Proc. Indian Acad. Sci. (Engg. Sci.), Vol. 3, Part I, March 1980, pp. 47-65. Printed in India.

Attitude and orbit control for broadcasting missions

C A MARKLAND Attitude and Orbit Control Division, European Space Research and Technology Centre, Noordwijk, The Netherlands M S received 3 July 1978; revised 5 February 1979 Abstract. This paper gives a broad introduction to the problems of attitude and orbit control of geostationary communications . It specifically discusses the relationships between the satellite user's requirements for a broadcasting mission and the design of the attitude and orbit control system. To put the subject in perspective, a brief review of past and present satellites is presented first. Then orbit control is described in terms of the forces that act on a satellite in geostation.~ orbit _and the necessary station-keeping strategies. The design of attitude control systems for tlaree-ax~sstabilised satellites is presented by considering the disturbance torques, attitude sensors and actuators and by identifying the various system problems and their solutions.. Sources of error in pointing the satellite towards the earth are discussed together with the formulation of error budgets. Finally, the design approach for missions that require extremely accurate pointing is considered, and some remarks are given regarding the achievable accuracy for this class of satellite missions. Keywords. Communication satellites; twenty-four hour orbits; orbit perturbations; station-keeping; attitude control; angular momentum; attitude indicators; accuracy; satellite broadcasting missions; broadcast satellite.

1. Introduction

The purpose of this paper is to give a broad introduction to attitude and orbit control of geostationary satellites and, in particular, to discuss the connections between the mission requirements imposed upon a broadcast satellite and the design of the corresponding attitude and orbit control system (AOCS). Thus, while no funda- mentally new knowledge is presented here, the main objectives are to highlight system-level interface problems that are rarely discussed in the literature and to show people involved in the planning of future broadcast missions some of the impact of their requirements. In order to define the class of satellites under discussion and the modes of attitude control suitable for it, it is appropriate to make a brief review of past and present satellites taking the Intelsat family of communications satellites shown in figure 1 as a point of reference. Intelsats I and II were essentially cylindrical in shape and they were 'spin- stabilised'. This means that the orientation in space of only one axis of the body (i.e. the spin axis) is controlled. Provided that the required accuracy for this orientation is not better than 3- to i degree, which was the ease for Intelsats I and II since the antennabeam width was 17 degrees, this leads to very simple on-board attitude control hardware. For Intelsat III, the same attitude control system was employed for the main body, but an increase in communications capability was

47 48 C A Markland

Figure 1. The developmentof INTELSAT satellites. obtained by mechanically despinning the antenna with respect to the body. Plainly, this requires an additional control loop for antenna pointing. The extension of the technique of spin-stabilisationto give more communications capacity (which implies larger antennas and more solar cells)was limited by a funda- mental law of physics. It follows from Newton's laws that the angular momentum of a body is constant unless torques are imposed upon it from outside. Internal torques cannot change the overall momentum, but they can affect the amount of kinetic energy in the body. Specifically, if they dissipate energy (e.g. in heat) then the body will move to the state of minimum energy. This minimum energy state for spin-stabilised satellites is the desired mode of spin only if the inertia about the desired spin axis is greater than the inertia about any other axis. That is, the body has to be roughly disc-shaped or ' oblate '. If any transverse axis has a greater inertia, then the body will br stable in spin only about this axis. Attitude and orbit control for satellite missions 49

Plainly, adding large despun antennas above the spinning body will contravene this condition, i.e., it will make the body prolate (pencil-shaped), so that it will spin- stably about a transverse axis and not about the axis of symmetry. Before Intelsat IV could be accepted, therefore, a solution to this stability problem had to be found. Hughes Aircraft Company found the solution and termed it the Gyrostat (Iorillo 1967) although now it is more generally referred to as the ' dual-spin' configuration. In this configuration, an energy dissipating device (e.g. a damped pendulum) is placed on the despun part, and this has the effect of stabilising the complete prolate satellite about the spin axis of its rotating section. Hughes exploited this principle very suc- cessfully in Intelsat IV and IVA in which 4~~ spot beams are employed, and a dual- spin configuration was one of the two winners selected by Comsat for Intelsat V in the first technical evaluation. From the point-of-view of AOCS design, it has proved to be a fine example of high performance with simple hardware. Now to consider the European side, dual-spin configurations received a great deal of attention at the time of the first broadcast satellite proposals in 1969. They were studied in some depth (Brewer et al 1970, 1974) but finally they were eliminated mainly on the basis of lack of growth capability due to the inefficiency of their cylind- rical solar arrays. The first European geostationary broadcast satellite was the Franco-German satellite Symphonie shown in figure 2. This satellite is not spin- stabilised but rather it has 'three-axis attitude stabilisation', i.e. the orientation in space of all three axes is controlled. In retrospect it does appear to have some similarity to spin-stabilised configurations (the body-fixed solar arrays and the general disc-shape) but from the control system point-of-view the major step has been made. ESA's first satellite in this field is the Orbital Test Satellite (OTS) illustrated in figure 3. In contrast to Symphonie, the solar arrays rotate to track the Sun while the body-fixed antennas track the Earth. This three-axis stabilised configuration has virtually become the ' classical' pattern for all present communication and broadcast satellites. Certainly, it is being adopted for most current missions including Intelsat V and the Indian APPLE. The remainder of this paper is concerned solely with this configuration and refinements thereof.

Figure 2. The Symphoniesatellite. Pro. C--4 50 C A Markland

Figure 3. The'orbital test satellite (OTS).

All the satellites mentioned above were designed for communications in the general sense and for telephone communications especially. Although this paper relates specifically to satellites used for broadcasting, its contents do apply to a very wide range of future communications satellites in which high power and high accuracy are requirements. The functions of attitude and orbit control are invariably combined in satellite design because they use the same on-board hardware. However, while they are closely related, they are also different in nature with orbit control being usually performed by commands from a ground station and attitude control being performed by closed-loop control systems on-board the satellite. Thus, for the moment, they will be considered separately. Attitude and orbit control for satellite missions 51

2. Orbit control

2.1. General

This discussion of orbit control is restricted to near-geostationary orbits, since con- tinuous visibility of the satellite from the Earth stations and the absence of large rela- tive motions are desirable features for all communications missions and they are mandatory for economic broadcasting to many simple ground receivers. Nonetheless, it is worth remembering that other orbits have been used; for example, the highly elliptical, inclined orbits of the Russian Molniya series. The characteristics of the ideal are: (i) it is perfectly circular (i.e. eccentricity = zero) (ii) it is in the plane of the Earth's equator (i.e. inclination : zero) (iii) the altitude is 35 786 km =5.611 Earth radii. When these three conditions are exactly satisfied, the orbital period is equal to the Earth's period of rotation (i.e., one sidereal day=23 hr 56 rain 4.09s) and the satellite is stationary when seen from the Earth. Deviations from these conditions cause relative motion. Specifically, a non-zero inclination causes the satellite to move daily in a narrow, North-South figure-of-eight, a non-zero eccentricity produces a daily East-West oscillation, and a different altitude produces a different orbital period and a constant drift eastward or westward. What are the environmental forces acting on a satellite that can disturb its ideal geostationary orbit? Of course, the principal force is that due to the gravitational attraction of the Earth. The Earth can be regarded as a point mass to a first order, which will not by itself disturb the orbit, but its second order effects are important. There are also important gravitational forces due to the Sun and the Moon, and solar radiation pressure gives a significant disturbance. Other forces, such as atmospheric drag, electric and magnetic fields, and meteorite impact, are negligible at geostationary altitude. A comprehensive survey of these phenomena has been given by Shrivastava (1978), and there is a detailed discussion in Michielsen & Webb (1970).

2.2. North-South control

First let us consider the environmental forces that move the satellite out of the equa- torial plane and thereby produce a North-South relative motion. These forces are gravitational, and they result from the fact that the plane of the geostationary orbit (the equatorial plane) is tilted with respect to the plane of the Earth's orbit around the Sun (the ecliptic plane) and also with respect to the plane of the Moon's orbit around the Earth. The situation with regard to the Sun is illustrated in figure 4. This shows the Earth in its annual rotation around the Sun and the satellite in its daily rotation about the Earth. The forces are shown in detail for the Winter Solstice. Considering the conditions at the Winter Solstice, the gravitational attraction on the satellite when it is at point A is greater than at any other point in the daily orbit because there it is closest to the Sun. The gravitational pull at B is minimum. Re- garding the orbiting satellite as a continuous rotating annulus with angular momen- tum H 0, this difference in gravitational force acts as a torque that preeesses the mo- mentum vector and thus produces an inclined orbit. The inertial direction of the 52 C A Markland

direction towards the vernaL equinox

1/~t" ~ ~~ ~ "'q~.~.. N /

//~ / s/~ i I i/ fl A B x~ winter "\ ~---- /.//summer ~-...

t" f"

spring

S Mgravlty

w inclination

detail, of the parameters czt w~nter so!,sUce G=sotar gravitat.lonaL force ~ F-compensating force Uo.= orbft frequency.7, 292 x 10-5 rad/sec i= inclination angle

Figure 4. Solar gravitational effect.

torque and the direction of motion of the tip of the momentum vector is into the paper as shown in figure 4. More specifically, the direction is toward the Vernal Equinox. (The Vernal Equinox is the point at infinity which lies on the line of intersection of the ecliptic plane and the equatorial plane and through which the Sun appears to pass when viewed from the Earth on about 21 March. It is sometimes called the First Point of Aries.) Exactly the same argument can be made for the forces at the Summer Solstice, i.e. the torque is in the same inertial direction as at Winter Solstice. At the equinoxes of Spring and Autumn zero torque is produced, but at all other times a torque component directed toward the Vernal Equinox exists. Hence solar gravity always produces a torque which precesses the orbital momen- tum vector--or the ' orbit pole '--toward the Vernal Equinox and so produces incli- nation drift. It follows that the line of nodes, which is the intersection of the inclined orbit with the equatorial, plane--the line AB on figure 4, also has a fixed inertial direction and hence the time of crossing this line varies with the time of year. Attitude and orbit control for satellite missions 53

The effect of the Moon's attraction on the satellite orbit is very similar to the effect of the Sun, because the Moon's orbit around the Earth is near to the ecliptic plane and also because its orbit is outside the geostationary orbit. Thus, the geometry of the situation is similar to that of figure 4 in terms of the tilt of the orbital momentum and the direction of the lunar gravitational forces. Accordingly, the Moon also produces a torque which precesses the orbit pole in the general direction of the Vernal Equinox, but the period is monthly rather than yearly. Thus, solar and lunar gravitational forces on a geostationary satellite combine to produce a torque component of constant sign about an inertially-fixed axis which precesses the orbit pole toward the Vernal Equinox. The drift rate is roughly 0.8 degree/year. There are also torque components orthogonal to this line, but they are oscillatory and do not produce a secular drift. Hence, they can be ignored except when extremely accurate station-keeping is required (i<0.03~ Secondary effects due to long period changes in the Moon's orbit are similarly neglected herein. If it is required to maintain the orbit inclination at zero then these effects must be counteracted by using the on-board propulsion system to provide forces that compen- sate the gravitational forces. This is called North-South station-keeping (NSSK). Clearly the optimum time to perform this propulsive manoeuvre is at the crossing of the line of nodes. The decision to employ or not to employ NSSK depends, of course, on the user's requirements which are dictated by the nature of the ground segment of the broad- casting system. If there are only a small number of fairly sophisticated ground stations, then tracking a satellite in an inclined orbit may well be acceptable. How- ever, if there are many simple ground stations, then such tracking will not be acceptable on account of the extra cost and reduced reliability. The latter is surely the case for broadcasting to individual receivers in Europe, and it will probably be the case for many Indian missions. From the point of view of attitude and orbit control, both options are feasible and the trade-off is mainly between satellite mass and antenna steering. With NSSK the propellant mass required is very serious. For example, for a satellite of the Ariane class (850 kg and 7-year life), it is about 146 kg with present-day hydrazine technology and it is still significant at 58 kg with the electric propulsion systems under development. Without NSSK both satellite and ground station antennas have to be steered in order to point to each other. This is a minor problem on-board, particularly when there is only one antenna or when there are several antennas all pointing to nearly the same latitude on the Earth so that they can be steered together. Secondary aspects in the trade-off are that a special attitude control mode is often required during NSSK manoeuvres and that pointing of the satellite away from the Earth centre is necessary in an inclined orbit and this is problematic with some infra- red earth sensors. However, these problems are insignificant when related to the user's requirement, and the clear conclusion is that electric propulsion must be developed for broadcast satellites to effect the above 88 kg mass saving.

2.3 East-West control

Now let us consider forces that give disturbances in the plane of the orbit and hence produce a relative East-West motion of the satellite: These forces are due mainly to triaxiality of the earth and solar radiation pressure. 54 C A Markland

(stabLe) 7 5.1 "E

161.g'E (unstabte) ~ / (unstable)

105.3" W ( s~a bte )

Figure 5. Triaxiality effect.

Triaxiality is the term used to describe the fact that the equatorial cross-section of the Earth is not perfectly circular but rather slightly elliptical. This is illustrated in figure 5 which shows the view looking down onto the North pole and onto the orbit plane. Because the Earth is not circular, the gravitational force is directed slightly away from the centre of the orbit with the result that the satellite experiences either an acceleration or a deceleration depending upon its longitude. A satellite located directly over India will be very close to one of the two stable points on the minor axis of the ellipse where the triaxiality force is zero (although it is quite possible that an Indian satellite may be located at some other longitude on account of particular conditions). For a satellite stationed over Europe, triaxiality results in a drag force on the satellite. Paradoxically, this causes an eastward drift of the satellite. This is explained by the fact that the drag reduces the orbital energy, hence the altitude and the orbital period are continuously reduced. Then, with the period being reduced, the angular velocity increases and the satellite drifts towards the East (Blizer et al 1962). If the satellite is not controlled against the triaxiality effect, it will drift toward the stable point at about 75~ over- shoot, and then oscillate about this longitude. Plainly such a drift is not acceptable, and all geostationary satellites have been provided with the capability to compensate this effect. Another in-plane disturbance is solar radiation pressure, and this is illustrated in figure 6. The resulting force on the satellite tends tO accelerate the satellite between midday and midnight and to decrease the satellite velocity over the other half of the orbit. This results in a slight eccentricity of the orbit, but in contrast with triaxiality this eccentricity is limited in magnitude due to the rotation of the Earth about the Sun. Accordingly, if the tolerance on East-West location is sufficient (4- 0.15 ~ for a satellite of 750 kg and 90 M S) then compensation of this effect may not be necessary (Lovell & O'Malley 1970). As compared with North-South station-keeping, the propellant mass required for East-West station-keeping (EWSK) is quite small--typically 3 to 10 ~ depending on the correction strategy and satellite configuration. Hence there is no interest in Attitude and orbit control for satellite missions 55

apogee Vsat, ~,,,, ~6Vsu= n j~" ~--~. -.\

/ 0600H "\ / / \ ,~ / \ '/ | \' I | ,J I 1 ~ \ / / ~ / / \ // \ ./

\~- 18 OOH / perigee ~" ~ -e~:~ Vsat AVsu n

Figure 6. Solar radiation effect.

electric propulsion for EWSK because the saving in propellant mass would be out- weighed by the extra thruster and power supply mass.

3. Attitude control

3.1 Definition of axes

The conventional body-fixed axes of the satellite are shown in figure 3. When the satellite is in its ideal operational attitude

(i) the yaw axis is in the plane of the orbit and it points to the centre of the Earth, (ii). the roll axis is also in the plane of the orbit pointing along the orbital velocity vector, and (iii) the pitch axis completes the fight-handed set by being perpendicular to the orbit plane, and if the orbit inclination is zero then it points southward.

Plainly the objective of the attitude control system is to maintain this ideal relationship or some commanded deviation from this nominal state.

3.2 Sensors and actuators

It is axiomatic that before any system can be controlled deviations from the desired condition must be measured, so let us first consider the problem of attitude sensing. Since the antenna must continually face the Earth, it is natural to place a sensor on this side and to measure rotations about the roll and pitch axes directly by reference to the apparent motion of the Earth's disc. However, yaw angles (i.e. rotations about the Earth-satellite line) cannot be measured in this way. Yaw could be measured by means of a sun sensor looking along the roll axis, but the Sun is not always in the field of view of such a sensor. Even if several sensors were used, there are still times when the Earth, satellite, and Sun are in line thus preventing continuous yaw measurement. Using a star sensor on the North or South face would provide a continuous measure- ment, but such sensors are complex and they would be subject to interference from 56 C A Markland the solar array. The most common solution to the problem of yaw sensing has been to use the fact that the satellite roll and yaw axes rotate with respect to inertial reference axes due to the daily orbital motion. Hence, with only pitch control, yaw errors are seen as roll errors after 6 hr. This is illustrated in figure 7. Then, it can be shown that by combining the correction of roll errors with a torque about the yaw axis, yaw attitude errors can be controlled indirectly (Dougherty et al 1968). In order to strengthen this inherent roll/yaw coupling in the presence of attitude disturbances, a flywheel or 'momentum bias system' needs to be installed in the satellite with its momentum vector parallel to the pitch axis, and this gives gyroscopic stiffness. There are many refinements to the way in which the momentum bias system can be implemented and some of these are shown in figure 8. The simplest is the single fixed momentum wheel (or flywheel) aligned with its axis of rotation parallel to the pitch axis. With this device, it is natural to use its motor also as the torque actuator for controlling pitch attitude. Since the wheel then absorbs the momentum ac- cumulated from the environmental torque, the wheel speed changes and when it reaches a limit it must be 'unloaded' by firing gas jets. When the environmental torques produce roll or yaw attitude deviations, these must be corrected by gas jet pulses as soon as the roll accuracy limit is reached. The pulses must be small in order to be compatible with roll accuracy, and for broadcast satellites (with severe accuracy requirements and large solar arrays, and hence large disturbance torques)the time interval between roll corrections also becomes small. This ultimately leads to a point (-t-2 kW) at which the OTS-type of control becomes unfeasible. This is because that system uses two pulses separated by half a nutation period in order to avoid continuous nutation, and this time interval becomes longer than the required roll correction interval. The first level of refinement in momentum bias systems is to be able to steer the momentum vector in one plane within the satellite body. These are known as. single degree-of-freedom systems, and three such mechanisations are shown in figure 8. Apart from giving a finer and more flexible control of roll attitude, these systems have the advantage that the gas jets need to be used only when the yaw accuracy limit is reached. Since the required yaw accuracy is always lower than the required roll accuracy (0.35 ~ versus 0.08 ~ in the case of OTS) this leads to fewer gas jet manoeuvres

~ ~ yclw

r~ /J f ~ \\ rot~

earth \ // ",,, /

Figure 7. Interchange of roll and yaw orrors, Attitude and orbit control for satellite missions 57

H

fixed momentum wheel

vee configuration

-h ~ "'h

triangle configuration

H

single gimbatted momentum wheel

/' H

double gimbal.ted momentum wheel.

Figure 8. Some momentumbias configurations. than with the fixed wheel. The final stage of refinement is the two degree-of-freedom system of which the double-gimballed momentum wheel is one realisation. This gives the greatest versatility in attitude control, and operation of the gas jets is required only when the gimbal angles approach their limits (typically 12~

3"3 Disturbances

The above discussion of attitude sensing led directly to actuators for attitude control, but now it is necessary to consider the environmental disturbances that create the need for attitude control. The main environmental disturbance is solar radiation pressure on the solar arrays. This creates torques in two ways. First, if both arrays do not exactly face the Sun but rather they are offset or twisted with respect to each other, then they create a torque like that in a windmill. Second, if the resultant centre-of-pressure on the entire body is not coincident with the ~ntre-of-gravity, then again there is a torque due to this misalignment. 58 C A Markland

Broadly speaking, the impact of an increasing environmental torque on the attitude control system is: (i) increasing propellant mass and frequency of gas jet manoeuvres in order to compensate these external torques, (ii) increasing yaw error (given by ~=torque--(momentum• frequency) on account of the indirect method of yaw sensing. Since the impacts will become more serious for satellites with large solar arrays such as broadcast satellites, it is worthwhile considering direct methods of compen- sating them. One method is to determine on ground the windmill torque, and telecommand an offset to the solar array pointing control system in order to reduce it. This requires no extra hardware but it is unlikely that the total disturbance torque can be reduced by more than 50 %. Another method is to fix electric coils in the body which interact with the magnetic field of the Earth so producing low level torques. This could be done either as a coarse open-loop compensation or as a complete closed-loop attitude control system like in the RCA Satcom (Muhlfelder 1976). A similar system has been proposed for APPLE (God & Rajaram 1979). The hardware required is very simple and it should be a worthwhile technique for high-power satellites. The above relation between yaw error, disturbance torque, and momentum (~=T/o, o H) is important because it shows an intrinsic limitation with momentum bias systems. The disturbance torques on future large arrays are not well known, but with present estimates the yaw accuracy will be marginal in terms of present re- quirements for large arrays (e.g. ~=0.64 ~ for H=50 Nms and a 5 kW array). This problem can certainly be solved (e.g. by magnetic bearing flywheels having higher momentum, by disturbance torque compensation, or by yaw sensing) but neverthe- less it does lead to a preference for circular rather than linear polarisation in order to have a less severe accuracy requirement on yaw and so to facilitate the use of existing hardware. Another attitude control problem that can arise with high power and large solar arrays is interaction between control system dynamics and flexible modes of the solar array. This problem has received a great deal of attention in the literature, but it is usually found to give no real problem in normal operational modes because the control bandwidth required is very low. The more critical aspect comes in mano- euvre modes--especially when high accuracy of the body is still required because this implies a wide bandwidth which can include the array resonances. Satisfactory control laws have been designed for present generation satellites (< 1 kW), but the problem will be more severe in the future and it may become a key factor in the choice of ACS acutators and solar array technology (ESA Symposium 1976, session 5).

4. Pointing accuracy

4.1. Requirements

The requirement on allowed pointing error is often 10 ~o of the antenna beamwidth. However, although this is typical of many missions, it is no more than a rule-of- thumb. In order to have a proper defi ifion of the real requirement, accuracy must Attitude and orbit control for satellite missions 59 be related to the communications link budget by considering the effect of a pointing error on the signal received by the ground stations. Considering a parabolic antenna, the antenna gain pattern has roughly a gaussian shape, and the slope at the --3 dB point (which is assumed here to correspond to the edge of the beam although it may not in practice) is approximately

slope = -- 12/0 dB/degree, where 0 is the beamwidth of the antenna. Hence, when the pointing error is e, the loss in signal at this point is

N=(12e/O) da.

This shows that for a given loss in signal the allowable pointing error reduces as the antenna beamwidth reduces. Furthermore, the effect of a given pointing error is greatest where the beam slope is maximum, i.e. at the edge of the nominal coverage zone and not at the centre. Overall boresight error can conveniently be divided into North-South and East- West components. From geometry, roll and pitch attitude errors contribute almost directly to NS and EW errors respectively. The contribution of yaw errors (rotation about the satellite-earth centre line) to overall boresight error is always small and it depends on the latitude of the coverage zone. It is zero when the coverage zone is at the sub-satellite point. In the case of European coverage it contributes about 10 % of an equal pitch error to the EW error and a negligible amount to the NS error budget, and the contributions will be about half these amounts for coverage of India. Hence, the allowed yaw error can be at least ten times greater than the pitch and roll accuracies unless there are special mission requirements, e.g. those due to linear polarisation.

4.2. Error sources

In the classical system with body-fixed antennas (such as OTS) pointing error is due to orbit imperfections, misalignments, sensor noise, electronic drift, offsets and dead- bands, disturbances and manoeuvre transients. Deviations from the ideal geostationary orbit cause relative motion between the satellite and an observer on ground as explained earlier, and if these are not tracked by the satellite as well as by the ground station (e.g., by a daily nodding motion to compensate for orbital inclination) then they contribute to the satellite pointing error budget. However, with normal orbit control accuracies (4- 0"1 ~ the contribution to pointing error is small. The misalignment error is the total effect of numerous inaccuracies and distortions between the real antenna boresight axis and the real infra-red (IR) sensor boresight. In terms of the structure, these comprise the initial misalignments between the align- ment blocks themselves and between the alignment blocks and the real boresights, and further misalignments due to launch stresses and temperature variations. On the sensor side, there are also misalignments due to non-uniformity in the Earth's IR radiation. (It is not a uniformly radiating disc; it has an irregular profile which changes with the seasons.) The seriousness of these factors is more severe for IR 60 C A Markland sensors that operate by balancing the radiation received. While they can be com- pensated out for pointing to the centre of the Earth, considerable difficulties arise if the mission requires pointing the sensor boresight even slightly (say 0.5 ~ away from the Earth centre. Sensor noise may or may not be reduced to a negligible level by filtering in the control electronics depending on the relative bandwidths of the noise and the control loop. Similarly the effect of electronic drifts, offsets, deadbands etc. are dependent on the design of the particular control laws. It is inevitable that manoeuvres with gas jets (e.g., station-keeping and unloading) produce attitude transients because the corresponding disturbance torques are several orders of magnitude greater than those due to the environment. If it is a mission re- quirement to maintain full accuracy during the entire 100% of the operational life, then the magnitude of these transients can be limited by implementing a high-gain, wide-bandwidth controller for manoeuvre modes in addition to the low-gain system employed for normal operation. The design and operation of a high-gain system is complicated by problems with sensor noise and solar array resonances. These problems have been solved for the present generation of communication satellites, but they are likely to be much more severe for high-power satellites. Furthermore, there remains a tendency for attitude transients to occur on switching over from the high-gain to the low-gain modes.

4.3. Error budgets

Most of the factors that contribute to the overall error budget are random, and there- fore values must be assigned in a statistical manner. To do this rigorously is not easy. It has become common practice to assume that all errors have a gaussian ampli- tude probability distribution and use the term' three-sigma ' to mean' worst case ' A better approach which avoids the gaussian assumption is to assign a pro- bability level to the accuracy requirement, i.e. to specify that the probability that the boresight pointing error is less than N degrees shall be P. The former use of three sigma has led to P=99.73 % which is an extremely conservative level. In computing the overall boresight error budget, the errors are first determined separately along the North-South and East-West directions and then combined to give the overall error. Unfortunately, the combination of error sources having different and ill-defined frequency spectra and amplitude distributions is analytically extremely difficult. One reasonable approach is to assume that all errors are independent random variables (hence they are combined by root-sum-square) but to add directly errors occurring in different frequency ranges and to separate completely the constant errors. Thus, for each axis we calculate:

time-varying error, e----2rrs~ control frequency errors +2rrs~ orbit frequency errors,

constant error, m=L'r,~ zero frequency errors.

Now, when combining EW and NS errors, it is unlikely that ' worst case' errors will occur in both axes simultaneously. Therefore, straightforward root-sum-square Attitude and orbit control for satellite missions 61 addition of these errors would be too pessimistic. A simple formula that gives a good approximation to the exact result for combining orthogonal errors with gaussian distributions at the probability level of 99-73 % is

overall boresight error ----- (m] -}- 0.3225 ml) + (e~ -q- 0.3225 ~) where m a ~ tn b and ex >t ey. Similar formulas can be found for other probability levels. However, this method of calculating the overall boresight error is only approximate, and it has practical utility rather than theoretical rigour. If exact results are required then precise statistical descriptions of the error sources must be obtained and these must be combined by numerical methods.

5. The approach to ultra-high accuracy missions

5.1. Introduction

It can be firmly predicted that future missions will employ antennas with narrower beamwidths than current satellites and therefore higher accuracy pointing of the antennas will be called for. This will necessitate important new developments in attitude control, and to avoid excessive complexity and cost one must adopt a realistic engineering approach to the problem, i.e., the requirements must be carefully consi- dered before new systems are developed. Requirements are inherently dependent on the nature of the mission, and two aspects that are discussed below are the probability level and the time frame which are specified for ultra-high accuracy pointing. Other aspects, which are outside the scope of the present paper but which can have great impact, are system reliability and outage performance (i.e., the ability of the system to maintain full performance in the event of a failure). In terms of new hardware, the. application of radio-frequency sensors is very appropriate for pointing narrow beam antennas and many missions will require gimbal mechanisms for moving the antennas with respect to the satellite body.

5.2. Probability level

It has been noted earlier that the historical figure of 99.73 % for the probability of maintaining the specified accuracy is an extremely conservative level. In fact, it means that a boresight error greater than the specified value will be an extremely rare event, and rare events are a specialised aspect of probability theory. Thus, extending the simplifying assumption that the errors are gaussian out to this point can hardly be justified. Furthermore, there is no reason to use a higher probability figure for bore- sight errors than for other factors influencing satellite broadcast performance, e.g., propagation conditions, which are quoted at lower levels. Adopting a lower probability level for the specified boresight pointing error obvi- ously does not affect the actual performance of any particular attitude control system, but it does have a significant effect on the quoted error figures. For example, supposing that a particular system has a gaussianly distributed error with zero mean and a standard deviation of 1~ then the probability of the error being less than 3~ is 62 C A Markland

99-73 ~ whereas if the probability level is set at 99.00 ~ then the corresponding error is reduced to 2.57 degrees. This shows how sensitive the accuracy figures are to the associated probability requirement, and hence the need to be realistic as well as conservative.

5.3. Manoeuvre schedule

During the operational phase of the mission, manoeuvres will be required from time to time in order to do station-keeping and momentum unloading. These manoeuvres involve using gas jets for a significant period of time (in the order of 30 rain every 20 days) and these generate much greater disturbance torques on the satellite than those due to the normal environment (the torques are typically 10-1 Nm for station-keeping with two 2 N hydrazine thrusters instead of 10-6 Nm due to solar pressure). Many problems arise in the design of the attitude control system if the specification requires that high accuracy is maintained in the presence of these large torques. Indeed, the general feasibility of doing so is doubtful for high-power, high-accuracy missions, unless one goes to very low thrust levels such as are given by electrical propulsion thrusters. These thrusters are being developed for NS station-keeping but their use for other functions is remote. Accordingly, it is interesting from the point of view of simplicity (and hence reliability) as well as accuracy to consider whether the manoeuvres can be predicted in time and then scheduled to occur outside the important broadcasting periods. Considering momentum unloading manoeuvres, it is probable that the control of wheel speed will not be needed more than once per day and this could be done at any time. As regards roll/yaw unloading, the frequency of manoeuvres depends on the number of degrees-of-freedom of momentum steering as discussed in w 3.2. Given either one or two degrees-of-freedom, it is again likely that unloading could be per- formed at an arbitrary time of day. For maximum efficiency, North-South station-keeping manoeuvres must be per- formed when the satellite crosses the line of nodes. The time of day of this crossing varies as the Earth moves around the Sun, and considering only the secular drift of the orbit pole toward the Vernal Equinox this variation is regular. Thus the schedule for NSSK is known in advance, and it can be shown that with present requirements on accuracy of station-keeping (4- 0.1 degree) the manoeuvre can always be scheduled between say midnight and 0600 hr (Markland 1976). Since this is outside normal television viewing time, such a mission constraint is likely to be acceptable to the satellite users. As regards EWSK, for which the attitude disturbances are much more controllable than for NSSK, the compensation of solar pressure ideally needs prograde and retro- grade impulses at 0600 and 1800 hr respectively. The correction of triaxiality requires two prograde impulses at any time. In general it is unlikely that the opposite require- ments at 1800 hr will cancel exactly. However, in practice EWSK is done in a single manoeuvre (i.e., one does not aim to perfectly circularise the orbit) and this can be scheduled quite flexibly. In summary then, it appears likely that for a broadcast satellite manoeuvres can be performed in an acceptable non-operational time period. Attitude and orbit control.for satellite missions 63

5.4. Radio frequency sensor

Turning now to the boresight errors arising from attitude sensing, the present method is to use an infra-red sensor to detect deviations between its boresight axis (which is nominally parallel to the satellite yaw axis) and the centre of the Earth's infra-red image. The attitude control system then drives this deviation to zero, but the point- ing of the antennas is achieved only indirectly through the alignment of the antenna boresight with respect to the sensor boresight. Consequently, any misalignment between these real boresights cannot be corrected by the onboard system (see figure 9). The use of a radio frequency (RF) sensor integrate~ with the communi- cations antenna and operating with a ground beacon in the coverage zone provides a means of eliminating these misalignments which constitute a major part of the present error budget. The actual errors of the RF sensor itself appear to be rather similar to those of an IR sensor (bias -----0.02 ~ and noise = 0"01~ but the noise is of a higher frequency and can be effectively filtered out. Additional benefits that accrue from RF sensing are: (i) the performance required of the IR earth sensor is lower (accuracy and offset pointing capability) and so a less sophisticated/more reliable device can be used (it is always required for Earth acquisition at the beginning of life), (ii) by combining information from the IR earth sensor and an RF sensor point- ing North or South of the equator, yaw attitude can be determined. This could eliminate the need for momentum bias (i.e. wheel mass) or at least allow a lower value of momentum.

~,eo~a~ -~ f zone

(~ yaw axis )

infra-red sensing

raaiO flre~u~ncy sensing

~gure 9. Comparisonof attitude sensing methods. 64 C A Markland

5.5. Separate antenna control

The next step forward is to separate attitude control of the antenna from that of the body by using the RF sensor in closed-loop with ,~n antenna pointing mechanism. "Ibis will lead to a much faster control, due to the great reduction in inertia, and hence to a more accurate control in transient situations. It will also simplify attitude control of the body (momentum steering, manoeuvres, and array modes) particularly as regards the roll control loop.

6. Achievable pointing accuracy

Pointing error budgets can be accurately calculated only after the satellite has been designed in considerable detail. Accordingly, for the purpose of this general discus- sion, the approach to estimating achievable accuracy will be to take present satellites as the basis and to estimate the impact of improvements on these systems. Taking the Orbital Test Satellite (OTS) as being representative of the present gene- ration of communications satellites, the realistically predicted boresight error for a probability level of 99.73 % is 0.14 ~ in normal operation and 0.20 ~ (which is the speci- fication value) with manoeuvre mode transients. Roughly half of the normal mode error is due to misalignments. These would be largely eliminated with an RF sensor, so reducing the total error by V'2 to 0.1 ~ in normal operation. With the addition of a separate antenna pointing control loop it would be possible to maintain this accuracy also during manoeuvres (except perhaps for transients of a few seconds). Improvements in accuracy beyond 0.1 ~ depend on the details of the control system. The steady-state accuracy of a linear system is limited mainly by sensor bias and inte- grator offset, but this ideal is never realised in practice due to sensor noise, motion of the solar arrays and the main body, friction and other nonlinearities. Nonetheless, the total error should not be much more than twice the sensor error which leads to an accuracy in the region of 0.05 ~ being foreseeable. However, insofar as planning for the immediate future is concerned, it would be prudent to add some margin to this last figure. Accordingly, it is reasonable to expect that 0.07 ~ could be achieved in the next generation of satellites and that im- provements to 0"05~ or better can be obtained after having real experience with RF sensing, large solar arrays, and other characteristics of this class of satellite.

7. Conclusions

The inevitable conclusion is that each step in increasing the severity of the mission performance requirements calls for a step in further developing the attitude and orbit control system. New developments involve cost and risk, and therefore it is essential to set realistic requirements and to utilise existing technology as far as possible. Some developments that will give significant improvement in AOCS performance in a broadcast mission are: (i) electric propulsion for NSSK with reduced mass, (ii) RF sensor for higher aecurac3/pointing, (iii) antenna pointing controlwith the RF sensor, Attitude and orbit control for satellite missions 65

However, some other methods which require less development have also been identi- fied (e.g., magnetic torquing, scheduling manoeuvres outside the operational periods, and steering the momentum vector). Naturally, a trade-off between these and other techniques will be required to determine the best system for a particular mission. With the advent of commercial utilisation of broadcast satellites, there will be more and more emphasis on cost and reliability. Flight experience will be an important factor here and this will inhibit radical design changes. Simplicity is the essence of reliability, and this too will inhibit some of the more exotic, super-control systems. The avoidance of a total breakdown during the operational phase (sometimes called ' outage ') is becoming an important factor in satellite specifications. Great care must be taken to ensure that this does not lead to unwarranted complexity in the attitude control system, since failures cannot be recovered rapidly when large inertias have to be moved. Thus, simplicity and high reliability in the basic design again appears to be the best approach. It must be evident that not all solutions to the AOCS design problems have been covered here and that not all the trade-offs have been completed. However, it is hoped that this general outline will facilitate and stimulate future discussions between satellite users and AOCS designers.

References

Blizer L, Broughton E M, Kang G & Page R M 1962 J. Geophys. Res. 67 329 Brewer M, Bushell R, Holt J & Swift N 1970 A study of dual-spin stability, ESRO CR-24 Brewer M, Bushell R & Swift N 1974 Dual-spin stability study, ESRO CR-471 Dousherty H J, Scott E D & Rodden J J 1968 AIAA 2nd Communications Satellite Conference, paper 68-461 ESA 1976 Symposium on Dynamics and control of non-rigid , Frascati Italy, ESA SP-117, Session 5 Goel P S & Rajaram S 1979 IFAC Symposium on Automatic Control in Space, Oxford, UK, Session 12 lorillo A J 1967 Symposium on Attitude Stabilisation and Control of Dual-Spin Spacecraft SAMS- OTR-68-191, p 257 Lovell R R & O'Malley T A 1970 Station-keeping of high power communication satellites, NASA TM-X-2136 Marldand C A 1976 Satellite Broadcasting Symposium, Stockholm, ESA SP-122 p 137 Michielsen H F & Webb E D 1970 Proceedings First Western Space Congress, Santa Maria, Cali- fornia, p 704 Muhlfelder L 1976 Proceedings AIAA Guidance and Control Conference, paper 76-1929 Shrivastava S K 1978 J. Spacecr. Rockets 15 67

Pro.,C~--5