail Tail
Control System Control System VerticalVertical Tail Tail
Tail RotorTail Rotor PilotPilot
Sensor ModelSensor Model AFCS ModelAFCS Model DisplayDisplay System ModelSystem Model
Figure 2.1: Block diagram of GENHEL flight simulation model (Ref. [11]) CHAPTER 2. HELICOPTER FLIGHT DYNAMICS MODEL 22 downwash is derived from momentum considerations, passed through a first order lag, and then distributed first harmonically as a function of rotor wake skew angle and the aerody- namic hub moment. The lift and drag forces of each blade are loaded from wind tunnel data which is a function of Mach number and angle of attack.
The fuselage is represented by six components of aerodynamic characteristic which are defined from wind tunnel data. The angle of attack at the fuselage is calculated using the free stream and interference effects of the main rotor. These interference are based on rotor loading and rotor wake skew angle.
The aerodynamics of the empennage are treated separately from the forward airframe.
This separate formulation allows good definition of non-linear tail characteristics. The angles of attack at the empennage are developed from the free stream velocity, plus rotor wash. Additional dynamic pressure effects from fuselage is accounted for by factoring the free stream velocity component.
The tail rotor is represented by the linearized closed form Bailey theory solutions. Terms in tip speed ratio greater than square of advance ratio have been eliminated. An empirical blockage factor, due to the proximity of the vertical tail, is applied to the thrust output.
The flight control system consists of the primary mechanical flight control system and the Automatic Flight Control System (AFCS) which includes the Stability Augmentation
System (SAS), the Pitch Bias Actuator (PBA), the Flight Path Stabilization (FPS) and the Stabilator mechanization. The flight control model represents the control system in a complete manner except for the FPS. In this case, only the attitude hold and turn features have been defined. The detailed definitions of each component are given in Ref. [11]. CHAPTER 2. HELICOPTER FLIGHT DYNAMICS MODEL 23
2.2 MATLAB Implementation
MATLAB based simulation model is implemented to facilitate model improvement and control law development (Figure 2.2). The new simulation model includes main rotor, fuse- lage, empennage, tail rotor and other subsystems (primary flight control system, stability augmentation system, sensors, etc.). The simulation model provides the simulation of any steady or maneuvering flight condition. In addition, numerically linearized dynamic model can be obtained for controller design.
So far, the simulation model presented in Figure 2.2 has been updated to include Peters-
He inflow model, gust penetration, and pilot model. Details are presented in Section 2.3,
Section 2.4, Chapter 3.
Figure 2.2: Overall structure of MATLAB based simulation program CHAPTER 2. HELICOPTER FLIGHT DYNAMICS MODEL 24
2.3 Peters-He Inflow Model
2.3.1 Background
Dynamic inflow modeling in helicopter flight dynamics is a means of accounting for the low frequency wake effects under unsteady or transient conditions. It has been known for years that the induced flow field associated with a lifting rotor responds in a dynamic fashion to changes in either blade pitch or rotor flapping angles. In recent years, it has been found that dynamic inflow for steady response in hover can be treated by an equivalent Lock number [15]. For more general conditions, such as transient conditions or a rotor in forward
flight conditions, it has been determined that the induced flow can be treated by additional degrees of freedom of the system.
The most popular model of dynamic inflow is that of Pitt and Peters [14]. The theory of Pitt-Peters dynamic inflow model relates the airloads of a rotor (CT , CL, and CM ) to
the induced flow distributions (λ0, λs, and λc) where CT , CL, and CM are the aerodynamic
perturbation in thrust, roll moment, and pitch moment; and λ0, λs, and λc are the magni-
tude of uniform, lateral and longitudinal variations in induced flow. The induced inflow is
assumed to have the following variations in the wind-axis coordinates.
r r λ(r, ψ)= λ + λ sin ψ + λ cos ψ (2.1) 0 s R c R
where r is blade radial coordinate and R is rotor radius. The time histories of λ0, λs, and CHAPTER 2. HELICOPTER FLIGHT DYNAMICS MODEL 25
λc are governed by the following first-order differential equation.
λ˙ 0 λ0 CT −1 [M] λ˙ +[L] λ = C (2.2) s s L λ˙ λ C c c M aero where [M] is the matrix of the apparent mass terms (a time delay effect due to the unsteady
wake), [L] is the nonlinear version of the inflow gains matrix. It should be noted that the
subscript “aero” implies that only aerodynamic contributions are considered in CT , CL, and
CM (i.e. inertial terms are omitted).
Peters-He inflow model, also called the generalized dynamic wake model, is characterized
as representation of induced inflow as dynamic degrees of freedom in a system of first order
differential equations in the time domain. The “Pitt-Peters” inflow model can be thought
of as a special case of this theory but with only 3 inflow expansion terms (uniform, lateral,
and longitudinal). Based on an unsteady wake model, Peters-He inflow model represents
essentially the unsteady wake-induced flow through the rotor disk excited by aerodynamic
loads in a global fashion.
2.3.2 Basic Equations of Peters-He Inflow Model
In the generalized dynamic wake model [18], the induced flow distribution can be represented
in terms of a harmonic variations in azimuth and arbitrary radial distribution functions.
∞ ∞ r r r w (¯r,ψ, t¯)= φj (¯r) αj (t¯) cos(rψ)+ βj (t¯) sin(rψ) (2.3) rX=0 j=r+1X,r+3,··· h i CHAPTER 2. HELICOPTER FLIGHT DYNAMICS MODEL 26 wherer ¯ and t¯ are nondimensional blade radial coordinate (¯r = r/R) and nondimensional
¯ r time (t = Ωt), respectively. The radial expansion function φj (¯r) has the following form,
j−1 ( 1)(q−r)/2(j + q)!! φr(¯r)= (2j + 1)Hr r¯q − (2.4) j j (q r)!!(q + r)!!(j q 1)!! q q=r,rX+2,··· − − −
where
(j + r 1)!!(j r 1)!! Hr = − − − , (n)!! = (n)(n 2) (2) or (1) (2.5) j (j + r)!!(j r)!! − ··· −
Equation (2.3) gives a harmonic content of induced inflow that can be truncated at any harmonic of interest; at the same time, it provides a complete description of the radial variation of induced inflow at rotor disk. With pressure and induced velocity represented
r r by the above expansion, pressure coefficients τ’s and the inflow coefficients αj and βj can
be related in the following matrix form
∗ 1 [M m] αr + V [Lc]−1 αr = τ mc (2.6) n j j 2 { n } n o n o ∗ 1 [M m] βr + V [Ls]−1 βr = τ ms (2.7) n j j 2 { n } n o n o
m where [Mn ] is called the apparent mass matrix and is given by
2 M m = Hm (2.8) n π n CHAPTER 2. HELICOPTER FLIGHT DYNAMICS MODEL 27 and where [Lc] and [Ls] are the induced inflow influence coefficient matrices and depend on the wake skew angle χ (χ = 0◦ in axial flow through χ = 90◦ in pure-edgewise flow).
c 0m m 0m Ljn = X Γjn (2.9) h i h i c Lrm = X|m−r| + ( 1)lX|m+r| Γrm (2.10) jn − jn h i h i s Lrm = X|m−r| ( 1)lX|m+r| Γrm (2.11) jn − − jn h i h i
where l = min(r, m), and X = tan χ/2 . Note that 0 X 1. All sine and cosine elements | | ≤ ≤ rm on the same coefficients Γjn that can be found in closed-form as follows.
(n+j−2r)/2 rm ( 1) 2 (2n + 1)(2j + 1) Γjn = − for r + m even (2.12) m r (j + n)(j + n + 2) [(j n)2 1] Hn Hj p − − q rm π sgn(r m) Γjn = − for r + m odd, j = n 1 (2.13) m r (2n + 1)(2j + 1) ± 2 Hn Hj Γrm = 0q p for r + m odd, j = n 1 (2.14) jn 6 ±
[L] matrix is partitioned such that the superscripts are row-column indices of the r, m partition, and the subscripts j, n are the row-column indices of the elements within each partition. It should be noted that these indices do not take the traditional matrix values of 1, 2, 3, . Instead, for the cosine equation, m = 0, 1, 2, 3, ; for sine equation, ··· ··· m = 1, 2, 3, ; and for either set, n = m + 1, m + 3, m + 5, (r and j follow the same ··· ··· convention).
In Equations (2,6) and (2.7), V is the mass flow parameter to account for energy added CHAPTER 2. HELICOPTER FLIGHT DYNAMICS MODEL 28 to the flow from the rotor
µ2 + (λ + λ )λ V = m (2.15) µ2 + λ2 p λ = λm + λf (2.16)
where V comes from momentum considerations, µ, λf are the nondimensional inplane and
normal components of V∞, and λm is the momentum theory value of steady induced flow
for a trimmed rotor. According to the approach followed for the low frequency dynamic
inflow model in Reference [17], a completely nonlinear version of Equations (2.6) and (2.7)
can be obtained by
2 2 c −1 1. taking V as VT = µ + λm corresponding to the first column (r = 0) of [L ] , but p as V for r = 0. 6
2. treating all quantities as total induced flow rather than perturbation.
0 3. replacing the static λm by the unsteady value, √3α1.
mc ms In order for the model to be coupled with blade lift theory, the τn and τn need to be
mc ms appropriately related to the blade lift. The pressure harmonic coefficients τn and τn can
then be given by
Q 1 0c 1 Lq 0 τn = 2 3 φn(¯r)dr¯ (2.17) 2π 0 ρΩ R qX=1 Z Q 1 mc 1 Lq m τn = 2 3 φn (¯r)dr¯ cos (mψq) (2.18) π 0 ρΩ R qX=1 Z Q 1 ms 1 Lq m τn = 2 3 φn (¯r)dr¯ sin (mψq) (2.19) π 0 ρΩ R qX=1 Z CHAPTER 2. HELICOPTER FLIGHT DYNAMICS MODEL 29 where Lq is blade sectional lift that can be evaluated from a lift theory and Q is number of
blades.
Thus, Equations (2.3) to (2.19) comprise a complete, three-dimensional unsteady wake
r r model written in terms of a finite number of states αj and βj . The fundamental idea of
this theory and some initial validations have been included in References [16] [18]. In ∼ this study, a 15 state Peters-He is used. Figure 2.3 shows the difference between Pitt-Peters
inflow model and Peters-He inflow model. It can be observed that Pitt-Peters inflow model
only estimates the average inflow distribution over the rotor disk.
Induced inflow ratio Induced inflow ratio
Advancing Advancing side Trailing side Trailing Y edge Y edge X X Retreating Leading Retreating Leading side edge side edge (a) Pitt-Peters 3 state inflow model (b) Peters-He 15 state inflow model
Figure 2.3: Comparisons of inflow ratio
2.4 Gust Penetration Model
The gust penetration model is used to model the effects of a three-dimensional ship airwake on the helicopter flight dynamics. There is a fundamental assumption that the velocity field of the airwake affects the aerodynamic forces on the helicopter, but the helicopter does not affect the ship airwake. CHAPTER 2. HELICOPTER FLIGHT DYNAMICS MODEL 30
The ship airwake velocity field can be found from output of CFD programs. For instance, the CFD solver called PUMA2 (Parallel Unstructured Maritime Aerodynamics)provides time-varying ship airwake solutions around an LHA class ship [39]. It uses a finite volume formulation of the Euler/Navier-Stokes equations for 3-dimensional, internal and external, non-reacting, compressible, steady/unsteady solutions for complex geometries (Figure 2.4).
PUMA2 can be run so as to preserve time accuracy or as a pseudo-unsteady formulation to enhance convergence to steady-state. It is written in ANSI C using the MPI library for message passing so it can be run on parallel computers and clusters. It is also compatible with C++ compilers and coupled with the computational steering system POSSE. It uses dynamic memory allocation, thus the problem size is limited only by the amount of memory available on the machine. Large eddy simulations can also be performed with PUMA2 [39].
The flow case represents both 0 and 30 degrees yaw angles and 30 knot of relative wind speed. A 4-stage Runge-Kutta explicit time integration algorithm with Roe’s flux difference scheme is used with CFL numbers of 2.5 and 0.8 for the steady and unsteady computations, respectively. A zero-normal-velocity boundary condition is applied on the ship surface and water surface (bottom surface of the domain) and a Riemann boundary condition is applied at all other faces of the domain. The pseudo steady-state computations are performed using local time-stepping and initialized with freestream values. The time-accurate computations are started from the pseudo steady-state solution, and the simulation time step (480 sec) is determined by the smallest cell size in the volume grid. The computations are performed on a parallel PC cluster Lion-XL consisting of 256 2.4 Ghz P4 processors with 4 GB ECC
RAM and Quadrics high-speed interconnect [39]. Iso-surfaces of vorticity magnitude of 0.8 sec−1 for both 0 and 30 degree WOD cases are shown in Figure 2.4. CHAPTER 2. HELICOPTER FLIGHT DYNAMICS MODEL 31
The 40 seconds of the time history data is stored for every 0.1 seconds to be used for the
DI simulations. Each flow solution file is 41 Mbytes in size, whereas a DI velocity data file is only 5.2 Mbytes. In this study, the discussion will be limited to how to use the outputs of the CFD program.
a) 0 degree WOD case b) 30 degree WOD case
Figure 2.4: Vorticity magnitude iso-surface at t = 40 sec (Ref. [39])
The ship airwake velocity field from Reference [39] has (81 30 23) rectangular grid × × points with 5ft equal intervals for the part of the ship where the helicopter is expected to fly.
In this study, a 3-dimensional look-up algorithm (including linear interpolation algorithm) is implemented to calculate the local velocity disturbances at each aerodynamic center of rotor blade elements, fuselage, empennage and tail rotor. The overall gust penetration model is presented on Figure 2.5.
The ship airwake velocity field provided by the CFD database is defined with respect to a ship-fixed coordinate system. Thus, the velocity field must be transformed to inertial axes, and then to the specific axis system used for each of the helicopter component models. For the fuselage, empennage, and tail rotor, the following coordinate transformation is required. CHAPTER 2. HELICOPTER FLIGHT DYNAMICS MODEL 32
Time-Accurate Ship Airwake Account for Local Velocities Velocities from CFD at Blade Elements, Fuselage, Empennage, Tail Rotor
Linear look-up algorithm
r Coordinate transformationr wake T target wake Vtarget = []ship Vship
3-D uniform grid
Figure 2.5: Gust penetration model
~ i s ~ Vbody =[T ]b[T ]i Vship (2.20)
where V~ship is the ship wake velocity vector in ship coordinate system, V~body is the ship
s i wake velocity vector in body coordinate system, and [T ]i , [T ]b are the coordinate transfor-
mation matrices from ship coordinate system to inertial coordinate system and from inertial
coordinate system to helicopter body coordinate system, respectively.
For each main rotor blade element, the airwake velocity in blade coordinate system is
obtained by
~ h b i s ~ Vrotor =[T ]b [T ]h[T ]b[T ]i Vship (2.21)
~ b h where Vrotor is the ship airwake velocity vector in each blade coordinate system, [T ]h, [T ]b
are the coordinate transformation matrices from helicopter body to hub coordinate system CHAPTER 2. HELICOPTER FLIGHT DYNAMICS MODEL 33 and from hub to each blade coordinate system, respectively.
Since only finite time-varying solutions of ship airwake can be processed and stored in computers, a simulation of shipboard operation may exceed the range of the data duration.
To overcome this limitation, the solutions are overlapped with sinusoidal filter for first and last 5 seconds once the simulation time exceeds the airwake data duration (Figure 2.6). The approach of the overlapped time history variation prevents any sudden jump in the airwake velocities at the time when the simulation lasts longer than data duration. If time step of airwake solution is different from that of simulation program, a simple linear interpolation can be applied to calculate the airwake velocity field at every simulation time step.
Figure 2.6: The approach of the overlapped time history of airwake Chapter 3
Pilot Modeling
Since the introduction of modern manual control research of dynamic systems during the
1940’s, the control theory which has evolved in the intervening years has been useful in quantifying control-related human behavior [62]. The so-called “crossover model” employs classical control methods to model human feedback control of single input, single output
(SISO) systems [52]. The method is based on the expected crossover frequency of the open loop transfer function of the human and controlled process. In fact, Bradley and Turner applied the crossover model, coupled with inversion control methods, specifically to model pilot workload for helicopter shipboard operations [53]. The main drawback of the crossover model is that the helicopter piloting task is inherently multi input, multi output (MIMO) system.
To analyze more complex manual control systems, most efforts have been concentrated on the problem of developing linear models for the human controller model in MIMO sit- uations. As regards this problem, two basic approaches have been emerging. The first ap- proach is to extend the classical crossover model developed for SISO system to the MIMO
34 CHAPTER 3. PILOT MODELING 35 system [63]. Their approach is based on classical multi-loop control theory and depends highly on judgments concerning the closed-loop system structure.
The second approach is based on modern MIMO control theory. It is capable of treating multivariable systems within a single conceptual framework using state-space forms which are more naturally suited to the analysis of complex man-machine systems, particularly since the design algorithms are readily automated using modern software such as MATLAB.
3.1 Optimal Control Model of the Human Pilot
The optimal control model (OCM) of the human pilot is applied for MIMO systems by solving the Linear Quadratic Gaussian (LQG) problem. The pilot control inputs are based on a compensatory tracking model of the human pilot. An optimal control model is used to allow realistic computer simulations of the shipboard operations. References [62] and [63] provide information on the model and introduce its application in linear or nonlinear flight dynamic models. Figure 3.1 shows a schematic of the optimal control model used in this study.
Optimal Control Model
OptimalOptimal Desired yd Deadband Kalman Desired + Deadband Time Delay Kalman Feedback - (collective only) Time Delay Feedback TrajectoryTrajectory (collective only) EstimatorEstimator y GainsGains
UH-60 FlightUH-60 Flight Neuromotor Dynamics + u Hysteresis Dynamic Hysteresis 1 Dynamic + (collective only) Model (collective only) Model t n s +1
Disturbance
Figure 3.1: Optimal control model of the human pilot CHAPTER 3. PILOT MODELING 36
In this study, the human pilot’s basic task is to control the helicopter to follow a specified shipboard trajectory. To design the human control model, the helicopter is represented with linearized equations of motion in state-space form:
x˙ (t) = Ax(t)+ Bu(t)+ w(t) (3.1)
y(t) = Cx(t)+ v(t) (3.2)
where x(t) is the state vector, u(t) is the pilot’s control input vector, w(t) is a vector of external disturbances, y(t) is the output vector (parameters perceived by the pilot), and v(t) represents observation noise.
The linearized system model used in this study is obtained through numerical lineariza- tion of the simulation model. The resultant linear model is a 24 state model, which includes
9 rigid body states and 15 states associated with rotor dynamics and inflow. For this study, the model is linearized at every 10 knots (e.g. hover, 10 knot, 20 knot, ... , 140 knot).
Assuming quasi-static rotor and inflow dynamics, the linear model is reduced to a 9 state
/ 6 DOF model of the rigid body motion. The linear model is decoupled into a 3 state longitudinal model, a 5 state lateral-directional model, and a 1 state vertical motion model.
Finally, the linear models must be augmented to include shaping filters for the gust dis- turbances and a dynamic model of the SAS for each axis. Integrators are added so that position and integrated position can be included in the performance index. A schematic of the augmented flight dynamics model used for longitudinal control is shown in Figure 3.2.
A similar model is used for lateral-directional control, which includes pilot inputs in both the lateral and directional axes. CHAPTER 3. PILOT MODELING 37
ò x Gust disturbance ò Linearized model (24 state) K x turb Longitudinal dynamics ò s +wturb u& X X - g cosq u Reduced model é ù é u q 0 ùé ù u êq&ú = êM M 0 úêqú + ê ú ê u q úê ú (9 state) + & q ëêq ûú ëê 0 1 0 ûúëêq ûú Pilot - é X ù Decoupled dlong q input + êM úd ê dlong ú long model ëê 0 ûú Include Pitch SAS shaping filter for the gust, 2.6 s(s + )1 SAS dynamics (s + 5.0 )(s + .0 143)
Figure 3.2: Augmented plant model in longitudinal axis
The OCM of the human pilot in Figure 3.1 is represented as an optimal linear regulator in combination with an optimal state estimator (Kalman estimator). Both the estimator and feedback gain matrix are determined by solving the LQG control problem. Assuming the linear dynamics of Equations (3.1), (3,2) and the disturbance are white noise signals, the objective is to find a dynamic compensator that minimizes the quadratic performance index given by
1 T J = E lim xT (t)Qx(t)+ u˙ (t)Ru˙ (t) dt (3.3) (T →∞ T 0 ) Z h i where Q and R are the state and control weighting matrices. The estimator and feedback
gains are readily solved from a pair of matrix Riccati equations [64]. Note that when
modeling human operators it is customary to use control rates instead of the control position
in the performance index. A simple augmentation of the plant dynamics model is used to
achieve this [62]. Details of the complete optimal control model of the human operator are
discussed in References [62] and [63]. CHAPTER 3. PILOT MODELING 38
The optimal control model is essentially specified by (1) the weighting matrices Q and
R in Equation (3.3) , (2) the covariances of the observation and external noises, and (3) the magnitude of the operation time delay. These parameters can be selected to yield optimal control model transfer functions. The effect of those parameter variations on the resulting model is not as clear as in the case of the crossover model of the human operator. This is due to the fact that the optimal control model parameters are essentially inputs to an optimization scheme that involves the solution of sets of nonlinear algebraic equations [63].
However, Reference [63] outlines an approximate method for selecting these parameters to achieve a desired crossover frequency for each control axis.
Typically, both the Q and R matrices are assumed to be diagonal. The weighting parameters in the Q matrix are selected such that each state variable is scaled by its
maximum expected deviation [63]. This leaves the task of selecting the control weighting
parameters in R. In this study, the objective is to develop a pilot model that can be
easily tuned to adjust the tracking tolerance in each control axis, where a high crossover
frequency corresponds to “tight” tracking and a low crossover frequency corresponds to
“relaxed” tracking.
Consider the longitudinal axis where the transfer function from longitudinal control
input to pitch attitude can be expressed as
θ K sm + a sm−1 + a sm−2 + + a s + a (s)= m−1 m−2 ··· 1 0 (3.4) δ (sn + b sn−1 + b sn−2 + + b s + b ) long n−1 n−2 ··· 1 0
An approximate but very useful relationship exists between the weighting coefficients, the CHAPTER 3. PILOT MODELING 39 controlled-element dynamics, and the closed-loop system bandwidth [62], [63].
1/(n−m+1) ω K(q /r ) (3.5) BW ≈ θ δlong h i
where qθ is the weighting parameter for pitch attitude, rδlong is the longitudinal control
weighting, and ωBW is the closed-loop bandwidth. The precise definition of ωBW is the
frequency where the amplitude of the closed-loop transfer function is 6dB below its zero-
frequency value. Equation (3.6) shows an approximate relation between the open-loop
corssover frequency and the closed-loop bandwidth.
ω 0.56ω (3.6) c ≈ BW
Thus, given a desired crossover frequency in each control axis, Equations (3.4), (3.5) and
(3.6) provide a method of determining appropriate control weighting parameters in R.
From the previous study, it was shown that the actual crossover frequencies were slightly
different from the desired crossover frequencies in the OCM design, due to the approximate
nature of Equations (3.4) - (3.6) [63]. In this study, an iterative method is used to obtain the
exact desired crossover frequencies. The design process begins with initial guess of control
weighting parameters based on Equations (3.4) - (3.6). Then the actual crossover frequency
is calculated for the full order model. The weighting parameters are adjusted proportional
to this discrepancy between the actual and expected values of the crossover frequency, and
the process is then repeated. This iteration process is automated in MATLAB, and in all
cases the iteration is repeated until the differences between the actual and desired crossover CHAPTER 3. PILOT MODELING 40 frequencies are negligible.
The blocks labeled “neuromotor dynamics” and “time delay” (Figure 3.1) represent psycho-physical limitations inherent in the human pilot. It should be noted, for example, that rapid control movements are rarely produced by trained pilots. Alternatively, these terms can be used to account indirectly for the physiological limitation on the ability of human pilots to make corrective actions. The neuromotor dynamics is often approximated linearly by an adjustable first-order lag filter [62]. The time delay represents an actual delay. In this study, τn = 0.1 is used and time delay is set to nominal value of 0.1 sec.
The procedure above provides a method for designing OCM gains for a single operating point. In order to operate over a range of airspeeds, the procedure is repeated in 10 knot increments from hover out to the maximum speed of the aircraft. A simple gain scheduling approach is used to adjust the OCM gains as the airspeed changes in flight. For example, the system matrices of controller for 30 knot and 40 knot are represented as
for 30 knot : Ac30knot , Bc30knot , Cc30knot , Dc30knot (3.7)
for 40 knot : Ac40knot , Bc40knot , Cc40knot , Dc40knot
And if the helicopter airspeed is 35 knot, then the final control system matrices are obtained
using linear interpolation of the matrices.
Ac35knot = 0.5Ac30knot + 0.5Ac40knot
Bc35knot = 0.5Bc30knot + 0.5Bc40knot (3.8)
Cc35knot = 0.5Cc30knot + 0.5Cc40knot
Dc35knot = 0.5Dc30knot + 0.5Dc40knot CHAPTER 3. PILOT MODELING 41
3.2 Nonlinear Elements of the Human Pilot
Control records from human helicopter pilots have shown that there is a stepped appearance in the collective input [53]. Pilots tend to make discrete rather than continuous adjustments to the collective lever. This effect can be modeled using nonlinear elements in the pilot model. A hysteresis is attached to the control leading to the helicopter and deadband is placed across the error prior to its processing by control model. Descriptions of these elements are presented in the following Sections 3.2.1 and 3.2.2
3.2.1 Hysteresis
The hysteresis represents a system in which a change in input causes an equal change in output. However, when the input changes direction, an initial change in input has no effect on the output. The amount of side-to-side play in the system is referred to as the deadzone.
The deadzone is centered about the output. A system can be in one of three modes:
1. Disengage - in this mode, the input does not drive the output and the output remains
constant.
2. Engaged in a positive direction - in this mode, the input is increasing (has a positive
slope) and the output is equal to the input minus half the deadzone width.
3. Engaged in a negative direction - in this mode, the input is decreasing (has a negative
slope) and the output is equal to the input plus half the deadzone width.
For example, Figure 3.3 shows the effect of a sine wave passing through a hysteresis element with deadzone width of 1. CHAPTER 3. PILOT MODELING 42
1
0.8
0.6 (c)
0.4
0.2 (b)
0 (a)
−0.2
(d) −0.4
−0.6
−0.8
−1 0 1 2 3 4 5 6 7 8 9 10 Time (sec)
Figure 3.3: Effect of a sine wave passing through a hysteresis
(a) Input engages in positive direction. Change in input causes equal change in output.
(b) Input disengages. Change in input does not affect output.
(c) Input engages in negative direction. Change in input causes equal change in output.
(d) Input disengages. Change in input does not affect output.
3.2.2 Deadband
The deadband represents a threshold of the perception of departure from the reference values. The deadband generates zero output within a specified region. The lower and upper limits of the deadband are specified as the start of deadband and end of deadband parameters. The output depends on the input and deadband:
1. If the input is within the deadband (greater than the lower limit and less than the CHAPTER 3. PILOT MODELING 43
upper limit), the output is zero.
2. If the input is greater than or equal to the upper limit, the output is the input minus
the upper limit.
3. If the input is less than or equal to the lower limit, the output is the input minus the
lower limit.
Figure 3.4 shows the effect of the deadband element (deadband width = 1) on the sine wave.
While the input (the sine wave) is between 0.5 and 0.5, the output is zero. −
1
0.8
0.6
0.4
0.2
0
−0.2
−0.4
−0.6
−0.8
−1 0 1 2 3 4 5 6 7 8 9 10 Time (sec)
Figure 3.4: Effect of a sine wave passing through a deadband Chapter 4
Numerical Examples : Departure and Approach Operations
4.1 Overview
The dynamic interface flight simulation model has been applied to simulate a UH-60A operating near an LHA class ship. The simulation has been performed for two different shipboard operations (departure, approach). Kinematic profiles of these shipboard tasks are given in Reference [49], and these profiles are modified slightly in this study. As discussed in Reference [49], the kinematic profile is determined using an Earth fixed coordinate frame with the origin at the sea surface directly under the initial position of the helicopter. The
X-axis is along with the North direction, Z-axis is downward, and Y-axis is along with the
East direction. The target spot of shipboard operations is spot 8 of the LHA class ship
(Figure 4.1).
The optimal control model is used to determine the required pilot control inputs for
44 CHAPTER 4. NUMERICAL EXAMPLES 45
3
9
3A
1
Spot 8
5 6
7
2 4 8
Figure 4.1: Top view of an LHA class ship given shipboard approach and departure tasks. The OCM of the human pilot used in the sections 4.2 and 4.4 is designed for the desired crossover frequency of the open-loop transfer function in the lateral (2.75 rad/sec), longitudinal (1.8 rad/sec), collective (2.0 rad/sec),
and pedal (2.0 rad/sec). These crossover frequencies are selected to have similar control
activities from JSHIP flight test. For both departure and approach operations, the ship is
assumed to be still with a steady-state wind of 30 knots for two different WOD conditions
(0◦ and 30◦). In this study, 30 degree WOD condition is considered as worst case because
the flight test results from Ref. [2] showed substantial increase in pilot workload due to
turbulence and this case was awarded as ‘unacceptable’.
4.1.1 Shipboard Departure Trajectory
Typical shipboard departure procedures include all actions that are required to conduct
an ascending, acceleration departure from a stationkeeping, ending in steady, level forward
flight [49]. Starting from the stationkeeping location, pilots typically initiate the departure
phase by yawing and/or translating the helicopter at a relatively constant altitude to a
position outboard of the recovery spot that is clear of obstructions. The entire shipboard
departure task can be divided into the following three phases:
1. Phase I : from the stationkeeping position, accelerating to a desired climb rate and a CHAPTER 4. NUMERICAL EXAMPLES 46
desired horizontal acceleration.
2. Phase II : keeping a constant climb rate and a constant horizontal acceleration.
3. Phase III : reducing the climb rate and horizontal acceleration to zero, and ending in
a steady level flight
In this study, in order to clear obstructions, the departure begins with 60 ft translational maneuver to the left (port side). The helicopter then transitions to a desired climb rate and horizontal acceleration. Finally, the helicopter achieves desired level flight speed. The key parameters for defining the departure trajectory profile are the helicopter initial level
flight speed, initial altitude, and desired final altitude for stationkeeping. The initial profile parameters of the departure operation are given in Table 4.1.
Table 4.1: Initial profile parameters for the departure task
Trajectory parameters Departure task Initial altitude 80 ft (17 ft above deck) Final altitude 300 ft Initial speed 0 knot Final speed 60 knot
4.1.2 Shipboard Approach Trajectory
Similar to the departure operation, typical shipboard approach procedures include all ac- tions that bring the rotorcraft from a point far away from the ship down to a point much closer to the recovery spot [49]. The key parameters for defining the approach profile are the helicopter initial level flight speed, initial altitude, initial distance from the ship, and desired final altitude for stationkeeping. CHAPTER 4. NUMERICAL EXAMPLES 47
The entire shipboard approach task can be divided into three phases:
1. Phase I : From steady level flight, the helicopter transitions to a desired descent rate
and horizontal deceleration.
2. Phase II : The helicopter maintains a constant descent rate and horizontal decelera-
tion.
3. Phase III : The descent rate and horizontal deceleration are reduced to zero, ending
in stationkeeping over a landing spot.
In this study, the helicopter approaches the ship from the port side at a 45 degree angle, and then performs a 45 degree left turn to align itself with the longitudinal axis of the ship after it crosses over the deck. This is similar to the trajectory used in the JSHIP study. For simplicity, the ship is assumed to be stationary in a 30 knots steady wind. Both a head wind and a wind from 30 degree starboard of the bow are considered. The entire procedures of shipboard approach are shown in Figure 4.2. The initial profile parameters of the departure operation are given in Table 4.2.
Phase III Phase II Phase I
0 deg WOD 60 knotVi 30 deg WOD
H300 fti 8 9
45
H80 ftf
Top view Shipboard approach - 45 deg approach
Figure 4.2: Shipboard approach operation procedures CHAPTER 4. NUMERICAL EXAMPLES 48
Table 4.2: Initial profile parameters for the approach task
Trajectory parameters Approach task Initial altitude 300 ft Final altitude 80 ft (17 ft above deck) Initial air speed 60 knot Final air speed 0 knot
4.2 Effects of Ship Airwake Model
In this study, the helicopter/ship dynamic interface simulation has been performed for three different airwake cases (no airwake, steady-state airwake, time-varying airwake) in 0 and 30 degree WOD conditions. The ship’s time-varying airwake and steady-state (time-averaged) airwake solutions are calculated using PUMA2 by Sezer-Uzol et al [39]. These solutions present the airwake velocity field over the 3-dimensional full-scale LHA geometry.
Figures 4.3 - 4.9 show the simulation results for departure operation in 0 and 30 degree
WOD cases. The dotted lines represent the no airwake condition, the dashed lines repre- sent the steady airwake condition, and the solid lines represent the time-varying airwake condition. The helicopter trajectory with respect to the ship coordinate system is shown in
Figure 4.3 for both 0 degree and 30 degree WOD conditions. Figures 4.4 and 4.7 show the helicopter velocity in NED (North-East-Down) coordinate system. Figures 4.5 and 4.8 show the helicopter attitude responses. The pilot stick inputs provided by the optimal control model are shown in Figures 4.6 and 4.9. The conventions for these control positions are as follows; full left lateral cyclic, full forward longitudinal cyclic, full down collective pitch, and full left pedal correspond to 0 %, full right lateral cyclic, full aft longitudinal cyclic, full up collective pitch, and full right pedal correspond to 100 %. The results show that the CHAPTER 4. NUMERICAL EXAMPLES 49 helicopter trajectory and velocities are very similar in each case. This is because the opti- mal control model of the human pilot is regulating these parameters. These variables are essentially constrained in the simulation; the optimal control model is effectively calculating the control inputs and aircraft attitude required to track the desired trajectory. However, when the helicopter is operating within the DI mesh, there is significant difference in the aircraft attitude response and the pilot control activity. The steady airwake results differ only slightly from the results with no airwake in that the trimmed controls and attitude are different. However, the time-varying airwake results in significant oscillations and pilot activity, particularly when hovering over the ship deck. This difference in the results with the steady and time-varying airwake was not entirely expected, since a stationary gust field can appear to be time-varying to the aircraft when it is moving (and especially to the rotor blades which are constantly moving). As discussed in the previous section, there is strong unsteadiness in the crossflow (y-component) and vertical (z-component) components of the velocity due to bow separation, deck-edge vortices and complex island wake for 30 degree
WOD condition. These effects can be clearly observed from results of aircraft attitude responses and pilot control activities (Figures 4.8 - 4.9). Note that the differences in the beginning are due to the different trim conditions. From the results, the 30 degree WOD condition results in significantly larger oscillations and higher pilot control activity, partic- ularly when hovering over the ship deck. This is consistent with the JHSIP flight test data
[2, 60]. CHAPTER 4. NUMERICAL EXAMPLES 50
400
200
0 Ship
Y, [ft] Helicopter trajectory
−200 DI mesh
−400 −4000 −3500 −3000 −2500 −2000 −1500 −1000 −500 0
400
300 Helicopter trajectory
200 DI mesh Z, [ft]
100
Ship 0 −4000 −3500 −3000 −2500 −2000 −1500 −1000 −500 0 X, [ft]
Figure 4.3: Helicopter position w.r.t. ship coordinate system - Departure task (30 knot, 0 and 30 degree WOD conditions) CHAPTER 4. NUMERICAL EXAMPLES 51
100
N 50 V
Escape from DI mesh 0 0 10 20 30 40 50 60 70 80 90
5
0 E V −5
−10 0 10 20 30 40 50 60 70 80 90
0
−2 D V −4
−6 0 10 20 30 40 50 60 70 80 90 Time, [sec]
Figure 4.4: Helicopter velocity [ft/sec] - Departure task (30 knot, 0 degree WOD condition) CHAPTER 4. NUMERICAL EXAMPLES 52
No airwake Steady-state airwake Time-varying airwake
2 0 −2
PHI −4 −6 Escape from DI mesh −8 0 5 10 15 20 25 30 35 40 45
2
THETA 0
−2 0 5 10 15 20 25 30 35 40 45
0
PSI −0.5
−1 0 5 10 15 20 25 30 35 40 45 Time, [sec]
Figure 4.5: Helicopter attitude angles [deg] in the DI mesh - Departure task (30 knot, 0 degree WOD condition) CHAPTER 4. NUMERICAL EXAMPLES 53
No airwake Steady-state airwake Time-varying airwake
54 Escape from DI mesh 52 50 Lateral 48
0 5 10 15 20 25 30 35 40 45
58
56
Longitudinal 54
0 5 10 15 20 25 30 35 40 45 63 62 61 60 Collective 59 0 5 10 15 20 25 30 35 40 45 42 40 38
Pedal 36 34 0 5 10 15 20 25 30 35 40 45 Time, [sec]
Figure 4.6: Pilot inputs [%] in the DI mesh - Departure task (30 knot, 0 degree WOD condition) CHAPTER 4. NUMERICAL EXAMPLES 54
100
N 50 V
Escape from DI mesh 0 0 10 20 30 40 50 60 70 80 90
5
0 E V −5
−10 0 10 20 30 40 50 60 70 80 90
0
D −2 V −4
−6 0 10 20 30 40 50 60 70 80 90 Time, [sec]
Figure 4.7: Helicopter velocity [ft/sec] - Departure task (30 knot, 30 degree WOD condition) CHAPTER 4. NUMERICAL EXAMPLES 55
No airwake Steady-state airwake Time-varying airwake
0 PHI −5 Escape from DI mesh
−10 0 5 10 15 20 25 30 35 40 45
4
2 THETA 0
0 5 10 15 20 25 30 35 40 45
1 0.5 0 PSI −0.5 −1
0 5 10 15 20 25 30 35 40 45 Time, [sec]
Figure 4.8: Helicopter attitude angles [deg] in the DI mesh - Departure task (30 knot, 30 degree WOD condition) CHAPTER 4. NUMERICAL EXAMPLES 56
No airwake Steady-state airwake Time-varying airwake
60 55 50 Lateral 45 Escape from DI mesh 0 5 10 15 20 25 30 35 40 45 60 55 50
Longitudinal 45 0 5 10 15 20 25 30 35 40 45
65 60 55 Collective 50 0 5 10 15 20 25 30 35 40 45
38 36 34 32 Pedal 30 28 0 5 10 15 20 25 30 35 40 45 Time, [sec]
Figure 4.9: Pilot inputs [%] in the DI mesh - Departure task (30 knot, 30 degree WOD condition) CHAPTER 4. NUMERICAL EXAMPLES 57
Figures 4.10 - 4.16 show similar simulation results for the approach operation. As expected, the attitude changes and control activity are fairly benign in the early part of the maneuver, when the helicopter is relatively far from the ship. Near the end of the maneuver, the helicopter begins to interact significantly with the time-varying airwake, as indicated by the fluctuations in attitude and increased control activity. It can also be observed that the oscillations immediately after entering the DI mesh are similar for the steady and time- varying airwake. At this point, the aircraft is still moving with significant velocity so the steady gust field has a time-varying appearance to the aircraft. However, once the aircraft approaches hover, the results indicate the time-varying airwake results in larger oscillations and higher pilot control activity than the steady airwake. This reflects the so-called cliff edge effect [2], where strong shear layers from the ship’s superstructure are blown across the landing spot with winds from 30 degrees.
For both shipboard operations, compared to the case with no airwake, the trim condi- tions of the helicopter with the ship airwake are different (in terms of pilot control inputs and helicopter attitude). These differences are clearly induced due to the ship airwake.
From the results, the optimal control model is reasonably effective in tracking the desired
flight path for both approach and departure operations. The results clearly indicate that the time-varying airwake has a significant impact on aircraft response and pilot control activity when the aircraft is flown for specified approach and departure trajectories. The differences are most notable when the helicopter is operating in or near a hover relative to the ship deck (stationkeeping). In the past, gust models for fixed-wing aircraft simulation have often used a stationary or frozen field model. This is adequate when the aircraft is moving at a significant forward speed. However, the model clearly breaks down as airspeed CHAPTER 4. NUMERICAL EXAMPLES 58 approaches zero. The same appears to be true of helicopters operating in turbulent ship airwake. The time-varying nature of the ship airwake becomes dominant as the helicopter approaches hover. And, the 30 degree WOD condition showed a substantial increase in pi- lot workload. Thus, these ship airwake effects can increase the pilot workload and possibly degrade handling qualities during shipboard launch and recovery operations.
0 Ship DI mesh −500
−1000
−1500
Y, [ft] Helicopter trajectory −2000
−2500
−3000 −1000 −500 0 500 1000 1500 2000 2500 3000
400
300
200 DI mesh Helicopter trajectory Z, [ft]
100
Ship 0 −1000 −500 0 500 1000 1500 2000 2500 3000 X, [ft]
Figure 4.10: Helicopter position w.r.t. ship coordinate system - Approach task (30 knot, 0 and 30 degree WOD conditions ) CHAPTER 4. NUMERICAL EXAMPLES 59
No airwake Steady-state airwake Time-varying airwake
100 Entering DI mesh
N 50 V
0 0 10 20 30 40 50 60 70 80 90
4
2 E V 0
−2
0 10 20 30 40 50 60 70 80 90
6
4 D V 2
0
0 10 20 30 40 50 60 70 80 90 Time, [sec]
Figure 4.11: Helicopter velocity [ft/sec] - Approach task (30 knot, 0 degree WOD condition) CHAPTER 4. NUMERICAL EXAMPLES 60
No airwake Steady-state airwake Time-varying airwake
Entering DI mesh −2
−4 PHI
−6
45 50 55 60 65 70 75 80 85 90
8
6
4 THETA
2
45 50 55 60 65 70 75 80 85 90
0
−10
−20 PSI −30
−40 45 50 55 60 65 70 75 80 85 90 Time, [sec]
Figure 4.12: Helicopter attitude angles [deg] in the DI mesh - Approach task (30 knot, 0 degree WOD condition) CHAPTER 4. NUMERICAL EXAMPLES 61
No airwake Steady-state airwake Time-varying airwake
44
42 Lateral 40 Entering DI mesh
45 50 55 60 65 70 75 80 85 90 68
64
Longitudinal 58 45 50 55 60 65 70 75 80 85 90
65
60 Collective 55 45 50 55 60 65 70 75 80 85 90
55 50 Pedal 45 40 45 50 55 60 65 70 75 80 85 90 Time, [sec]
Figure 4.13: Pilot inputs [%] in the DI mesh - Approach task (30 knot, 0 degree WOD condition) CHAPTER 4. NUMERICAL EXAMPLES 62
No airwake Steady-state airwake Time-varying airwake
100 Entering DI mesh
N 50 V
0 0 10 20 30 40 50 60 70 80 90
2 E
V 0
−2
0 10 20 30 40 50 60 70 80 90
6
4 D V 2
0
0 10 20 30 40 50 60 70 80 90 Time, [sec]
Figure 4.14: Helicopter velocity [ft/sec] - Approach task (30 knot, 30 degree WOD condition) CHAPTER 4. NUMERICAL EXAMPLES 63
No airwake Steady-state airwake Time-varying airwake
Entering DI mesh −2
−4 PHI −6
−8 45 50 55 60 65 70 75 80 85 90
8
6
THETA 4
2 45 50 55 60 65 70 75 80 85 90
0 −10 −20 PSI −30 −40
45 50 55 60 65 70 75 80 85 90 Time, [sec]
Figure 4.15: Helicopter attitude angles [deg] in the DI mesh - Approach task (30 knot, 30 degree WOD condition) CHAPTER 4. NUMERICAL EXAMPLES 64
No airwake Steady-state airwake Time-varying airwake
48
43 Lateral 38 Entering DI mesh 45 50 55 60 65 70 75 80 85 90
65 60 55 Longitudinal
45 50 55 60 65 70 75 80 85 90
70
63 Collective 55 45 50 55 60 65 70 75 80 85 90
55
45 Pedal 35 45 50 55 60 65 70 75 80 85 90 Time, [sec]
Figure 4.16: Pilot inputs [%] in the DI mesh - Approach task (30 knot, 30 degree WOD condition) CHAPTER 4. NUMERICAL EXAMPLES 65
4.3 Effects of Different Tracking Performance
The OCM of the human pilot is designed for three different levels of tracking performance by varying the desired crossover frequency of the open-loop transfer function in the pitch, roll, and yaw axes. The three different cases are termed “normal”, “relaxed”, and “tight” tracking. Table 4.3 summarizes the desired crossover frequencies for each case and each control axis. In this study, the desired crossover frequencies are arbitrarily chosen. However, it is not necessary to specify exact values, only to develop a “tunable” human pilot model and observe the relative behavior for different levels of tracking precision.
Table 4.3: Crossover frequencies for different tracking performance (rad/sec)
Longitudinal Lateral Collective Yaw Case 1 (relaxed) 0.5 1.0 0.5 1.0 Case 2 (normal) 1.5 1.75 1.5 1.5 Case 3 (tight) 2.0 2.75 2.0 2.1
Three different pilot models are compared for approach operation for 0 and 30 degree
WOD conditions (time-varying airwake model). Figures 4.17 4.18 show the simulation ∼ results in 0 degree WOD condition. Figures 4.19 4.20 show the simulation results in 30 ∼ degree WOD condition. The results of position errors (Figure 4.17, Figure 4.19) indicate that when using a lower crossover frequency, as in case 1 (relaxed) pilot model, there are significantly larger errors in the tracking but less control activity (Figure 4.18, Figure 4.20).
This represents a situation where the pilot is under controlling, and allowing the airwake turbulence to move the helicopter about with relatively little compensation. On the other hand, when using a higher crossover frequency, as with the case 3 (tight), there is actually relatively little improvement in tracking performance, but significantly more control activity. CHAPTER 4. NUMERICAL EXAMPLES 66
This is example of a pilot over controlling the helicopter, increasing workload with relatively little payoff in terms of holding the desired trajectory.
Case 1 (relaxed) Case 2 (normal) Case 3 (tight)
40
20
X 0 ∆
−20
−40 0 10 20 30 40 50 60
60
40
Y 20 ∆
0
−20 0 10 20 30 40 50 60
10
5
Z 0 ∆
−5
−10 0 10 20 30 40 50 60 Time, [sec]
Figure 4.17: Helicopter position error [ft] - 30 knot, 0 degree WOD condition CHAPTER 4. NUMERICAL EXAMPLES 67
Case 1 (relaxed) Case 2 (normal) Case 3 (tight)
60
50
Lateral 40
30 0 10 20 30 40 50 60 70
60
50 Longitudinal 40 0 10 20 30 40 50 60 80
60
40 Collective 20 0 10 20 30 40 50 60 80
60
Pedal 40
20 0 10 20 30 40 50 60 Time, [sec]
Figure 4.18: Pilot control input [%] - 30 knot, 0 degree WOD condition CHAPTER 4. NUMERICAL EXAMPLES 68
Case 1 (relaxed) Case 2 (normal) Case 3 (tight)
20 X ∆ 0
−20 0 10 20 30 40 50 60 70 80 90
20
10 Y
∆ 0
−10
0 10 20 30 40 50 60 70 80 90
10
0 Z ∆
−10
0 10 20 30 40 50 60 70 80 90 Time, [sec]
Figure 4.19: Helicopter position error [ft] - 30 knot, 30 degree WOD condition CHAPTER 4. NUMERICAL EXAMPLES 69
Case 1 (relaxed) Case 2 (normal) Case 3 (tight)
60
50 Lateral 40 0 10 20 30 40 50 60 70 80 90
60
50 Longitudinal 40 0 10 20 30 40 50 60 70 80 90
60
50 Collective 40 0 10 20 30 40 50 60 70 80 90
60
50
Pedal 40
30 0 10 20 30 40 50 60 70 80 90 Time, [sec]
Figure 4.20: Pilot control input [%] - 30 knot, 30 degree WOD condition CHAPTER 4. NUMERICAL EXAMPLES 70
4.4 Validation with Flight Test Data
In this section, a typical shipboard approach trajectory was simulated. At this point, measured performance and flight test data for departure tasks are unavailable for verifying the simulation. Thus, the verification in this section is made based on the flight test data from JSHIP program for the approach tasks only. The simulation has been performed for two different WOD conditions (0 degree and 30 degree) with the time-varying airwake solutions. The approach trajectory profile is modified slightly to be consistent with approach maneuvers used in the JSHIP program. Since the exact aircraft positions with respect to the ship are not available at this point, the initial parameters for each approach operation are defined using the information from the flight test data, and these profile parameters are given in Table 4.4.
Figures 4.21 - 4.24 show the simulation results for the approach in 0 degree WOD con- dition. The dashed lines represent the flight test data from JSHIP program, the solid lines are results from simulation model. Figure 4.21 shows helicopter air speed in knots. Figure
4.22 shows the height above ground level (representative of a radar altitude measurement on the aircraft). The sudden jump in the time history corresponds to the aircraft flying over the edge of the ship deck. Figure 4.23 shows the aircraft angular rate responses. The
Table 4.4: Initial profile parameters for the approach tasks from JSHIP program
Trajectory parameters 0 degree WOD 30 degree WOD Initial altitude 280 ft 250 ft Final altitude 60 ft (10 ft above deck) 63 ft (13 ft above deck) Initial air speed 83.5 knot 68 knot Final air speed 38 knot 30 knot CHAPTER 4. NUMERICAL EXAMPLES 71 pilot stick inputs provided by the optimal control model are shown in Figure 4.24.
Similarly, Figures 4.25 - 4.28 show the simulation results for the approach operation in
30 degree WOD condition. The time domain results in Figures 4.21 - 4.28 are intended to show that the simulation faithfully recreated the same maneuver conducted in flight test and to provide a qualitative comparison of the transient aircraft responses and pilot control activity.
The results show that the helicopter trajectory and speed are very similar in each case.
This is expected since the optimal control model of the pilot is designed to track these trajectories. The oscillation in the airspeed from flight test is assumed to be sensor noise, which was not modeled in the simulation. The 30 degree WOD condition results in sig- nificantly larger oscillations and higher pilot control activity, particularly when helicopter hovering over the ship deck. This reflects the so-called a cliff edge effect [60, 65], where strong shear layers from the island are blown across the spot 8 with winds from 30 degrees.
This is backed up by qualitative results of the JSHIP flight test program, which showed that the 30 degree WOD condition at spot 8 resulted in high pilot workload.
The attitude changes and control activity predicted by the simulation and those mea- sured in the flight test are somewhat different in the early part of the maneuver, when the helicopter is relatively far from the ship. This difference is likely due to the presence of the atmospheric turbulence in the flight tests which is not modeled in this simulation. There is also a discrepancy in the prediction of trim when the helicopter is far from the ship.
However, the results are qualitatively similar when the helicopter operates near the ship deck, where the helicopter interacts significantly with the ship airwake.
Figures 4.24 and 4.28 are comparisons of control activity as predicted by simulation and CHAPTER 4. NUMERICAL EXAMPLES 72 measured in the JSHIP flight tests. The 30 degree WOD condition results in significantly larger oscillations and higher pilot control activity, particularly when the helicopter is hover- ing over the ship deck. The control activity predicted by the simulation, and those measured in the flight test, are somewhat different in the early part of the maneuver, when the heli- copter is relatively far from the ship. This difference is likely to be due to the presence of atmospheric turbulence in the flight tests, which is not modeled in this simulation.
There is also a discrepancy in the prediction of trim when the helicopter is far from the ship, particularly in the pedals. There are two factors that contribute to this discrepancy.
First, the OCM pilot model uses a zero sideslip trim for all low speed flight conditions; whereas the flight test pilot appears to use more of a zero bank angle trim strategy until the airspeed is very near zero. There are also some discrepancies in the trim characteristics between the aircraft and the simulation model. However, the pilot control activity results are qualitatively similar when the helicopter operates near the ship deck, where the helicopter interacts significantly with the ship airwake. These last phases of the approach maneuvers are of the most interest. The magnitude and frequency of the collective and pedal control activity, when the helicopter is operating near the ship deck, appear to have good qualitative agreement with flight test.
The simulation seems to predict a somewhat lower level of longitudinal and lateral activity. The increased level of high frequency control activity observed in flight test might be due to a number of factors including: details in the ship airwake not captured in the
CFD solutions, the presence of vestibular feedback in the pilot feedback loop not used in the
OCM pilot model, or even biomechanical feedback effects due to vibration on the aircraft. CHAPTER 4. NUMERICAL EXAMPLES 73
Flight test Simulation
90
80
70
60 Vehicle Air Speed
50
40
30 0 10 20 30 40 50 60 Time, [sec]
Figure 4.21: Helicopter airspeed [knot] - 30 knot, 0 degree WOD condition CHAPTER 4. NUMERICAL EXAMPLES 74
Flight test Simulation
250
200
150 Helicopter altitude 100
50
0 0 10 20 30 40 50 60 Time, [sec]
Figure 4.22: Helicopter altitude [ft] - 30knot, 0 degree WOD condition CHAPTER 4. NUMERICAL EXAMPLES 75
Flight test Simulation
10
5
P 0
−5
−10 0 10 20 30 40 50 60
10
5
Q 0
−5
−10 0 10 20 30 40 50 60
10
5
R 0
−5
−10 0 10 20 30 40 50 60 Time, [sec]
Figure 4.23: Angular rate [deg/sec] - 30knot, 0 degree WOD condition CHAPTER 4. NUMERICAL EXAMPLES 76
Flight test Simulation
60
50
40 Lateral 30 0 10 20 30 40 50 60 80
70
60 Longitudinal 50 0 10 20 30 40 50 60 80
60
40 Collective 20 0 10 20 30 40 50 60 80
60 Pedal 40
0 10 20 30 40 50 60 Time, [sec]
Figure 4.24: Pilot stick inputs [%] - 30 knot, 0 degree WOD condition CHAPTER 4. NUMERICAL EXAMPLES 77
Flight test Simulation
75
70
65
60
55
50
45 Vehicle Air Speed 40
35
30
25
20 0 10 20 30 40 50 60 70 80 Time, [sec]
Figure 4.25: Helicopter airspeed [knot] - 30 knot, 30 degree WOD condition CHAPTER 4. NUMERICAL EXAMPLES 78
Flight test Simulation
250
200
150 Helicopter altitude 100
50
0 0 10 20 30 40 50 60 70 80 Time, [sec]
Figure 4.26: Helicopter altitude [ft] - 30 knot, 30 degree WOD condition CHAPTER 4. NUMERICAL EXAMPLES 79
Flight test Simulation
10
P 0
−10
0 10 20 30 40 50 60 70 80 90
5
Q 0
−5
0 10 20 30 40 50 60 70 80 90
5 0
R −5 −10 −15 0 10 20 30 40 50 60 70 80 90 Time, [sec]
Figure 4.27: Angular rate [deg/sec] - 30knot, 30 degree WOD condition CHAPTER 4. NUMERICAL EXAMPLES 80
Flight test Simulation
60
40 Lateral
20 0 10 20 30 40 50 60 70 80 80
60 Longitudinal 40 0 10 20 30 40 50 60 70 80 80
60 Collective 40 0 10 20 30 40 50 60 70 80 80
60
Pedal 40
20 0 10 20 30 40 50 60 70 80 Time, [sec]
Figure 4.28: Pilot stick inputs [%] - 30 knot, 30 degree WOD condition CHAPTER 4. NUMERICAL EXAMPLES 81
4.4.1 Frequency Domain Analysis
In general, simulation requires the adoption of a priori engineering assumptions to allow the formulation of model equations. These simulation models are then used to predict aircraft or subsystem motion. To achieve sufficient accuracy in simulations of helicopter-ship com- binations, model verifications are required for simulated testing of the helicopter shipboard operations. It is well known that a frequency domain analysis provides good correlation between test and simulation data. The most common method of acquiring frequency in- formation is to use spectrum averaging, i.e. averaging is performed in frequency domain.
This method has the advantages that it is relatively easy to use and it will work with any type of signal. In the spectrum averaging method, the Fourier transform is applied to blocks of time history data, possibly after a weighting function has been used. The Fourier spectrum is then squared, to yield a real-valued spectrum called the autospectrum (some- times also referred to as power spectrum or mean square spectrum). In this study, CIFER
(Comprehensive Identification from FrEquency Responses) is used to get frequency domain comparisons against flight test data from the JSHIP program. CIFER is an interactive fa- cility for system identification and verification developed by U.S Army/NASA and Sterling
Federal Systems [66].
Figures 4.29 - 4.30 show comparisons of input autospectra from pilot stick inputs with those from optimal control model and flight test data. The results are averaged over 5 different simulation runs for different airwake starting points (e.g. 0 sec, 8 sec, 16 sec, 24 sec, 32 sec). In this study, 4 different window sizes (3sec, 5sec, 10sec, and 15sec) were used in the FFT analysis to obtain a composite average that is accurate over a wide range of CHAPTER 4. NUMERICAL EXAMPLES 82 frequencies. This is a feature available in the CIFER software package. Only the last phase of the approach maneuver where the aircraft is interacting with the airwake, is considered.
From the figures, it can be observed that there is reasonable agreement in the collective and pedal input autospectra for the frequency range of 0.2 to 1.8 Hz but the lateral and longitudinal cyclic autospectra both underestimate the control activities for the frequency region over 1 Hz. There are some additional discrepancies in the lateral control activity for the 0 degree WOD case over the entire frequency range. Control activity in the frequency range of 0.2 to 2 Hz has the most significant impact on pilot workload [2]. Although the present work has provided a good initial estimate of pilot control activity, some improve- ment is warranted. In particular, it is critical to improve the accuracy of the lateral and longitudinal control activity predictions in the 1-2 Hz region. It is expected that this could be achieved with further tuning of the OCM pilot model. CHAPTER 4. NUMERICAL EXAMPLES 83
Flight test Simulation
0 −20 −40
Lateral −60 −80 −1 0 1 10 10 10 0 −20 −40 −60 Longitudinal −80 −1 0 1 10 10 10 0
−40 Collective −80 −1 0 1 10 10 10 0 −20 −40 Pedal −60 −80 −1 0 1 10 10 10 Frequency, [Hz]
Figure 4.29: Pilot input autospectrum [dB] - 30 knot, 0 degree WOD condition CHAPTER 4. NUMERICAL EXAMPLES 84
Flight test Simulation
0 −20 −40
Lateral −60 −80 −1 0 1 10 10 10 0
−40 Longitudinal −80 −1 0 1 10 10 10 0 −20 −40
Collective −60 −80 −1 0 1 10 10 10 0 −20 −40 Pedal −60 −80 −1 0 1 10 10 10 Frequency, [Hz]
Figure 4.30: Pilot input autospectrum [dB] - 30 knot, 30 degree WOD condition Chapter 5
Task-Tailored Control Design
5.1 Overview
From the previous section, shipboard helicopters operate in an environment where task performance can be easily affected by ship airwake, which contains large velocity gradients and areas of turbulence. In fact, ship airwake or wind-over-deck conditions can be a factor in limiting these shipboard operations. For this reason, it would be desirable to include task-tailored modes in the automatic flight control system that are specifically designed to compensate for airwake disturbances.
The task-tailored control system lets a pilot fly the aircraft throughout its operational
flight envelope with optimized control augmentation supplied by the system at each oper- ating point in day, night or adverse weather operations. Operating conditions are defined as points in the operating space of the aircraft with dimensions including, but not lim- ited to, mission profile, mission task, weather conditions, visual conditions, air speed, alti- tude, glide slope, side-slip angle, attitude, g-loading, aircraft-failure state, and level-of-flight
85 CHAPTER 5. TASK-TAILORED CONTROL DESIGN 86 control-system augmentation. The rotorcraft control laws are tailored to provide a seamless transition between control/system modes and maintaining desired handling qualities.
The use of a task-tailored stability augmentation system could potentially improve safety for shipboard operations and even expand the operational envelope, by allowing the aircraft to operate in WOD conditions currently deemed unsafe. The SAS should also conform to the handling qualities requirements currently dictated in military specifications [67]. There are a number of technical challenges in the design of such a system, as it is possible to approach limits on stability, robustness, and other constraints of the rotorcraft.
There have been some detailed simulation studies of the potential improvements of dis- turbance rejection flying qualities using flight test data [34, 68, 69]. These studies mainly focused on meeting current handling qualities specifications, and did not attempt to extend the specification beyond the requirements in ADS-33E. Although these studies have per- formed disturbance rejection handling qualities studies, very few quantitative or qualitative parametric studies in the ADS-33 handling qualities requirement exist. In fact, there are little or no supporting data for the disturbance rejection requirements in ADS-33 [67]. Fur- thermore, design requirements for rotorcraft handling qualities involve a large set of design specifications, including metrics based on bandwidth, cut-off frequency, actuator saturation, and disturbance response [70]. Many innovative flight control design methods have been proposed to improve flight control system performance. However, there is rarely an effort to optimize the control parameters to achieve the disturbance rejection requirement.
The present work investigates the optimization of a flight control system for the UH-
60A Black Hawk helicopter operating in the turbulent airwake of a LHA class ship. A stochastic model of the ship airwake is derived from simulations with a full time-accurate CHAPTER 5. TASK-TAILORED CONTROL DESIGN 87
CFD solution of the airwake. The stochastic model can be used to simplify and facilitate off-line or real-time simulation models. It can also be readily applied for flight control system design. The main objective is to optimize the automatic flight control system in order to improve disturbance rejection properties of the helicopter when operating in the airwake. This could be achieved by minimizing the magnitude of the transfer function from the gust shaping filter input to the aircraft response. In this study, the gains of a SAS are optimized using CONDUIT in order to ensure good handling qualities and stability, while minimizing a weighted objective of gust response and actuator saturation. Then the optimized SAS are tested using a full non-linear simulation model. The overall schematic of the current task-tailored control system design is shown in Figure 5.1.
In addition, a H∞ controller is designed to provide an alternative for a helicopter au- tomatic flight control system. It is widely recognized that a robust control design can provide methods for addressing the control problems associated with poorly modeled sys-
Designed to fit the spectral properties Stochastic airwake model of the airwake Linear White noist shaping filter
+ Pilot stick inputs + Helicopter Dynamics
Optimized to reject disturbance SAS
Figure 5.1: Task-tailored control system design scheme CHAPTER 5. TASK-TAILORED CONTROL DESIGN 88 tems. These robust design methods use frequency information about the disturbances to limit the system sensitivity. However, there has not been implicit consideration of the effect that airwake disturbance would create. By incorporating practical knowledge about the disturbance characteristics, and how it affects the real helicopter, then improvements to the overall performance should be made.
5.2 Stochastic Airwake Modeling
From previous section, the time-accurate airwake model provided reasonable predictions of helicopter/ship dynamic interface testing. However, the use of time-accurate ship airwake data was found to present some practical implementation difficulties, in that the method requires that the simulation handle large quantities of data.
For every grid point a set of time history data must be stored for each component of velocity. Memory storage can become an issue, particularly if the simulations are to be run in real-time, in which case accessing data from disk storage may not be feasible. It was helpful to select a subset of the flow field when performing the simulations in which the landing spot is known. However, for real-time simulations the pilot might want to access different deck spots during the same simulation run.
The use of stochastic airwake model (based on the time-accurate CFD results) might be an attractive alternative. The stochastic airwake model can be designed using shaping
filters based on the statistical characteristics of the turbulent airwake. This approach of
finding an approximate airwake model promises to provide a better real-time application capability, and will ultimately be used to optimize the automatic flight control system in CHAPTER 5. TASK-TAILORED CONTROL DESIGN 89 order to improve disturbance rejection properties of the aircraft.
Methods of simulating the effects of gust on rotorcraft range from the straight forward approach of superimposing frozen-field turbulence models at the vehicle center of gravity
(the von Karman and Dryden approximations), as in fixed-wing aircraft, to complex rotating frame turbulence models (SORBET) [40]. Although including gust velocities at the center of gravity has obtained favorable pilot comments at high speeds, as the aircraft speed is decreased, this type of gust model has been criticized for its high frequency content and lack of variation. Improved pilot comment of simulated hover/low speed turbulence has been achieved through the implementation of complex rotating frame turbulence models
[33]. However, this type of model is not well suited for use in control system design.
To simulate the effects of an empirical turbulence on a rotorcraft, Labows developed a simple, empirically based turbulence model for UH-60 helicopter [34]. The turbulence model used white noise driven filters that were scalable with wind speed and turbulence intensity, to generate equivalent turbulent control inputs. These control inputs could then be fed directly into the aircraft to create equivalent actuator data traces, which generated aircraft roll and pitch rates that had spectral characteristics that were comparable to the spectral characteristics of measured rotorcraft rates from flight test in two levels of atmospheric turbulence. A technical approach similar to that used by Labows to extract equivalent airwake model is employed in this study.
In this study, the features of the airwake that primarily affect the flying qualities of the helicopter is wanted to characterize, while ignoring higher-order flow features that may only be responsible for vibration and other high frequency effects. Thus, the airwake is represented as a disturbance vector of 3 velocity and 3 angular rate components, similar CHAPTER 5. TASK-TAILORED CONTROL DESIGN 90 to the von Karman turbulence model. The current disturbance modeling process is similar to the process in Reference [34]. In that study, a disturbance model was developed by extracting the aircraft remnant rates due to atmospheric turbulence from flight test data.
The remnant rates were then put into an inverse model of the aircraft to create equivalent control inputs that could then be fed into the aircraft actuators to simulate response to turbulence.
The present disturbance modeling effort is different in that the equivalent disturbances are expressed in terms of body velocities and angular rates, and that the effort focuses specifically on modeling the gust velocities due to the turbulent wake of a ship’s super- structure. In this study, the nonlinear helicopter/ship DI simulation model discussed in the previous section is used to extract the ship airwake disturbances. Hover tasks for 30 knot, 0 degree and 30 degree WOD conditions were conducted over landing spot 8 on a LHA class ship (Figure 4.1). Similar to the method used in Reference [34], the first step in modeling procedure is to extract the remnant aircraft rates caused by the time-varying ship airwake.
The remnant rates are then filtered to reduce the effects of low frequency drift and high frequency noise. The overall schematic of current modeling process is shown in Figure 5.2.
A 9 state linearized model is used to create an inverse model in order to extract equivalent disturbances that recreate similar aircraft responses as the full airwake. The 9 rigid body state linear model and corresponding linear model without gust effects are given by
x˙ = Ax + Bu + Gw (5.1)
x˙ ng = Axng + Bu (5.2) CHAPTER 5. TASK-TAILORED CONTROL DESIGN 91
UH-60 Recorded Helicopter dynamic control position remnant rates model +
Recorded helicopter rate responses Inverse model Step 1 of UH-60 Step 2 Step 3 Check Design Equivalent airwake pilot inputs spectral filter disturbance that with CIFER cause remnant motions
Figure 5.2: Derivation of stochastic airwake disturbances
T T where x = [u,v,w,p,q,r,φ,θ,ψ] is rigid body states, w = [ug,vg,wg,pg, qg,rg] is the
equivalent airwake disturbance vector, and G represents a 9 6 gust matrix. By subtracting × Equation (5.1) from Equation (5.2), the remnant state model can be written as
r˙ = Ar + Gw (5.3)
where r = x x . Since G is not square, the equivalent disturbances can be obtained − ng using a pseudo-inverse method:
w = G+(˙r Ar) (5.4) −
where G+ is the left inverse of G. The resulting disturbance vector gives the best least
squares fit of the overall effect of the airwake on the aircraft. The three velocity components CHAPTER 5. TASK-TAILORED CONTROL DESIGN 92 of the gust vector represent the average gust velocity over the body of the aircraft, while the three angular velocity components represent a linear variation of the gust field over the body of the aircraft. More complex non-linear variation of the gust field over the body of the aircraft may not be captured, but it has been shown that this model would be sufficient for workload analysis [71].
The equivalent disturbance model is verified using autospectrum of aircraft roll, pitch, and yaw rate responses. There appears to be good agreement with the responses from the higher-order simulation model as presented in Figures 5.3, 5.4. In addition, the resultant pilot control inputs are analyzed using CIFER. The autospectra of pilot inputs caused by the equivalent airwake model are compared to the original control responses of full-time varying airwake model (Figures 5.5, 5.6). The results (Figures 5.3 - 5.6) are averaged over
5 different simulation runs for different airwake starting points (e.g. 0 sec, 8 sec, 16 sec,
24 sec, 32 sec). Comparisons indicated that the equivalent airwake produced very similar frequency content of full-time varying airwake.
The final step of the overall modeling process, is to simulate the airwake disturbances by passing zero mean white noise with variance one through spectral filters whose transfer function yield the desired power spectral density (PSD). In this study, the power spectral density function is based on the von Karman turbulence model and is modified to represent the ship airwake. The filters are approximations of the von Karman velocity-spectra that are valid in a range of normalized frequencies of less than 50 radians. These filters can be found in both the Military Handbook MIL-HDBK-1797 and Reference [72]. CHAPTER 5. TASK-TAILORED CONTROL DESIGN 93
Equivalent airwake Time-varying airwake
0
−20 P −40
−60 0 1 10 10 0
−20
Q −40
−60
0 1 10 10
−20
−40 R
−60
−80 0 1 10 10 Frequency, [rad/sec]
Figure 5.3: Comparisons of aircraft angular rates [dB] (time-varying airwake vs. equivalent airwake) - 0 degree WOD condition CHAPTER 5. TASK-TAILORED CONTROL DESIGN 94
Equivalent airwake Time-varying airwake
20
0
P −20
−40
0 1 10 10 20
0
Q −20
−40
0 1 10 10 20
0
R −20
−40
0 1 10 10 Frequency, [rad/sec]
Figure 5.4: Comparisons of aircraft angular rates [dB] (time-varying airwake vs. equivalent airwake) - 30 degree WOD condition CHAPTER 5. TASK-TAILORED CONTROL DESIGN 95
Equivalent airwake Time-varying airwake
−20
−40
Lateral −60
−80 0 1 10 10 −20
−40
−60
Longitudinal −80
0 1 10 10
−20
−40
−60 Collective −80 0 1 10 10 −20
−40
−60 Pedal −80
0 1 10 10 Frequency, [rad/sec]
Figure 5.5: Comparisons of pilot inputs [dB] (time-varying airwake vs. equivalent airwake) - 0 degree WOD condition CHAPTER 5. TASK-TAILORED CONTROL DESIGN 96
Equivalent airwake Time-varying airwake
0 −20 −40
Lateral −60 −80 0 1 10 10 0 −20 −40 −60
Longitudinal −80 0 1 10 10 0 −20 −40
Collective −60 −80 0 1 10 10 0 −20 −40
Pedal −60 −80 0 1 10 10 Frequency, [rad/sec]
Figure 5.6: Comparisons of pilot inputs [dB] (time-varying airwake vs. equivalent airwake) - 30 degree WOD condition CHAPTER 5. TASK-TAILORED CONTROL DESIGN 97
For example, the transfer function for the vertical gust component from von Karman turbulence model is given by:
2 Lw Lw Lw 4σw V 1 + 2.7478 V s + 0.3398 V s Hw(s)= q 2 3 (5.5) Lw Lw Lw 1 + 2.9958 V s + 1.9754 V s + 0.1539 V s where Lw represents scale length, the variable σw represents turbulence intensity, and V
is the reference airspeed. Because the von Karman model is typically used to represent
atmospheric turbulence at higher altitudes and speeds, it is not appropriate to model the
ship airwake. Thus, Equation (5.5) is slightly modified to produce the ship airwake power
spectral density for a white noise input.
2 Lw Lw Lw 4σw V 1+ b1 V s + b2 V s Hw(s)= q 2 3 (5.6) Lw Lw Lw 1+ a1 V s + a2 V s + a3 V s where the coefficients an (n = 1, 2, 3), bm (m = 1, 2) are obtained from a best fit to the
vertical airwake gust PSD data using nonlinear least-square fitting algorithm automated in
MATLAB.
Figure 5.7 shows the power spectral density for the vertical component of airwake dis-
turbance model for the 30 knots, 0 degree WOD condition (17 ft above landing spot 8).
The results shown in this paper are for V = 30 knots (50.6343 ft/sec) since the aircraft is
hovering in a 30 knot relative wind. And the coefficients of the “best fit” spectral filter in
Equation (5.6) are Lw = 12.56 ft, σw = 16.03 ft/sec, a1 = 11.01, a2 = 7.66, a3 = 9.78, b1 = 0.56, and b2 = 0.13. The resulting PSD of the spectral filter overlays well in the region of frequency range of 0.2 20 rad/sec. A similar process is applied to the other ∼ CHAPTER 5. TASK-TAILORED CONTROL DESIGN 98
five airwake components. Figures 5.8 - 5.13 show the resulting PSD of 6 gust components
([ug,vg,wg,pg, qg,rg]) for 30 knot, 30 degree WOD condition. Table 5.1 shows the final gust shaping filters for 0 and 30 degree WOD conditions.
The white noise source utilized herein is a random number generator with a mean of zero and a variance of 1 for each airwake component. The resulting autospectra of angular rate responses for 0 degree and 30 degree WOD conditions are plotted in Figures 5.14 -
5.15. The autospectra of pilot inputs caused by the stochastic airwake model are compared to the original control responses of full-time varying airwake model (Figures 5.16, 5.17).
The resulting frequency domain analyses show good fits over the frequency range of 0.4 ∼ 10.0 rad/sec, supporting the current stochastic airwake modeling scheme.
Best Fit Spectral Filter
2
Extracted from simulation with full time-varying airwake
PSD of vertical gust component, [(ft/sec) /(rad/sec)]
Frequency, [rad/sec]
Figure 5.7: Power spectral density for vertical airwake disturbance component (30 knot, 0 degree WOD condition) CHAPTER 5. TASK-TAILORED CONTROL DESIGN 99
Best Fit Spectral Filter
2
Extracted from simulation with full time-varying airwake
PSD of longitudinal gust component, [(ft/sec) /(rad/sec)] Frequency, [rad/sec]
Figure 5.8: Power spectral density of longitudinal airwake disturbance component (30 knot, 30 degree WOD condition) CHAPTER 5. TASK-TAILORED CONTROL DESIGN 100
Best Fit Spectral Filter
2
Extracted from simulation with full time-varying airwake
PSD of lateral gust component, [(ft/sec) /(rad/sec)]
Frequency, [rad/sec]
Figure 5.9: Power spectral density of lateral airwake disturbance component (30 knot, 30 degree WOD condition) CHAPTER 5. TASK-TAILORED CONTROL DESIGN 101
Best Fit Spectral Filter
2
Extracted from simulation with full time-varying airwake
PSD of vertical gust component, [(ft/sec) /(rad/sec)]
Frequency, [rad/sec]
Figure 5.10: Power spectral density of vertical airwake disturbance component (30 knot, 30 degree WOD condition) CHAPTER 5. TASK-TAILORED CONTROL DESIGN 102
Best Fit Spectral Filter
2
Extracted from simulation with full time-varying airwake
PSD of roll gust component, [(rad/sec) /(rad/sec)]
Frequency, [rad/sec]
Figure 5.11: Power spectral density of roll airwake disturbance component (30 knot, 30 degree WOD condition) CHAPTER 5. TASK-TAILORED CONTROL DESIGN 103
Best Fit Spectral Filter
2
Extracted from simulation with full time-varying airwake
PSD of pitch gust component, [(rad/sec) /(rad/sec)]
Frequency, [rad/sec]
Figure 5.12: Power spectral density of pitch airwake disturbance component (30 knot, 30 degree WOD condition) CHAPTER 5. TASK-TAILORED CONTROL DESIGN 104
Best Fit Spectral Filter
2
Extracted from simulation with full time-varying airwake
PSD of yaw gust component, [(rad/sec) /(rad/sec)]
Frequency, [rad/sec]
Figure 5.13: Power spectral density of yaw airwake disturbance component (30 knot, 30 degree WOD condition) CHAPTER 5. TASK-TAILORED CONTROL DESIGN 105
Table 5.1: Gust shaping filters for 0 degree and 30 degree WOD conditions
Gust component 0 degree WOD 30 degree WOD
0.1042s2+2.3588s+19.1603 14.2261s2+306.1786s+198.2738 Hu(s) 0.1075s3+.1741s2+2.5696s+1 2.8484s3+2.3466s2+11.2279s+1
0.0838s2+0.5626s+12.9292 0.3103s2+3.6789s+94.2622 Hv(s) 0.0402s3+0.2108s2+1.2048s+1 0.0257s3+0.4211s2+1.0154s+1
0.2475s2+4.4454s+31.9292 11.3834s2+409.0059s+433.3580 Hw(s) 0.1494s3+0.4718s2+2.7311s+1 1.6950s3+0.9448s2+12.5721s+1
1.2591s2+24.3807s+0.3617 0.0628s2+0.4665s+25.4193 Hp(s) 105.3086s3+94.7148s2+738.2469s+1 0.4983s3+5.5760s2+20.4112s+1
3.3859s2+49.8481s+0.5244 0.0475s2+0.3093s+11.5695 Hq(s) 192.6s3+279.4s2+1015.8s+1 0.1955s3+2.5249s2+7.0773s+1
0.0763s2+0.6526s+9.4927 0.0115s2+0.1520s+4.7283 Hr(s) 0.7871s3+1.8020s2+24.0094s+1 0.0069s3+0.2645s2+0.3370s+1 CHAPTER 5. TASK-TAILORED CONTROL DESIGN 106
Stochastic airwake Equivalent airwake Time-varying airwake
0
−20
P −40
−60
0 1 10 10 0
−20
Q −40
−60
0 1 10 10 0
−20
R −40
−60
0 1 10 10 Frequency, [rad/sec]
Figure 5.14: Comparisons of aircraft angular rates [dB] (time-varying airwake vs. equivalent airwake vs. stochastic airwake) - 30 knot, 0 degree WOD condition CHAPTER 5. TASK-TAILORED CONTROL DESIGN 107
Stochastic airwake Equivalent airwake Time-varying airwake
20
0
−20 P −40
−60
0 1 10 10 20
0
−20 Q −40
−60
0 1 10 10 20
0
−20 R −40
−60
0 1 10 10 Frequency, [rad/sec]
Figure 5.15: Comparisons of aircraft angular rates [dB] (time-varying airwake vs. equivalent airwake vs. stochastic airwake) - 30 knot, 30 degree WOD condition CHAPTER 5. TASK-TAILORED CONTROL DESIGN 108
Stochastic airwake Equivalent airwake Time-varying airwake
0 −20 −40
Lateral −60 −80 0 1 10 10 0 −20 −40 −60
Longitudinal −80 0 1 10 10 0 −20 −40
Collective −60 −80 0 1 10 10 0 −20 −40
Pedal −60 −80 0 1 10 10 Frequency, [rad/sec]
Figure 5.16: Comparisons of pilot inputs [dB] (time-varying airwake vs. equivalent airwake vs. stochastic airwake) - 30 knot, 0 degree WOD condition CHAPTER 5. TASK-TAILORED CONTROL DESIGN 109
Stochastic airwake Equivalent airwake Time-varying airwake
0 −20 −40 Lateral −60 −80 0 1 10 10 0 −20 −40 −60 Longitudinal −80 0 1 10 10 0 −20 −40
Collective −60 −80 0 1 10 10 0 −20 −40 Pedal −60 −80 0 1 10 10 Frequency, [rad/sec]
Figure 5.17: Comparisons of pilot inputs [dB] (time-varying airwake vs. equivalent airwake vs. stochastic airwake) - 30 knot, 30 degree WOD condition CHAPTER 5. TASK-TAILORED CONTROL DESIGN 110
5.3 Optimization of a Stability Augmentation System
Previous studies showed that with an increasing magnitude of disturbance responses, an increasing pilot compensation level was required to achieve desired task performance [34,
68, 69]. If the flight control system has satisfactory handling qualities in a disturbance- free environment, these results indicate that to meet desired performance in a turbulent environment an additional design criteria must be required. Currently, the disturbance rejection requirements in ADS-33E-PRF state that roll, pitch, and yaw responses to control inputs shall meet the bandwidth threshold limits based on aircraft response to pilot stick inputs [67]. However, there has not been an effort to optimize the control parameters to reduce pilot workload.
An effort to optimize the automatic flight control system is attempted in order to improve disturbance rejection properties of the helicopter when operating in the turbulent ship airwake. This can be achieved by minimizing the magnitude of the transfer function from the gust shaping filter input to the aircraft response. In this work, the gains of a basic stability augmentation system are optimized using CONDUIT in order to ensure good handling-qualities and stability, while minimizing a weighted objective of gust response and actuator energy. CONDUIT is a “state-of-the-art” computational tool for integrating simulation models and control law architectures with design specifications and constraints for modern fixed-wing and rotary-wing aircraft. In addition, CONDUIT allows for the optimization of multiple objectives with multiple constraints by tuning a set of selected design parameters (e.g. controller gains, time constants, etc.). Details of the CONDUIT design environment can be found in References [73] and [74]. CHAPTER 5. TASK-TAILORED CONTROL DESIGN 111
The case problem is based on the flight dynamics of a UH-60 Black Hawk helicopter
(Figure 5.18). The key elements of the block diagram are:
24-state linear model of UH-60 •
ship airwake spectral filters •
helicopter SAS •
washed-out pitch and yaw channel feedback •
analog-to-digital filter for roll, pitch, yaw sensors •
longitudinal acceleration feedback control •
pitch attitude feedback control •
In this study, the digital SAS of the UH-60A is used as a starting design point and for comparisons in this study (it is assumed to have 10% authority). In low speed mode, this
SAS features roll, pitch, and yaw rate feedback through separate SAS channels. The roll
SAS also includes limited authority roll attitude feedback. The compensators use a rate plus lagged rate feedback approach, which is essentially equivalent to a phase-lag compensator.
The pitch and yaw channels also include washout filters to reduce steady-state feedback in prolonged maneuvers.
In the modified SAS, longitudinal acceleration feedback and pitch attitude feedback are added as shown in Figure 5.18. The acceleration feedback is expected to improve gust response, while pitch attitude feedback is added to provide closed-loop stability at low speed. Figure 5.19 shows a schematic of the modified SAS architecture. The compensators CHAPTER 5. TASK-TAILORED CONTROL DESIGN 112
Figure 5.18: Augmented plant model for a SAS optimization are put in the classical phase-lag form. In addition, a phase lead/lag type controller is added to the roll channel. The SAS gains, the lead/lag time constants, and the pitch attitude and longitudinal acceleration feedback parameters are all selected as design parameters to be optimized using CONDUIT. In the diagrams, these design parameters include the prefix
“dpp ”. The analog-to-digital filters and washout filters from the original SAS are retained and not modified in the optimization process.
In this paper, four design specs are selected from the CONDUIT libraries as constraints.
The relative priority of each spec is designated as indicated by “Hard specifications (H)” indicated in the upper right corner of the spec. The role of the spec priority in the CON-
DUIT optimization process is described fully in Reference [73]. In summary, the “hard CHAPTER 5. TASK-TAILORED CONTROL DESIGN 113
Figure 5.19: Modified SAS configuration specification” selected for this study are:
Crossover frequencies for the individual broken loops (CrsLnG1) : • This specification is intended as an objective to minimize crossover frequency in phase
3. The boundaries should be set to ensure that the design is in the Level 1 region for
phase 1 and 2.
All closed-loop eigenvalues (absolute stability) (EigLcG1) : • This criterion is used to ensure that all the real parts of the eigenvalues of the system
are zero or negative, ensuring that all the dynamics are stable or neutrally stable. At
any given iteration, the sum of unstable eigenvlaue real parts or the largest stable
eigenvalue is returned as the spec metric.
Gain/phase margin requirement (StbMgG1) : • This spec has logic for treating stable, conditionally stable, and unstable systems. It CHAPTER 5. TASK-TAILORED CONTROL DESIGN 114
also has logic for correctly accounting for right-half plane poles and zeros. A table of
margins is built for all crossings of the 0db and -180 deg lines and displayed in the
supporting plot. The spec returns the minimum gain and phase margin values from
the table. The Level I boundaries are taken from MIL-F-9490D. In this document
that required margins depend on the frequency of the first aeroelastic mode and on
the airspeed. In the CONDUIT gain/phase margin spec, the requirements for rigid
body modes is implemented. Stability margin specs for other frequency ranges are
easily implemented by shifting the splines.
Bandwidth requirement for roll/pitch axes (BnwAtH1) : • The pitch (roll) response to longitudinal (lateral) cockpit control force or position
inputs shall meet the limits specified. It is desirable to meet this criterion for both
controller force and position inputs. If the bandwidth for force inputs falls outside
the specified limits, flight testing should be conducted to determine that the force feel
system is not excessively sluggish.
The crossover frequency spec (CrsLnG1) is generally intended as an objective to minimize feedback control activity in the last phase of optimization. However, the current design ob- jective is not to minimize control activity, but rather to minimize disturbance response while retaining similar crossover frequencies as the original SAS. Thus, the crossover frequency spec is enforced as constraints in the optimization.
A new spec (DisRnL1) for disturbance rejection is designed based on the PSD of angular rate response to corresponding gust input. Here, the design parameters are tuned to attempt to minimize the magnitude of the transfer function from the gust shaping filter input to the CHAPTER 5. TASK-TAILORED CONTROL DESIGN 115
Level III Transfer function White Level II q(s) PSD noise H (s) = qg (s) Magnitude [dB] Level I Frequency [rad/sec]
Figure 5.20: A new disturbance rejection spec design (ex. pitch axis) aircraft response. Figure 5.20 shows a schematic of the proposed disturbance rejection spec.
This new spec is designated as a “summed objective specification (J)”. The use of summed objective allows the optimization process to improve a set specific performance objectives of the controllers while maintaining compliance with Level 1 requirements. Currently, the boundaries for Level 1/Level 2 and Level 2/Level 3 are selected arbitrarily for this spec since there are no supporting data for the disturbance rejection requirements in ADS-33 at this time. This is sufficient for the current analysis, the level boundaries are simply used to provide a measure of how well gust disturbances are rejected and are not used as constraints. Note that the new spec for roll axis has more generous level boundaries as the aircraft is inherently more sensitive in roll due to lower inertia in that axis.
Figure 5.21 shows the performance of the original SAS for the selected design specs.
The blue region reflects Level 1 handling qualities ratings, the magenta region represents
Level 2, and the red region reflects Level 3 handling qualities. Note that the basic UH-
60A SAS does not fully stabilize the aircraft in hover and low speed flight. There is a low frequency unstable mode. The mode can be stabilized by the outer loop Flight Path
Stabilization system (FPS) which is not considered in this analysis. Closed loop stability CHAPTER 5. TASK-TAILORED CONTROL DESIGN 116 is not necessarily required to achieve Level 1 or Level 2 handling qualities, but nonetheless the eigenvalues and stability margin (pitch axis) specs identify any instability as “Level 3”.
The disturbance rejection requirements defined for this study show Level 3 for pitch and yaw axes and Level 2 behavior for roll axis, although as noted before these boundaries are somewhat arbitrary.
For the optimization process, only the 30 degree WOD condition is considered. The optimized SAS is then tested using non-linear simulation for both 0 and 30 degree WOD conditions. This is a logical approach since the 30 degree WOD condition resulted in significant higher pilot workload [60].
After several iterations CONDUIT reaches the final phase, which is a “feasible solution” where all specs are in the Level 1 region. Figure 5.22 shows the fully converged result. The
CrsLnG1:Crossover Freq. EigLcG1: StbMgG1: Gain/Phase Margins Roll (1) Roll (1) (linear scale) Eigenvalues (All) (rigid−body freq. range) H H H Pitch (2) Pitch (2) 80
Yaw (3) Yaw (3) 60
CrsLnG1 (1) 40 PM [deg] CrsLnG1 (2) 20 CrsLnG1 (3)
EigLcG1 (1) Ames Research Center Ames Research Center 0 MIL−F−9490D 0 5 10 15 20 −1 0 1 0 10 20 EigLcG1 (2) Crossover Frequency [rad/sec] Real Axis GM [db] EigLcG1 (3) BnwAtH1:Bandwith (pitch & roll) DisRnL2:Gust Response DisRnL1:Gust Response Other MTEs;UCE>1; Div Att Roll Pitch/Yaw 0.4 40 40 StbMgG1 (1) H J J 20 StbMgG1 (2) 20 0.3 0 StbMgG1 (3) 0 −20 BnwAtH1 (1) 0.2 −40 BnwAtH1 (2) −20 Magnitude [db] Magnitude [db] −60 Phase delay [sec] 0.1 DisRnL1 (2) −40 −80 DisRnL1 (3) 0 ADS−33D −60 PSU RCOE −100 PSU RCOE 0 1 0 1 DisRnL2 (1) 0 1 2 3 4 10 10 10 10 Bandwidth [rad/sec] Frequency [rad/sec] Frequency [rad/sec]
Figure 5.21: HQ windows for the original SAS configuration - 30 knot, 30 degree WOD CHAPTER 5. TASK-TAILORED CONTROL DESIGN 117 disturbance rejection properties are improved and moved into Level 1 for the gust rejection spec. Closed loop stability is also achieved, due to the addition of pitch attitude feedback.
The crossover frequency for each axis is increased somewhat. The optimization effectively resulted in higher gain in all three axes, so it will be necessary to check that the increased gain does not result in rate or position saturations. Note that the stability margins in the roll axis are reduced and are against the 6 dB and 45◦ gain and phase margin Level
1 constraints. This is because the optimization tends to increase the roll axis gain until it hit stability margin limits. The stability limits on maximum roll gain are due to rotor- body coupling issues that are typically observed on helicopters with articulated rotors. The disturbance rejection requirements would probably drive the crossover frequencies and roll and yaw feedback gains higher if it were not for this stability constraint. It is found that
CrsLnG1:Crossover Freq. EigLcG1: StbMgG1: Gain/Phase Margins Roll (1) Roll (1) (linear scale) Eigenvalues (All) (rigid−body freq. range) H H H Pitch (2) Pitch (2) 80
Yaw (3) Yaw (3) 60
CrsLnG1 (1) 40 CrsLnG1 (2) PM [deg] CrsLnG1 (3) 20
EigLcG1 (1) Ames Research Center Ames Research Center 0 MIL−F−9490D 0 5 10 15 20 −1 0 1 0 10 20 EigLcG1 (2) Crossover Frequency [rad/sec] Real Axis GM [db] EigLcG1 (3) BnwAtH1:Bandwith (pitch & roll) DisRnL2:Gust Response DisRnL1:Gust Response Other MTEs;UCE>1; Div Att Roll Pitch/Yaw 0.4 40 40 StbMgG1 (1) H J J 20 StbMgG1 (2) 20 0.3 0 StbMgG1 (3) 0 −20 BnwAtH1 (1) 0.2 −40 BnwAtH1 (2) −20 Magnitude [db] Magnitude [db] −60 Phase delay [sec] 0.1 DisRnL1 (2) −40 −80 DisRnL1 (3) 0 ADS−33D −60 PSU RCOE −100 PSU RCOE 0 1 0 1 DisRnL2 (1) 0 1 2 3 4 10 10 10 10 Bandwidth [rad/sec] Frequency [rad/sec] Frequency [rad/sec]
Figure 5.22: HQ windows for the optimized SAS configuration - 30 knot, 30 degree WOD CHAPTER 5. TASK-TAILORED CONTROL DESIGN 118 using a lead-lag type compensator resulted in some improvement in the optimization of the roll axis, as compared to the original lag compensator.
The ability to achieve an optimized solution is quite sensitive to the initial values for the design parameters. If the design parameters are started too far from a feasible solution, the optimization tends to wander and often does not reach a satisfactory result because there are too many design parameters to tune. It is possible that the problem is somewhat over- parameterized. Future work might focus on reducing the number of controller parameters to achieve a more robust optimization.
The optimized SAS is converted to discrete form and tested using the non-linear simula- tion model for the hovering operation on the spot 8 (included time-varying airwake solutions for 0 and 30 degree WOD conditions). Figure 5.23 and 5.26 show the responses of aircraft angular rate for 0 degree and 30 degree WOD conditions. The solid lines represent the results with optimized SAS, the dotted lines are simulation results with the baseline SAS configuration. The corresponding pilot stick inputs (generated by an optimal control model of the human pilot) are shown in Figures 5.24 and 5.27. The results with an optimized SAS show some significant improvement over the original SAS. The aircraft roll rate and lateral stick input are only slightly improved, due to the limits on the roll axis gain discussed above and the fact that the aircraft gust response is more sensitive in roll. Nonetheless the overall aircraft angular rates and pilot control inputs are reduced with the optimized SAS for both 0 and 30 degree WOD conditions. Note that there is no attempt to optimize the control system for heave axis. Figures 5.25 and 5.28 show the response of SAS outputs. The optimized SAS appears to result in slightly higher SAS actuator activity in the 0 degree
WOD condition, while the magnitude and frequency of the SAS actuator activity in the CHAPTER 5. TASK-TAILORED CONTROL DESIGN 119
30 degree WOD condition is similar to the baseline SAS. In both cases, the SAS actuators stayed well within the rate and position saturation limits. Note that the difference in the roll SAS outputs in 0 degree WOD case is mainly due to the small roll attitude feedback gain from the optimized SAS.
Figures 5.29 and 5.30 show comparisons of input autospectra from pilot stick inputs. In this study, 4 different window sizes (3, 5, 10, and 15 seconds) are used in the FFT analysis to obtain a composite average that is accurate over a range of frequencies. From the figures, it can be observed that the optimized SAS shows some improvement over the original SAS configuration in the frequency range of 1 to 10 rad/sec. It is generally recognized that control activity in the frequency range of 0.2 to 2 Hz (about 1.2 12 rad/sec) has significant impact ∼ on pilot workload [60]. CHAPTER 5. TASK-TAILORED CONTROL DESIGN 120
Results with the original SAS Results with the optimized SAS
0.5
0 P −0.5
−1
0 5 10 15 20 25 30 35 40
0.5
Q 0
−0.5 0 5 10 15 20 25 30 35 40
0.4
0.2
R 0
−0.2
−0.4 0 5 10 15 20 25 30 35 40 Time, [sec]
Figure 5.23: Aircraft angular rate responses [deg/sec] - 30 knot, 0 degree WOD CHAPTER 5. TASK-TAILORED CONTROL DESIGN 121
Results with the original SAS Results with the optimized SAS
0.5
0 Lateral −0.5
0 5 10 15 20 25 30 35 40 0.5 0 −0.5 −1 Longitudinal
0 5 10 15 20 25 30 35 40
1
0 Collective −1 0 5 10 15 20 25 30 35 40
0.5
0 Pedal −0.5
0 5 10 15 20 25 30 35 40 Time, [sec]
Figure 5.24: Pilot control stick inputs [%] - 30 knot, 0 degree WOD CHAPTER 5. TASK-TAILORED CONTROL DESIGN 122
Results with the original SAS Results with the optimized SAS
1.5
1
0.5 RSAS 0
−0.5 0 5 10 15 20 25 30 35 40
1
0
PSAS −1
−2 0 5 10 15 20 25 30 35 40
1
0.5
0 YSAS −0.5
−1 0 5 10 15 20 25 30 35 40 Time, [sec]
Figure 5.25: SAS outputs [%] - 30 knot, 0 degree WOD CHAPTER 5. TASK-TAILORED CONTROL DESIGN 123
Results with the original SAS Results with the optimized SAS
4 2 0
P −2 −4 −6
0 5 10 15 20 25 30 35 40
4
2
Q 0
−2
−4 0 5 10 15 20 25 30 35 40
4
2
R 0
−2
−4 0 5 10 15 20 25 30 35 40 Time, [sec]
Figure 5.26: Aircraft angular rate responses [deg/sec] - 30 knot, 30 degree WOD CHAPTER 5. TASK-TAILORED CONTROL DESIGN 124
Results with the original SAS Results with the optimized SAS
5
0 Lateral −5 0 5 10 15 20 25 30 35 40 4 2 0 −2 −4 Longitudinal −6 0 5 10 15 20 25 30 35 40
5 0 −5 Collective −10 0 5 10 15 20 25 30 35 40 4 2 0 −2
Pedal −4 −6 −8 0 5 10 15 20 25 30 35 40 Time, [sec]
Figure 5.27: Pilot control stick inputs [%] - 30 knot, 30 degree WOD CHAPTER 5. TASK-TAILORED CONTROL DESIGN 125
Results with the original SAS Results with the optimized SAS
10
5
RSAS 0
−5 0 5 10 15 20 25 30 35 40
5
0
PSAS −5
−10 0 5 10 15 20 25 30 35 40
10
5
0 YSAS −5
−10 0 5 10 15 20 25 30 35 40 Time, [sec]
Figure 5.28: SAS outputs [%] - 30 knot, 30 degree WOD CHAPTER 5. TASK-TAILORED CONTROL DESIGN 126
Results with the original SAS Results with the optimized SAS
Figure 5.29: Control stick input autospectra [dB] - 30 knot, 0 degree WOD CHAPTER 5. TASK-TAILORED CONTROL DESIGN 127
Results with the original SAS Results with the optimized SAS
Figure 5.30: Control stick input autospectra [dB] - 30 knot, 30 degree WOD CHAPTER 5. TASK-TAILORED CONTROL DESIGN 128
5.4 H Control of a Helicopter SAS ∞
It is widely agreed that high levels of feedback augmentation will be needed, if the enhanced
flying qualities required of the next generation or current rotorcraft are to be realized. The use of modern multivariable control analysis tools such as robust control method allows a more rigorous analysis and, consequently, improved stability robustness of the closed- loop system. The design of robust control laws for a helicopter is, however, difficult due to several factors: parametric and structural uncertainty in the model caused by the limitation of current flight-mechanic models to predict helicopter response to control and disturbance inputs.
Robust control theory has evolved since the early 1980s and provides methods for ad- dressing the control problems associated with poorly modeled systems. Methodologies such as H∞ optimization now provide systematic procedures for designing robust controllers for multivariable system. The H∞ design method generates optimal controllers that provide
good performance even when the characteristics of the plant are not modeled exactly or are
varying periodically with time. Frequency-dependent weighting functions are included in
the performance index. It is not necessary to measure or estimate the entire state vector.
The singular value loop shapes are directly prescribed to meet performance and robustness
bounds formulated in the frequency domain.
Recently, the DERA (Defence Evaluation and Research Agency) Bedford have been
collaborating to narrow the gap between the theoretical developments in Robust Control
and the more practical problems associated with designing helicopter flight control systems
meeting exacting flying-qualities requirements in ADS-33 [75, 76, 77]. Earlier work from CHAPTER 5. TASK-TAILORED CONTROL DESIGN 129
DERA has focused on the Westland Lynx. Yue and Postlethwaite designed H∞ based
controller based on the HELISIM model. That work led to successful piloted simulation,
through which the potential of H∞ based design methods was clearly demonstrated [75].
Building on those results, Walker et al. designed single and two-degree-of-freedom H∞
controllers which were extensively evaluated in the DERA Bedford Large Motion simulator
[76, 77]. Desired handling qualities ratings were consistently obtained during aggressively
performed Mission Task Elements in ground-based simulation on the Lynx model of a
series of two-degree-of-freedom controllers. The limitations of ground-based simulation
were, however, recognized, and it was concluded that appropriately validated mathematical
models containing higher order dynamics would be important if similar results were to be
replicated in flight [77].
In this study, the design of flight controller on the UH-60A is described. It presents a
critical assessment of the use of H∞ control in the design of robust flight controllers for the
UH-60A operating in the turbulent ship airwake conditions. The emphasis in the design
is to meet stringent U.S. Army handling qualities specifications (ADS-33, [67]) against the
constraint of robust stability to plant disturbances. The brief review of H∞ controller
design will be given in the section 5.4.1. In Section 5.4.2, the helicopter control problem is
formulated and evaluated using nonlinear DI simulation program.
5.4.1 Review of H∞ Control Design Method
Every control system is constantly subject to command-disturbance input uncertainties
and plant uncertainties. The issue of robust control is to design a controller such that
the closed-loop system remains stable for all possible plant perturbations, and that the CHAPTER 5. TASK-TAILORED CONTROL DESIGN 130 response is admissible for every disturbance and command in the prescribed set under all possible plant perturbations. The prescribed set of disturbances and commands is modeled by the designer according to the actual environment of the system. For many practical control problems, the external input signals are not known precisely, but instead belong to a prescribed norm-bounded (energy-bounded) set. In this case, it is more meaningful for a design engineer to minimize the maximum error (worst case) that can occur subject to all possible input signals belonging to this set. This min-max approach (H∞ control law) was
introduced for feedback design from a frequency-domain point of view [78]. Since then, this
research area has attracted many researchers and significant progress has been made. The
basic formulation can be found in various textbooks and articles [7, 78, 79].
Mathematically, H∞ controller design is a frequency-dependent optimization problem.
Therefore all design specifications need to expressed in the frequency domain. This is not
always straightforward, particularly for time-domain specifications, but the approach is
ideally suited for robustness considerations. In the optimization procedure, a controller is
selected which stabilizes a nominal plant model and minimizes the energy gain (H∞ norm)
of a closed-loop transfer function which describes the design objectives.
Figure 5.31 shows the standard compensator configuration. In here, G(s) is a system
with two kinds of inputs and two kinds of outputs. The input ω is an exogenous input
representing the disturbance acting on the system. The output z is an output of the
system, whose dependence on the exogenous input ω to be minimized. The output y is a
measurement, which is used to choose the input u, which in turn is the tool to minimize
the effect of ω on z. A constraint is that this mapping from y to u should be such that the
close-loop system is internally stable. This is quite natural since the states are not wanted CHAPTER 5. TASK-TAILORED CONTROL DESIGN 131 to become too large while regulating the performance. The effect of ω on z after closing the
loop is measured in terms of the energy and the worst disturbance ω. The measurement,
which will turn out to be equal to the closed-loop H∞ norm, is the supremum over all
disturbances unequal to zero of the quotient of the energy flowing out of the system and
the energy flowing into the system.
w z G(s)
y u K(s)
Figure 5.31: Standard compensator configuration
The H norm of a stable transfer function matrix G(s), denoted G(s) , is the max- ∞ k k∞ imum over all frequencies of the largest singular value of the frequency response G(jω). Its
power stems from two important results:
(1) A sufficient condition for closed-loop stability to be robust against a set of plant
perturbation is given by a bound on the H∞ norm of a stable closed-loop transfer
function (model uncertainty problem).
(2) The H∞ norm of a stable transfer function matrix represents a bound on the maximum
energy gain from the input signal to the output (mixed sensitivity problem).
For the model uncertainty problem, consider the feedback system in Figure 5.32, where
the uncertainty in the nominal plant model G(s) is represented by an additive perturbation CHAPTER 5. TASK-TAILORED CONTROL DESIGN 132
D(s)
+ + K(s) G(s) + -
Figure 5.32: Additive perturbation
∆(s). Suppose, for simplicity, that ∆(s) is stable and that ∆(s)W (s) 1 where W (s) k k∞ ≤ is a weight which represents the variation of uncertainty with frequency and also normalizes the H∞ norm of the uncertainty to a maximum of 1. Then the perturbed feedback system is
stable if the nominal feedback system (∆(s) = 0) is stable and W −1K(I + GK)−1 < 1. k k∞ Therefore, minimizing W −1K(I + GK)−1 over the set of all stabilizing controllers for k k∞ G(s) maximizes the margin of stability.
The mixed sensitivity problem is a special kind of H∞ control problem. In the mixed
sensitivity problem it is assumed that the system under consideration can be written as
the interconnection where K(s) is the controller which has to satisfy certain prerequisites.
Consider the feedback configuration shown in Figure 5.33, the problem is to regulate the
d(s)
u(s)+ y(s) r(s) + K(s) G(s) + -
Figure 5.33: Disturbance rejection at the plant output CHAPTER 5. TASK-TAILORED CONTROL DESIGN 133 output y(s) of the system G(s) to look like some given reference signal r(s) by designing a
precompensator K(s) which has as its input the error signal, i.e. the input of the controller is
the difference between the output y(s) and the reference signal r(s). To prevent undesirable
surprises internal stability is required. Then the problem can be formulated as “minimizing”
the transfer function from r(s) to r(s) y(s). As one might expect we shall minimize the −
H∞ norm of this transfer function under the constraint of internal stability. The transfer
matrix from r(s) to u(s) should also be under consideration. In practice the process inputs
will often be restricted by physical constraints. This yields a bound on the transfer matrix
from r(s) to u(s). These transfer matrices from r(s) to r(s) y(s) and from r(s) to u(s) − are given by:
S := (I + GK)−1 (5.7)
T := K(I + GK)−1 (5.8)
Here S is called the sensitivity function and T is called the control sensitivity function. A
small function S expresses good tracking properties while a small function T expresses small
inputs u(s). Note that there is a trade-off: making S smaller will in general make T larger.
Figure 5.34 shows the general form of the mixed sensitivity problem. An external input
w is added to the output y(s) as in Figure 5.34. Then the transfer matrix from ω(s) to
y(s) is equal to the sensitivity matrix S and the transfer matrix from ω(s) to u(s) is equal
to the control sensitivity matrix T . As noted in previous paragraph the H∞ norm can be
viewed as the maximum amount of energy coming out of the system, subject to inputs with
unit energy. However, if the Laplace transform is applied, then we obtain a frequency- CHAPTER 5. TASK-TAILORED CONTROL DESIGN 134
z1 (s) d(s)
W1 (s) Wd (s)
w(s)
+ u(s) + + y(s) r(s) K(s) G(s) W (s) z2 (s) - 2
Figure 5.34: General block diagram of the mixed sensitivity problem
domain characterization. For a SISO system the H∞ norm is equal to the largest distance
of a point on the Nyquist contour to the origin. Hence the H∞ norm is a uniform bound
over all frequencies on the transfer function. It is assumed that the tracking signal will
have a limited frequency spectrum. It is in general impossible to track signals of very high
frequency reasonably well. On the other hand, since in general the model is only accurate
up to a certain frequency, the system is only required to track signals of frequencies up to a
certain bandwidth. In this situation straightforward application of H∞ control might yield
bad results because it only investigates a uniform bound over all frequencies. Also, certain
frequencies may be more important than others for the error signal and the control input.
Thus in Figure 5.34, the systems W1(s), W2(s), Wd(s) are weighting functions which are
chosen in such a way that we put more effort in regulating frequencies of interest than one
uniform bound. For practical purposes the choice of these weights is extremely important.
For SISO systems expressing performance criteria into requirements on the desired shape
of the magnitude Bode diagram is well established. This immediately translates into the
appropriate choice for the weighting functions. On the other hand, for MIMO systems CHAPTER 5. TASK-TAILORED CONTROL DESIGN 135 it is in general very hard to translate practical performance criteria into an appropriate choice for the weighting functions. It should be noted that in practical circumstances it is often better to minimize the integrated tracking error. This can also be incorporated in the weighting functions and is simply one way to emphasize the interest in tracking signals of low frequency.
In this way, the interconnection system from Figure 5.34 can be obtained. Note that the transfer function matrix from the disturbance d(s) to z1 and z2 is:
W1TWd G˜(s)= (5.9) W2SWd Note that these weighting functions can be used to stress the relative importance of min-
imizing the sensitivity matrix S with respect to the importance of minimizing the control
sensitivity matrix T by multiplying W1(s) by a scalar. The solution to this problem is
now well understood and can be computed automatically within a computer-aided design
package such as Matlab/Robust control toolbox [80].
5.4.2 Design of H∞ Controller for a Helicopter SAS
This section presents an application of H∞ optimization to the design of the SAS for a
UH-60A utility helicopter and illustrates how practical problems may be formulated in the
H∞ framework. Particular attention is paid to the presence of the external disturbance and
the motivation behind the selection of the weighting functions. Attention will be restricted
to designing a fixed-gain linear controller which is able to both stabilize the closed-loop
system and maintain some nominal performance in the hovering flight. CHAPTER 5. TASK-TAILORED CONTROL DESIGN 136
The H∞ optimization framework used here is shown in Figure 5.35. The main steps in the design process are: (i) augmentation of the plant P (s) at input and output with weighting functions We, Wu and gust filter Wg; (ii) synthesis of stabilizing controller K∞
minimizing the H∞ norm of the transfer function from (dg, w) to (u, y, eu, ee).
The aircraft model used here is a 8-state/6 degree-of-freedom linear model extracted
from the non-linear simulation model. The plant output y is the aircraft angular rate
responses (p, q, r) and H∞ controller produces corresponding SAS outputs (u) for lateral
(rsas) and longitudinal (psas) cyclic and pedal collective (ysas). The inputs for the gust shaping filter (Wg(s)) are zero-mean white noise with a variance of 1. The same gust shaping filters from previous section 5.2 are used, in here only 30 degree WOD condition is considered. In this case, if the pseudo-inverse of the plant distribution matrix (Bp) is
implemented, then the disturbance could be considered as entering at the plant input. The
disturbance (w) in the model represents as unbounded perturbations to the plant output y.
A state-space realization for the augmented system G(s) can be obtained by directly
realizing the transfer matrix G(s) using any standard multivariable realization techniques
Gust filter dg (W)g w d + + + Aircraft + + y Weighting r ee - (P) (W)e
Weighting u H controller¥ eu (K)¥ (W)u
Figure 5.35: Augmented system for airwake disturbance rejection CHAPTER 5. TASK-TAILORED CONTROL DESIGN 137
(e.g. Gilbert realization). However, the direct realization approach is usually complicated.
Here another way is shown to obtain the realization for G(s) based on the realizations of each component. To simplify the expressions, it is assumed that r is zero, and P, We, Wu, Wg
have, respectively, the following state-space realization.
Ap Bp Ae Be Au Bu Ag Bg P = , We = , Wu = , Wg = (5.10) Cp Dp Ce De Cu Du Cg Dg That is,
x˙ = A x + B ( u + d), y = C x + D ( u + d) p p p p − p p p p −
x˙ e = Aexe + Be(yp + w), ee = Cexe + De(yp + w)
x˙ u = Auxu + Buu, eu = Cuxu + Duu (5.11)
x˙ g = Agxg + Bgdg, d = Cgxg + Dgdg
y = yp + w
Now define a new state vector (¯x), an external disturbance (w ˜) and a new output (z) as
T T T x¯ = x x x x , w˜ =[dg w] , z =[ee eu] (5.12) " p e u g #
and eliminate the variable yp to get a realization of G as
x¯˙ = Ax¯ + B1w˜ + B2u
z = C1x¯ + D11w˜ + D12u (5.13)
y = C2x¯ + D21w˜ + D22u CHAPTER 5. TASK-TAILORED CONTROL DESIGN 138
Note that the augmented problem must be well posed. In particular, the matrices D12 and
D21 must have full rank. The physical interpretation of these constraints is that, if D12
loses rank, this would lead to unconstrained controller action, and, if D21 loses rank, this
would correspond to a output being uncontrollable.
In general, the selection of weighting functions for a specific design problem often in-
volves ad hoc fixing, many iterations, and fine tuning. It is very hard to give a general
formula for the weighting functions that will work in every case. In choosing the weighting
functions, there are some guidelines by looking at a typical design specification [79]. For
the initial design, a high-gain low-pass filter is used for the output weighting function We,
since the sensitivity function S must be keep small over a range of frequencies, typically
low frequencies where the disturbances are significant. Correspondingly the control weight-
ing function Wu must be a low-gain high-pass filter to emphasize the control sensitivity
function T at high frequencies so that the robustness is improved, and actuator activity
is reduced. This process gives a general shape for the weighting functions. The desired
frequency responses should be in inverse proportion to the magnitudes of the weights. In
this study, the weighting functions are tuned iteratively based on the disturbance rejection
property described in previous section 5.2. The final design weighting functions We and Wu
are given by
We = diag 1.5 0.025s+10 , 1.5 0.025s+10 , 5 0.05s+5 " s+10 s+10 s+5 # (5.14)
Wu = diag 0.4 s+0.001 , 0.05 s+0.5 , 0.004 s+0.6 " s+15 0.9s+5 0.9s+6 # CHAPTER 5. TASK-TAILORED CONTROL DESIGN 139
20
W (r) 10 e
W (p), W (q) 0 e e
−10
W (rsas) −20 u
W (psas) −30 u
−40 Magnitude, [dB]
−50
−60
−70 W (ysas) u
−80 −2 −1 0 1 2 10 10 10 10 10 Frequency, [rad/sec]
Figure 5.36: Magnitude of weighting functions We and Wu
The magnitude of We and Wu are plotted in Figure 5.36.
The design process leads to a controller with as many as the interconnection structure
of Equation (5,13). In this study, the resulting controller has 14 states. The frequency
response of the controller is shown in Figure 5.37. It can be seen that the controller has
high gain at low frequency, for good tracking, and low gain at high frequency, for robustness.
This is consistent with the specification of the performance weighting function We(s).
Similar to previous section 5.2, the final H∞ controller is then converted to discrete form
and tested using the non-linear simulation model for the hovering operation on the spot
8 (0 and 30 degree WOD conditions, time-varying airwake model). Figures 5.38 and 5.43
illustrate the aircraft relative position with respect to the spot 8. The solid lines represent
the results with H∞ SAS, the dotted lines and dashed lines are simulation results with the CHAPTER 5. TASK-TAILORED CONTROL DESIGN 140
80
60
40
20
Magnitude, [dB] 0
−20
−40
−4 −3 −2 −1 0 1 2 3 4 10 10 10 10 10 10 10 10 10 Frequency, [rad/sec]
Figure 5.37: Singular values of controller K∞
baseline SAS and the optimized SAS configurations respectively from previous section for
comparison purpose. Figures 5.39 and 5.44 show the responses of aircraft angular rate for 0
degree and 30 degree WOD conditions. Figures 5.40 and 5.45 show the helicopter attitude
responses. The corresponding pilot stick inputs are shown in Figures 5.41 and 5.46. The
results with the H∞ SAS show some significant improvement over both the original SAS and
the optimized SAS. The aircraft pitch rate and longitudinal stick input are only slightly
improved compared to the optimized SAS case. Nonetheless the overall aircraft angular
rates and pilot control inputs are reduced with the H∞ SAS for both 0 and 30 degree WOD
conditions. Note that there is no attempt to optimize the control system for heave axis in
this design process. Figures 5.42 and 5.47 show the response of SAS outputs. The H∞ SAS
produces higher SAS actuator activity than both original SAS and optimized SAS. In both CHAPTER 5. TASK-TAILORED CONTROL DESIGN 141 cases, however, the SAS actuators stay well within the rate and position saturation limits.
Figures 5.48 and 5.49 show comparisons of input autospectra from pilot stick inputs.
Same 4 different window sizes (3, 5, 10, and 15 seconds) from previous section 5.2 are used in the FFT analysis to obtain a composite average that is accurate over a range of frequencies. From the figures, it can be observed that the optimized SAS shows some improvement over the original SAS configuration in the frequency range of 1 to 10 rad/sec.
The H∞ controller practically halved the airwake disturbance effect on roll, pitch, and yaw rate responses against the original SAS configuration. CHAPTER 5. TASK-TAILORED CONTROL DESIGN 142
Original SAS Optimized SAS H SAS¥
1.2
1
0.8
0.6 X ∆ 0.4
0.2
0
−0.2 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6
81
80.5
80 Altitude
79.5
79 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 ∆ Y
Figure 5.38: Aircraft position w.r.t. the spot 8 [ft] - 30 knot, 0 degree WOD CHAPTER 5. TASK-TAILORED CONTROL DESIGN 143
Original SAS Optimized SAS H SAS¥
0.5
0 P −0.5
−1
0 5 10 15 20 25 30 35 40
0.5
Q 0
−0.5 0 5 10 15 20 25 30 35 40
0.4
0.2
R 0
−0.2
−0.4 0 5 10 15 20 25 30 35 40 Time, [sec]
Figure 5.39: Aircraft angular rate responses [deg/sec] - 30 knot, 0 degree WOD CHAPTER 5. TASK-TAILORED CONTROL DESIGN 144
Original SAS Optimized SAS H SAS¥
−2.2 −2.4
PHI −2.6 −2.8 −3 0 5 10 15 20 25 30 35 40
2.4
2.2
2 THETA 1.8
0 5 10 15 20 25 30 35 40
0.1
0 PSI
−0.1
0 5 10 15 20 25 30 35 40 Time, [sec]
Figure 5.40: Aircraft attitude responses [degree] - 30 knot, 0 degree WOD CHAPTER 5. TASK-TAILORED CONTROL DESIGN 145
Original SAS Optimized SAS H SAS¥
0.5 0 Lateral −0.5
0 5 10 15 20 25 30 35 40 0.5 0 −0.5 −1 Longitudinal
0 5 10 15 20 25 30 35 40
1
0 Collective −1 0 5 10 15 20 25 30 35 40
0.5
0 Pedal −0.5
0 5 10 15 20 25 30 35 40 Time, [sec]
Figure 5.41: Pilot control stick inputs [%] - 30 knot, 0 degree WOD CHAPTER 5. TASK-TAILORED CONTROL DESIGN 146
Original SAS Optimized SAS H SAS¥
1.5
1
0.5 RSAS 0
−0.5 0 5 10 15 20 25 30 35 40
1
0
PSAS −1
−2 0 5 10 15 20 25 30 35 40
1
0.5
0 YSAS −0.5
−1 0 5 10 15 20 25 30 35 40 Time, [sec]
Figure 5.42: SAS outputs [%] - 30 knot, 0 degree WOD CHAPTER 5. TASK-TAILORED CONTROL DESIGN 147
Original SAS Optimized SAS H SAS¥
3
2
X 1 ∆
0
−1 −4 −3 −2 −1 0 1 2 3 4
83
82
81
Altitude 80
79
78 −4 −3 −2 −1 0 1 2 3 4 ∆ Y
Figure 5.43: Aircraft position w.r.t. the spot 8 [ft] - 30 knot, 30 degree WOD CHAPTER 5. TASK-TAILORED CONTROL DESIGN 148
Original SAS Optimized SAS H SAS¥
4 2 0
P −2 −4 −6
0 5 10 15 20 25 30 35 40
4
2
Q 0
−2
−4 0 5 10 15 20 25 30 35 40
4
2
R 0
−2
−4 0 5 10 15 20 25 30 35 40 Time, [sec]
Figure 5.44: Aircraft angular rate responses [deg/sec] - 30 knot, 30 degree WOD CHAPTER 5. TASK-TAILORED CONTROL DESIGN 149
Original SAS Optimized SAS H SAS¥
0
−2 PHI
−4
0 5 10 15 20 25 30 35 40
5
4
THETA 3
2 0 5 10 15 20 25 30 35 40
1
0 PSI
−1
0 5 10 15 20 25 30 35 40 Time, [sec]
Figure 5.45: Aircraft attitude responses [degree] - 30 knot, 30 degree WOD CHAPTER 5. TASK-TAILORED CONTROL DESIGN 150
Original SAS Optimized SAS H SAS¥
5
0 Lateral −5 0 5 10 15 20 25 30 35 40 4 2 0 −2 −4 Longitudinal −6 0 5 10 15 20 25 30 35 40
5 0 −5 Collective −10 0 5 10 15 20 25 30 35 40 4 2 0 −2
Pedal −4 −6 −8 0 5 10 15 20 25 30 35 40 Time, [sec]
Figure 5.46: Pilot control stick inputs [%] - 30 knot, 30 degree WOD CHAPTER 5. TASK-TAILORED CONTROL DESIGN 151
Original SAS Optimized SAS H SAS¥
10
5
RSAS 0
−5 0 5 10 15 20 25 30 35 40
5
0
PSAS −5
−10 0 5 10 15 20 25 30 35 40
10
0 YSAS
−10 0 5 10 15 20 25 30 35 40 Time, [sec]
Figure 5.47: SAS outputs [%] - 30 knot, 30 degree WOD CHAPTER 5. TASK-TAILORED CONTROL DESIGN 152
Original SAS Optimized SAS H SAS¥
Figure 5.48: Control stick input autospectra [dB] - 30 knot, 0 degree WOD CHAPTER 5. TASK-TAILORED CONTROL DESIGN 153
Original SAS Optimized SAS H SAS¥
Figure 5.49: Control stick input autospectra [dB] - 30 knot, 30 degree WOD Chapter 6
Conclusions and Future Works
6.1 Conclusions
A helicopter/ship dynamic interface simulation tool has been developed to model a UH-60A operating off an LHA class ship. To achieve a high fidelity simulation model, high-order dynamic inflow model and time-accurate ship airwake solutions of an LHA class ship are integrated with the flight dynamics simulation model. An optimal control model of the human pilot has been developed to perform the desired shipboard operations. The optimal control model of the human pilot proved to be an efficient method for simulating approach trajectories.
Typical shipboard operations have been simulated from landing spot 8 on the LHA
(CFD results showed significant time-varying flow effects over this spot). Simulation results are compared to the flight test data for the 0 degree and 30 degrees WOD conditions. Pilot control activity is then compared to JSHIP flight test data in terms of time domain and frequency domain analysis.
154 CHAPTER 6. CONCLUSIONS AND FUTURE WORKS 155
In addition, the present work investigates the optimization of a flight control system for the UH-60A Black Hawk helicopter operating in the turbulent airwake of a LHA class ship. A stochastic model of the ship airwake is derived from simulations with a full time- accurate CFD solution of the airwake. In this study, the gains of a SAS are optimized using CONDUIT, and a H∞ controller is designed to provide an alternative for a helicopter
automatic flight control system. New SAS configurations are then tested using a full non-
linear simulation model.
Overall, the main objectives of this thesis, as stated in section 1.3, have been achieved.
The following general conclusions can be drawn from this work:
1. The simulation results from Section 4.2 clearly indicate that the time-varying airwake
has a significant impact on aircraft response and pilot control activity when the aircraft
is flown for specified approach and departure trajectories. The differences are most
notable when the helicopter is operating in or near a hover relative to the ship deck
(stationkeeping). In the past, gust models for fixed-wing aircraft simulation have
often used a stationary or frozen field model. This is adequate when the aircraft is
moving at a significant forward speed. However, the model clearly breaks down as
airspeed approaches zero. The same appears to be true when helicopters are operating
in turbulent ship airwake. The time-varying nature of the ship airwake becomes
dominant as the helicopter approaches hover on the ship deck. And, the simulation
results of 30 degree WOD condition showed a substantial increase in pilot workload.
2. An optimal control model of the human pilot is successfully implemented to solve the
“inverse simulation” problem. Given a specified trajectory, the pilot controls can be CHAPTER 6. CONCLUSIONS AND FUTURE WORKS 156
calculated using forward simulation in conjunction with a feedback controller. This
is found to be highly useful for this research task. Inverse simulations can be time
consuming and difficult to implement computationally. The pilot model is easily tuned
and seemed to produce reasonable predictions of trajectory tracking and pilot control
activity.
3. By comparison with data from flight test data, it is found that the control activities are
similar in low frequency range but underestimate in magnitude in the high frequency
range (over 1.5 Hz). There is clear evidence that the human pilot is continually moving
cyclic stick in the maneuver. At this stage of the study no attempt has been made to
optimize the parameters of the human pilot model.
4. The stochastic disturbance model of ship airwake appears to result in similar overall
behavior of the coupled aircraft/pilot system as the simulation with the full time-
varying airwake. The 40 seconds of the time-varying airwake solutions are stored for
every 0.1 second, and each flow solutions for the target DI mesh is 5.2 Mbytes in
size. Therefore, the proposed stochastic airwake modeling approach avoids the large
computational and storage requirements of the CFD data.
5. The shaping filters used in the stochastic model are readily incorporated in the flight
control optimization using CONDUIT and H∞ control design. The filters provide a
tool for flight control design.
6. The optimized SAS results in higher gain in all three axes compared to the original
SAS, but it does not appear to result in excessive control activity in the SAS. Upper
limits on roll gain are due to stability margin limits from rotor-body coupling. Results CHAPTER 6. CONCLUSIONS AND FUTURE WORKS 157
with the non-linear simulation model show significant reduction in pilot workload in
pitch and yaw, with slight improvement in roll compared to the original SAS. Although
further improvements could be obtained, the results appear to validate the current
design approach.
7. The potential of H∞ control method for a helicopter flight control system design has
been demonstrated. Successful engagement is achieved on the non-linear simulation.
The final H∞ controller considerably reduces the aircraft angular rate responses and
corresponding pilot control inputs compared to the original SAS. Thus pilot workload
would be significantly reduced, allowing more aggressive maneuvers to be carried out
with a higher degree of precision. Also passenger comfort and safety will be increased.
6.2 Recommendations for Future Work
The following are suggested for future study:
1. Currently, the helicopter/ship aerodynamic interactions are not included. To examine
the effect of complex helicopter/ship aerodynamic interactions, the deck ground effect
should be considered, and the appropriate condition at the ground surface needs to
be determined in order to model unsteady effects.
2. In this study, the stochastic airwake model is designed for one location (17 ft above
the spot 8). In order to increase the computational efficiency, an array of airwake
shaping filters would still need to be designed for different WOD conditions and for
different locations on the ship. CHAPTER 6. CONCLUSIONS AND FUTURE WORKS 158
3. For further validation, it should be apply an equivalent airwake disturbance method
to validate ship airwake CFD analysis. Airwake disturbance can be extracted from
flight test and compared to simulation with CFD airwake solutions.
4. At this stage of the study no attempt has been made to optimize the parameters of
the human pilot model and this work should be completed in the future work.
5. A new spec for disturbance rejection is designed based on PSD of angular rate response
to corresponding gust input. Currently, the boundaries for Level 1/Level 2 and Level
2/Level 3 are arbitrarily selected, but the optimization with respect to this spec results
in a reduction in the aircraft response and pilot control activity required to stabilize
the aircraft in a turbulent airwake. It would be desirable to perform a more detailed
handling qualities study of the spec to establish appropriate level boundaries.
6. The ability to achieve an optimized solution using CONDUIT is sensitive to the initial
values for the design parameters. The problem may be over-parameterized. Future
work should seek to reduce the number of control parameters used in the synthesis
process in order to get more consistent behavior in the optimization.
7. To design a flight control system to improve handling qualities, a series of design
specifications are required to guarantee the performance of the controller. However,
there is no attempt to establish the performance measurement for flight control system
design with modern control theory. Thus, future work must include an investigation
into different measures of performance to design a robust flight control system.
8. Although performance and robustness are achieved using the current H∞ design CHAPTER 6. CONCLUSIONS AND FUTURE WORKS 159
method, how adequately this captures the discrepancies between the low-order lin-
ear model used in the design and the true non-linear aircraft dynamics is debatable.
Questions remain concerning the fidelity of the plant model used in this study; large
amounts of flight test data must be gathered to help shed light on that.
9. Future shipbased rotorcraft will require high levels of agility and maneuverability
as well as capabilities for operations in degraded visual environments and adverse
weather conditions. Thus it is desirable to expand flight control design efforts to
establish the autonomous landing flight control system and position hold over ship
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Mr. Dooyong Lee was born on December 25, 1971, in Busan, Republic of Korea. He received his bachelor’s degree in Aerospace Engineering in February 1997 from INHA Uni- versity, Inchon, Korea. He earned his master’s degree in Aerospace Engineering in February
1999 from the INHA University before entering the Graduate Program in the Aerospace
Engineering at the Pennsylvania State University where he worked as a research assistant.
He was awarded the Vertical Flight Foundation Scholarship in 2002. Mr. Lee is a student member of the American Helicopter Society and American Institute of Aeronautics and
Astronautics.