Controller Design and Performance of the Space lab Instrument Pointing System

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CONTROLLER DESIGN AND PERFORMANCE OF THE SPACELAB INSTRUMENT POINTING SYSTEM A. Woelker AIl/OlI/a/if COli/rut D"/)(II(II/I'II/. Dumier SYS/I'III GII/hll. Fril'ririr/i.,liaji' ll. FR(;

Abstract. The Spacelab Instrument Pointing System (IPS) is designed for high precision pointing of space experiments. The IPS demonstrated its performance during the maiden flight onboard the Shuttle in July 1985. The control system provides three axes pointing and stabilization in the arc second range for a variety of experiments. The envisaged pointing accuracy as well as the structural flexibility of the plant and disturbances imposed challanging requirements on the controller design. The control system comprises a feedback loop with attenuation filters and PlO control as well as feedforward compensation of external disturbances. Based on optical sensor and gyro measurements the attitude is determined via a special version of the Kalman filter. For preflight verification of the IPS performance a comprehensive simulation model representing the system dynamics was indispensable. The predictions of the simulation were confirmed by the results of the Spacelab-2 mission. Att i tude control; Digital control; Feedforward; Frequency Response; Kalman filters; Modelling; PlO control; Pointing system; Stability; Tracking

Keywords.

INTRODLCTIOIJ Figure 1 presents the IPS in its Space lab 2 mi ssion configuration. The scientific experiments mounted on top of the IPS served for the investigation of the sun. The versatility of the IPS allows for various other applications, such as stellar pointing or earth observation (e.g. by landmark tracking).

Figure 1.

IPS with Spacelab-2 Paylaod

The IPS has been developed by Dornier System since more than 10 years under contract of the European Space Agency (ESA). As a subsystem of the Space lab the IPS was delivered to NASA in two units. The long development resulted not only from the complexity of the system but mainly from a redesign in 1980 due to revised Shuttle lift-off

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load specifications. Presently, the IPS is the only flight proven pointing system providing a high degree of versatility and precjsion.

o Acce lerometer Package (ACP) : The ACP, located at the mounting base of the IPS serves for feedforward disturbance compensation. o Resolvers: The motor resolvers measure the gimbal angles, that is the relative orientation of the IPS w.r.t. the Orbiter.

Due to the limited accuracy and flexibility of the Shuttle to orient payloads, a stabilized platform was required to accommodate a variety of pay loads with rrasses up to 7000 kg. The IPS provides a pointing range up to +/- 60 deg about the lateral axes and +/- 180 deg about the roll axis. This viewing cone is realized by a three axis gimbal system. The erection of the payload is done by the Elevation Drive Unit (EDU), side looking out of the shuttle cargo bay is possible via the Cross-Elevation Drive unit (XDU) and rotation is provided by the Roll Drive Unit (RDU). The drive motor torquing capability of 30 I\I'n is sufficient for disturbance compensation and yields a reasonable acceleration for large angle manoeuvring.

The following section contains more details on the structure and functions of the control system, the parametric design and the stability assessment. The achievement of various requirements is described while regarding boundary conditions due to the structural flexibility of the plant, disturbances and computer limitations. Subsequently the simulation model of the IPS is described, because it is essential in the preflight verification of the IPS performance and stability. Furthermore both simulation and actual mission results are presented. The paper is concluded with an outlook to further improvements of the control system.

In addition to the drive assembly, the control system comprises the following IPS equipments: CXJNTROL SYSTEM o Data Control Unit (DCU) : This unit contains a fixed point processor for control law execution. o Gyro Package: Three axes, inertial rate measurement is accomplished by three orthogonal and one (redundant) skewed gyro. o Optical Sensor Package (OSP) : The absolute celestial reference is provided by the OSP containing one boresighted and two skewed (side-looking by 12 to 45 deg) Fixed Head Star Tracke rs (FHST) . For solar missi.ons the boresighted FHST can be used as sun sensor by means of a special optical device. The OSP is mounted on the payload in order to minimize misalignments between the experiments and the control system reference. A star catalogue is applied to ~dentify particular stars in the sensor field of views (2 deg x 2 deg ) .

The blockdiagram of the IPS control system is shown in Figure 2. The algorithms are executed by two computers. The fast control loop algorithms are implemented in the IPS Data Control Unit (DCU) , whereas the slow control loop tasks are allocated to the Spacelab (Command & Data Mangement) Subsystem Computer (SSC). The primary and fast control loop feedback is established by the three axes IPS rate measurement of the gyro package. The rate is sampled with 100 Hz and transformed into the platform axes, i. e. essentially the payload axes. The (prefiltered) rate is submitted to a quaternion integration to obtain the attitude and subsequently the attitude error. The quaternion representation of the attitude has been chosen to ease the computation load. The Command & Data Mgmt S/S

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control law consists of a sequence of attenuation filters and a PlO controller. The controller output must be transformed from the platform axes into the gimbal axes to exert the control torque via power amplifier and drive units. The payload cent er of gravity is far outside the gimbal center of rotation to accommcdate various types of payloads. However, this implies sensi tivity to external disturbances, caused e.g. by Orbiter thruster firing or crew motion. Therefore the accelerometer package (ACP) measures any linear acceleration at the IPS mounting base in order to enable feedforward compensation. Attitude Determination and Pointing Control The absolute measurement reference is provided in three axes by means of the three Fixed Head Star Trackers (FHST) of the Optical Sensor Package (OSP). The optical sensor signals are sampled with 1 Hz for correction of the quaternions according to the actual attitude error with respect to the celestial target. To this end a dedicated Attitude Determination Filter (ADF) is applied. Refering to Figure 2, the loop comprising the quaternion integration block and the 'Gyro Drift and Attitude Estimation' block forms a modified version of the Kalman filter. This Kalman filter (or ADF) estimates the current quaternions, the gyro drift and the relative misalignment between the star trackers. The quaternion integration yields the current attitude with a sampling rate of 25 Hz. Considering the 1 Hz cycle, this signal represents the attitude estimate based on gyro information. Via the observation matrix this attitude is transformed into the optical sensor axes. This enables a comparison between the optical sensor measurements and the gyro based estimate. The resulting error signal is fed through the Kalman filter gain matrix to obtain the corrections of the quaternions, the gyro dr i ft and the tracker misalignments. The signal correction and thus the main part of the Kalman filter is executed in the 1 Hz cycle. However, the quaternion integration running with 25 Hz frequency is part of the filter. This implies that the state transition matrix of the filter depends on the gyro rate signal during a 1 Hz cycle. For the generation of the Kalman filter gain matrix the state transition and observation matrices are linearized to enable a precalculation of the Kalman filter gain matrix based on the following informations: o a time-invariant state and observation model. The model applies 10 states: 3 quaternions (one is redundant), 3 gyro drifts, and 4 misalignments (2 lateral misalignments of the skewed w.r.t. the boresighted FHST * 2 skewed sensors), o the system noise due to gyro noise and numerical errors of the quaternions, o the measurement noise of the optical sensors. These informations allow the generation of the time variant optimal filter gains. To ease computation load, these gains are approximated by hyperbola functions, which can be represented by a few coefficients only. The att i tude determinat ion is the basis for achieving high pointing accuracy and stability in three axes by minimizing the effects due to gyro and optical sensor noise, gyro drift and sensor misal ignments. After filter settl ing, last ing typically 100 sec from initial target acquisition, long term stabilization is provided to the experiments.

As an option an experiment sensor can substitute the OSP as absolute measurement reference. Also attitude offset commands from the experiments are accepted by the OCU. DynamiC Control Operations Large angle manoeuvres, that is slew manoeuvres from one IPS orientation to another can be performed inertially referenced if the (integrated) gyro signals are adopted. To orient the IPS w.r.t. the Orbiter a resolver for each gimbal axis is available. For both cases the Spacelab Subsystem Computer (refer to Figure 2) contains an algorithm to generate the time-optimal trajectory for slew manoeuvres. To account for disturbances as well as for Orbiter motions the command trajectory is updated in 5 sec intervals. The command trajectory in terms of attitude and rate is subsequently fed to the PID control law at a sampling frequency of 5 Hz. The different needs for pointing and slewing require two sets of PID gains, the High Gain Controller (!-GC) optimized for pointing and the Low Gain Controller (LGC) for large angle manoeuvres. To avoid oscillations caused by the command shape and torque limitation the LGC applies a lower proport ional and integral gain than the !-GC to form essentially a rate controller. Thus the LGC minimizes the generated torque and hence the heat dissipation of the drive units. The maximtlTl slew rate is limited by the selected gyro spin speed: 1 deg/sec slew rate is selected for inertial pointing missions because of the lower gyro noise. For target and earth tracking missions 3 deg/sec is used. For these modes appropriate attitude and rate commands can be generated via the Subsystem Computer. In addition the following control operations can be performed: o Gimbal hold: This 'parking' mode applies the LGC to keep the IPS in a fixed position w.r.t. the Orbiter. o Scan: Attitude control according to various scan profiles can be performed by means of appropriate rate and attitude commands. o Manual pointing control: This allows open loop motions of the IPS by means of a joystick. o Activation/Deactivation: These operations essentially apply the gimbal angle slewing algorithm based on specific commands to erect respectively to stow the IPS. o Emergency Controller: This is a separate hardwired controller to enable safe stowage of the IPS in case of hardware or software failures. Fast Loop Algorithms Figure 3 presents the IPS fast control loop as it is implemented in the Data Control Unit (OCU). The three axes gyro loop applies a sequence of filters with different sampling frequencies. This is necessary because the OCU computer is not able to execute all filter algorithms within fastest (100 Hz) cycle. On the other hand the averaging of gyro data (100 Hz) and the prefilters (50 Hz) require high sampling rates, in order to avoid aliasing of high frequency structural modes and gyro noise. The rate filters running with 25 Hz are designed to attenuate structural modes with minimum phase shift. Each filter consists of a transfer function with a second order nominator and denominator. Figure 3 also illustrates the generation of the PlO controller inputs via updated quaternions and error integration.

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The second branch of the DCU consists in the three axes ACP loop. Although the ACP rreasurement is designed to form a feedforward, in fact it must be regarded as a feedback loop for stability analyses due to the coupling with the dynamics of the plant. Hence in total six feedback loops establish the multivariable system. The ACP loop contains as well a sequence of filters, designed according to similar criteria as the rate filters. Parametric Design (Filter Layout) and Stability Figure 4 presents the frequency response of the structural plant. That rreans, the drive torque is applied as input while the IPS angular rate is taken as output. The transfer functions for four different pointing orientations have been overlayed to cover parameter variations. The overlay is feasible by inclusion of the transformations which are actually applied in the fast loop. The low frequency resonance is caused by bearing and cable friction behaving like a spring in a small angular range. The high frequency resonances of the structural plant have to be attenuated by the filters of the fast control loop. To provide sufficient robustness against variations and uncertainties pure gain stabilisation has been envisaged such that the resonance peaks obtained gain margins of at least 6 dB. In an iterative design the PID gains are defined to obtain maximum control loop bandwidth and sufficient integral feedback. The result for one pointing orientation is given by Figure 5 showing the open loop frequency response. That rreans, one lateral gyro loop is opened whereas the other two gyro loops and all three ACP loops were kept closed. Although the applicability of the Nyquist criterion in such a Bode diagram for stability assessrrent of a mul tivariable con-.:rol system is doubtful, it is valuable for the design and assessrrent of stability rrargins. For preflight verification, however, also the evaluation of the

eigenvalues of the overall closed loop system is necessary. The important stability criteria as there are the low and high frequency gain margins, the phase margins and the gain margins of the structural modes can be derived from the Bode diagram. A significant constraint in parameter setting is that the IPS DCU computer is working with fixed point arithmetics. This requires normalization of the controller parameters and thus selection of appropriate limits. For each individual payload, it is required to select and verify the complete set of normalized, computer compatible parameters, which are therefore called Mission Dependent Parameters (MOP·s). DYNAMIC MODELLING AND SIMULATION To ensure the success of IPS missions a comprehensive verification on ground has been performed. For the control system a functional test only could be carried out under one-g conditions. The pointing accuracy and stability had to be demonstrated via analyses and simulation. To this end the IPS simulator PERFSIM (IPS PERFormance SIMulation) has been developed. It comprises the provisions for time and frequency response analyses, which are indispensable to verify system performance and stability complementary to one-g functional tests. PERFSIM is running on MicroVAX 11 and IBM 3081/3083 computers.

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Three different approaches are in use for the dynamics modelling of the coupled structures compr1s1ng the Orbiter, the Spacelab pallet , the IPS gimbal system and finally the payload:

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o Lumped Mass Model (LMM): This model represents the major structural elements as a chain of nine rigid bodies, connected by linear springs to include flexibilities. o Finite Element Model (FEM) : This model directly uses modal frequencies, displacements etc. of a structural finite element model of the overall system including Orbiter and payload. o Nonlinear Rigid Body Model (OCAP) : This model is based on the ESA OCAP (Dynamic and Control Analysis Package) program, to represent the nonlinear dynamics in particular for large angle manoeuvres. Since the FEM is applied for verification of the pointing performance and for stability analyses it is outlined in more d~tail. The dynamic model for the controller design and simulation has been derived from NASTRAN modal data in the following steps. 1. Starting point are NASTRAN modal data compri-

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Figure 6 gives an overview on the three-axes simulation model, which is rrodular and includes the following characteristics : o rigid and flexible system dynamics o man rrotion and Orbiter thruster firing characteristics o sensor rrodels (internal functions and disturbing effects)

sing generalized masses, modal frequencies and rotational and / or translational displacements. The modal data are transformed into a conrnon reference system and are truncated to retain (about 50) high gain modes above a specified limit value and below a frequency of 50 Hz. The retained modes are represented as 2nd order transfer functions yielding the continuous plant model (see Figure 7 ) . The plant model is augmented by 2nd order transfer functions of the gyros and the accelerometers. Via partial fraction expansion the representation by parallel oscillators can be retained. The modified modal gains are evaluated accordingly. The augmented plant model is transformed such , that the inputs and outputs can be given, respecti vely accepted, in their inherent coordinate system. The transformed continuous plant model is finally discretized at 100 Hz . The oscillator representation allows computation of the trans it ion matrix for one sampling interval in a closed form. Thus, assuming a constant input over the short interval of 0 . 01 sec, an e xac t z-transformation is obtained.

The FEM based model is a high order, linear i zed model providing high confidence for a small angular range and thus for pointing simulations and stability analyses. To cover the whole pointing range six models have been established for various, representative pointing orientations. The performance verification of the IPS is based on the IPS simulator PERFSIM. Therefore it is required to demonstrate that the model represents t he real behaviour under zero-g conditions. Checking the whole model against a ground test of the overall system is not sufficient due to disturbing effects under one-g conditions. Therefore all elements of the model, especially computer representation of the self-contained

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units and interfaces, have been compared to unit level tests and/or specifications to obtain a comprehensive model verification. For instance the DCU has been simulated by an emulator representing the fixed point arithmetics of the computer. As to the gyro and the star tracker, their internal functions have been represented and verified against tests. Also the FEM has been submitted to 'modal survey' tests, which applied certain excitations to the real structure to identify the flexible modes of the model.

Table 1 contains the IPS performance characteristics in view of the most important criteria, the quiescent stability and the disturbance response. All results are given for the worst of the two lateral axes and for the roll axis. The quiescent cases assume an undisturbed inertially fixed Orbiter, such, that any pointing error is only caused by IPS internal effects like noise, friction, quantization, misalignments etc. The stability is evaluated over an observation interval of five minutes, which is representative for an unlimited period of time. The results are gained from a multitude of simulation runs under varying boundary conditions. The lateral stability, kept below 0.7 arc sec , is most important to the experiments in order to obtain high quality images of their targets. Evaluations, in addition to the quoted results, revealed that a steadily, at 4 deg/min drifting Orbiter degrades the quiescent stability error by merely 10",(, caused by the drive unit bearing and cable friction. The disturbance response represents the variation of the attitude due to external disturbances: the man motion profile is defined by two opposite wall push-offs by an astronaut in the Orbiter flight deck, generating pairs of 80 Nsec impulses occurring every minute. The thruster firing is specified in accordance with the Orbi ter limit cycling within +/- 0.1 deg during inertial attitude hold, where the thrusters fire repeatedly 80 msec pulses in different combinations. The disturbance errors are defined as worst peak values of the response, i. e. as the worst result over all disturbance directions and pointing orientations. The IPS is designed to accorrmodate various types and sizes of payloads. To demonstrate the performance of the IPS two generic payloads, the 2000 kg and 7000 kg pay loads have been taken for an exemplary design of the controller parameters. It is remarkable that the differences between the 2000 kg and 7000 kg performance characteristics are fairly small. The reason is the almost invariable structural flexibility of the plant allowing the selection of similar control system bandwidths (0.8 Hz for 2000 kg and 0.5 Hz for 7000 kg payload mass).

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The mission dependent parameters, which are selected according to the actual payload properties have to be evaluated with regard to their flightworthiness, that is the performance and stability margins have to be predicted. Therefore Table 1 contains also the comparison between the performance prediction and the actual flight results. In general, the simulation was confirmed quite well. For the quiescent stability a coincidence between simulation and flight results was obtained while for the disturbance response the flight data obtained were not conclusive enough to derive the actually applied disturbances, in particular for the man motion case. Figure B compares the simulated response upon the specified man motion disturbance for the 2000 kg and 7000 kg payload. A typical thruster firing response is shown in Figure 9. While the disturbance impact is compensated after about 2 sec, settling is achieved only after 10 sec due to the Orbit er rotation starting after thruster firing. This induces an increase of the drive unit cable hysteresis torque up to its limitation. Subsequently, however the disturbance irrpact by the bearing and cable fr-iction is not essential compared to sensor noise and quantization. Figure 10 presents the disturbance reponse as obtained during the Spacelab-2 mission. The atti tude error in the two lateral axes y and z have been obtained via the integrated gyro measurements. The corresponding errors derived from the optical sensor differ from the gyro based error due to unequal sampling frequencies. The gimbal resolver angle is the relative motion of the IPS w.r.t. the Orbiter. Since the IPS is inert ially stabilized the gimbal resolvers essentially indicate the Orbiter rotation due to the thruster firing pulses. Figure 11 presents the attitude errors during pointing in the absence of disturbances. The standard deviations are 1.22 arc sec in roll (x) and 0.5 respectively 0.6 arcsec in the two lateral axes y and z. The variation of the attitude error is essent ially caused by three factors, in the sequence of their influence:

o quantization effects due the fixed point arithmetics, o gyro noise, o star tracker noise. Primarily the quantization is a point for future improvement of the IPS as outlined in the final section. Nevertheless it was a great success of the Spacelab-2 mission to achieve the high pointing performance, coincident with predictions. Also the fact that some initial problems could be overcome during the mission was important. Three control system related problems occurred during the flight: (1) During the first erections of the IPS it seemed that the IPS got stuck and only after some minutes it achieved the erected position. Analyses revealed, that the Orbiter attitude coordinates were transmitted in the wrong sequence to the IPS. These coordinates were applied in the slewing algorithm for erection in order to account for Orbiter motions. Therefore a wrong command was given to the controller as long as the Orbiter was moving. The problem was solved by an Orbiter software change. (2) The IPS could not achieve fine tracking during the first days of the mission . This problem was caused by two sources. First, the software parameters of the Fixed Head Star Trackers (FHST) were not accurately adjusted according to orbital sun viewing conditions. Intermediately this problem was overcome by less sensi tive Kalman filter gains avoiding large variations for the FHST measurements. Later the problem was solved by reloading of FHST software parameters. The second reason was, that at times one skewed FHST was oriented towards the earth, causing an FHST shutter closure due to the brightness of the earth. This in turn avoided the boresighted tracker to achieve fine tracking. The problem was solved by a change of operational procedures. (3) It was known before the flight that the controller parameter sett ing in the software

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Finally all control operations of the IPS were successfully verified, that is in addition to the fine pointing : o inertial and gimbal angle slewing, o gimbal hold, o activation / deactivation, o emergency stowage, o manual pointing controller. ooJ\CLUSICN AND FUTURE OUTLOOK The IPS demonstrated its high pointing performance during the Spacelatr-2 mission. Essential experiences could be gained from both the design and the first demonstration flight : o Besides the requirements, the design had to regard a lot of boundary conditions (flexibili ties, disturbances, hardware constraints). This implied a complex system structure. o Due to restraints in testing the closed loop control system on ground, the performance prediction had to rely on modelling and simulation . Therefore, also a verification of the simulation program is essential. o The maiden flight of the IPS served as additional proof of the design and confirmed preflight predictions based on simulations . o The flexibility of the IPS to reload parameters was important to overcome initial problems in the course of the flight. The performance of IPS was fully satisfactory to the experiments of the Spacelatr-2 mission . Nevertheless, due to the mature design of the gimbal system the IPS bears a considerable potential for improvements with regard to pointing performance as well as new applications. In particular the growth in computer and in sensor technology lead to solutions which only require exchange of individual control system units without interface modification and requalification of the whole IPS. The use of a fast floating processor and of more accurate sensors is under consideration to achieve the following improvements : o avoidance of quantization effects due to fixed point arithmetics o implementation of advanced control algorithms for disturbance compensation, o implementation of quasi continuous and more efficient attenuation filters, o use of an enhanced Kalman filter in one computer and with online gain generation for faster settling and higher quiescent stability, o widening of the range of applications such as target tracking and compatibility with the Space Station . is envisaged to achieve a pointing stability error below 0.1 arcsec and a disturbance response below 1 arcsec. In order to investigate improvements and future applications, che IPS simulator PERFSIM has been enhanced since the flight to form a more generic program. Also prOV1S1ons for simulating the dynamics and control of fast target tracking have been implemented into PERFSIM. First tracking simulat i ons revealed that the achievable accuracy and stability will be close to the present pointing performance, if an appropriate (experiment ) sensor is applied. To assess the basic IPS capabilities an ideal sensor is assumed. Figure 12 shows a t ypical landmark tracking rate profile apparent to the IPS when the Orbiter overflies the target in 300 km altitude . Once the target appears in the sensor field of view the IPS has to It

accelerate from zero rate to acquire the trajectory. By using a special tracking controller, settling is aChieved within a period of 20 sec after which the tracking error is kept below 7.15 arcsec, while the rate error is below 6.23 arcsec / sec. REFEREJ\CES Koesters, B. (1986). The first mission of the Instrument Pointing System (IPS). Annual AAS Guidance and Control Conference. AAS 86 053 . Vallely,

D.P . , (1985) IPS Control and Performance for Spacelatr-2 on Mission 51F. NASA George C. Marshall Space Flight Center.

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IPS attitude errors in the absence of disturbances (measured during the Space lab-2 mission)

Roll

t a n d rna r' k . t:racki ng siml l l at ir:m

o Orbiter overflying the t arge L i n 300 km altitude, o ideal target tracking se nsor assumed o FEM based model for the 2000 kg payload, o zero i nitial rate, o zero initial attitude error, o 60 deg gimbal half cone