Real-Time Computer Control of a Flexible Spacecraft Emulator

Gary W. Crocker, Peter C. Hughes, and Tony Hong

ABSTRACT: This article describes a ground-based test facility named “Daisy” established to study control issues for large flexible spacecraft. The validation of modem algorithms for system identification, and shape and attitude control and the develop ment of new control devices can be per- formed using this flexible spacecraft emu- lator. The experimental structure consists of a radial mesh of ribs attached flexibly to a rigid hub. The structure is instrumented with position and rate sensors and controlled by a real-time computer and data acquisition system via torque actuators. The more im- portant aspects of these subsystems and their integration are presented along with sample experimental results.

Introduction

The trend in spacecraft design has been toward larger, more complex structures re- lying on the increased use of lightweight ma- terials. As a consequence of size and weight, these designs will possess significant struc- tural flexibility, and maintaining correct spacecraft orientation and shape poses a great challenge. The development of more ad- vanced attitude control systems (ACS) in- volving modem multi-input/multi-ou@ut controllers will be needed to implement strict directional control over spacecraft with structural flexibility.

Driven by this fact, extensive theoretical research has been conducted in the field of identification and control of flexible struc- tures [l], [2]. However, there exists rela- tively little experience in its application. Ground-based testing is necessary to validate the many simplifying assumptions often made in the theory and to separate promising control techniques from unviable ones. The testing is also required to help develop ex- pertise in resolving practical issues such as the number, location, and type of sensors and actuators necessary for actual control system implementation.

Peter C. Hughes is Cockbum Professor and Gary W. Crocker and Tony Hong are Graduate Students at the Institute for Aerospace Studies, University of Toronto, Downsview, Ontario, Canada M3H 5T6.

In surveying ground-based facilities pres- ently in existence [3], there are many flexi- ble-structure test beds, but very few facilities available for the general study of large space structures (LSS). Most academic facilities are based on simple, purely flexible substruc- tures, such as plates, beams, trusses, or meshes [3]-[5]. These test beds offer insight on generic problems such as vibration suppression and small angle slewing, but the applicability of their reseatch to more com- plex structures is limited. The remaining fa- cilities tend to be designed for specific re- search goals, or to model particular spacecraft, or else they are proprietary [3], 161, 171.

A ground-based test facility, named “Daisy,” was established in 1985 at the University of Toronto’s Institute for Aero- space Studies to study the dynamics and con- trol of large flexible space structures. The main goal of this facility has been to provide a suitable test bed to evaluate the effective- ness of modeling, identification, and control techniques for LSS as well as to investigate sensor and actuator development.

This goal required the design of a suitable test structure that could, in an earth gravity environment, physically mimic the charac- teristic dynamic behavior of an LSS. The test bed was built to fulfill the following physical criteria: it must be physically complex; it must be composed of both rigid and flexible substructures of appropriate inertia ratios to allow for significant coupling of their mo- tion; it must have a large number of lightly damped, clustered, low-frequency vibration modes; and it should ideally have three un- damped “rigid” degrees of freedom.

In addition to the physical specifications of the test bed, there are requirements for the ACS. The test bed must be instrumented realistically with “spacelike” sensors and actuators, distributed throughout the entire structure. The sensors must offer sufficient resolution to provide desired pointing accu- racy, whereas the actuators mpst have suf- ficient power output and bandwidth to im- plement effective control. The computer and data acquisition system must be powerful enough to maintain a consistently high con- troller update rate necessary for the imple- mentation of real-time control.

Since its inception, this facility has gone through several stages of development. Most recently, a new real-time computing and data acquisition system was installed, providing the facility with significantly greater com- putational power and allowing a factor of 10 increase in controller sampling rate. This in- creased capability will be required to vali- date some of the more complex proposed control techniques for LSS [3].

Test-Bed Description Daisy Structure

The radially symmetric test structure (Fig. 1) consists of 10 ribs representing the flexi- ble substructure, attached to the rigid hub representing the “main body” of the satellite suspended on a set of gimble bearings. The hub has a full three degrees of rotational freedom, commonly referred to as roll, pitch, and yaw, whose axes are denoted by xh, yh, and zh, respectively, in Fig. 1. In a zero- gravity environment, these “rigid” modes would have zero frequency and be un- damped, but this ideal is not practical in a ground-based laboratory. In reality, friction in the hub bearings, which allow for hub rotation as well as support, produces damp- ing in all three rotational directions. Roll and pitch have some pendulosity as well to pre- serve the static stability of the suspended test StNCtUre. These pendulous modes, however, do not affect significantly the control prob- lem, having been placed at a frequency well below the elastic modes of the ribs (Fig. 2).

Each rib is mounted radially to the hub using gimble bearings (Fig. 2) and possesses two degrees of rotational freedom, being able to move vertically “out-of-cone” and hori- zontally “in-cone” with respect to the hub. The ribs are balanced about these gimble supports and comprise a rigid tube, counter- balance arm, tip mass, counterbalance mass, and a mechanism to lock the rib to the hub. The gimbles are preloaded to reduce friction and to hold each rib at 30 deg to the hori- zontal. Springs mounted in the bearing sup- port are used to provide the rib proportional restoring force, which sets the frequency of the elastic modes. These individual ribs are coupled to each other in a radial pattern by

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means of simple interconnecting springs to form essentially one flexible meshlike sub- structure.

Even though the “flexibility” of the Daisy structure is discrete, being located only at the rib supports, and represented only by this “joint flexibility,” this does not impair its ability to emulate structures with distributed

Fig. 1. Daisy diagram [ 71

flexibility. It is due to the ribs’ dynamic properties that Daisy emulates the most im- portant characteristics of a large flexible space structure: many vibration modes, low vibration frequencies (U, = 0.1 Hz), very light damping ({, = 0.006), and “clus- tered” frequencies. This indirect approach was taken because of the difficulty of reduc-

ing structural damping in an earth gravity environment. The space substructures we seek to model cannot support their own weight on Earth and cannot be used directly. Reference [8] describes a facility where truly structural flexible ribs are used with the aid of counterweights to offset gravity, but at the expense of introducing significant damping.

4 IEEE Control Systems Magazine

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Sensors and Actuators

The present sensor complement is com- prised of absolute and incremental shaft en- coders about each hub axis to measure in- dependently angular positions (angular velocity), respectively, and two accelerom- eters mounted on one rib tip. The present actuator complement consists of three reac- tion wheels and a gas jet (thruster) cluster. It would be desirable to have an accelerom- eter package and thruster cluster mounted on all 10 rib tips; future funding may permit this.

The absolute encoders produce a 16-bit natural binary number proportional to the position of the hub, whereas the incremental encoders output 5000 pulses per hub revo- lution (on separate lines, indicating the di- rection of motion). The incremental encod- ers can be used to resolve the hub angular rates to about 1 percent of the maximum an- gular velocity. This resolution depends on the hub angular rate and acceleration and is least when the hub is changing direction. The absolute encoders can resolve the hub posi- tion to about 20 arcsec with an accuracy of 10 arcsec.

The two accelerometers are aligned with the in-cone and out-of-cone axes and are mounted on the rib tip to allow maximum acceleration measurement. The accelerome- ters have a range of 2 g with an accuracy of

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2 pg. The output of the accelerometers is a differential current loop. Presently, these ac- celerometers are the only flexible structure sensors installed. However, several expen- ments [8]-[lo] illustrate the use of optics in estimating the amplitude of excited modes and the position of substructures. An opti- cally based rib-tip sensor is expected to be installed on this test bed in the near future.

The primary control actuator on Daisy is the reaction-wheel system consisting of a re- action wheel, a wheel angular velocity sen- sor, and its own embedded controller. There are three reaction-wheel systems mounted on the hub, each one having its spin axis aligned with one of the principal axes (xh, yh, zh).

The reaction wheel is comprised of a DC motor attached through a gear reducer to a large inertia wheel. The reaction wheel can be considered a momentum exchange de- vice, accelerating the inertia whed in one direction applies a counteracting torque to the hub. The reaction-wheel system has been sized so that Daisy is controllable [7], hav- ing a bandwidth large enough to be able to damp out the pendulous vibration of the hub.

Reaction-wheel velocities are measured using incremental shaft encoders. These in- cremental encoders output 2500 pulses per revolution. With an embedded controller sample rate of 200 Hz, these incremental en- coders have a resolution of about 1 percent of the maximum reaction-wheel velocity.

The reaction wheel is digitally controlled by an Intel 8096 embedded microcontroller implementing proportional-integral-deriva- tive (PID) feedback control of velocity. It produces a pulse-width-modulated (PWM) control signal that is sent to a high-speed power amplifier connected to the DC motor.

Daisy’s shape control actuators consist of two sets of two collinear thrusters attached to one rib tip. Each thruster consists of a normally closed valve and nozzle, through which up to 90 psi of air is released when 120 V-AC is applied to the valve. An anal- ysis in [ l l ] shows that these thrusters pro- vide, at worst, an active-control damping factor of { = 1.29 for the highest frequency flexible mode. (See Fig. 3.) Thus all the flexible modes can be forced to have greater than critical damping.

Computer System

Daisy’s computer system is essentially a local area network of single board computers (SBCs) connected by a Multibus 11 bus. Each SBC is a complex computer with a central processing unit, memory, serial port, appli- cation-specific hardware, and all the mes- sage passing hardware necessary to com- municate information with other SBCs. The computer system, Fig. 4, has five data ac- quisition SBCs made by MicroIndustries. The iRMX 11 real-time operating system re- sides on four Intel SBCs, which provide con- trol of external peripherals.

Functional partitioning is the dividing of a large task into smaller tasks that run on separate SBCs and communicate a limited amount of data to each other. The most ob- vious advantage of functional partitioning is the aggregation of computer power, pro- vided there is no substantial increase in over- head. The idea of distributing control tasks is not new [12]; other Multibus 11 systems can be found in applications such as flight simulators [13] and robotics [14]. However, the application of a Multibus 11 system in the control of flexible structures is unique and, we feel, a particularly powerful implemen-

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mina1 controller to allow the attachment of additional terminals; and a 16-channel ana- log output board.

Assuming a system with 46 state vari- ables, five inputs, and five outputs, simple calculations indicate that current control re- quirements can be met and that simple SBC upgrades will allow us to meet Daisy’s future requirements. The Table presents the mini- mum times (in milliseconds) required to ex- ecute a linear-quadratic-Gaussian (LQG) controller on various computer systems for 5- and 23-I/O configurations.

Another advantage of intelligent data ac- quisition boards is that most of the sensor and actuator signal conditioning can be done in software. The interface circuits can be simpler and the complete data acquisition system can be modified easily. Furthermore, the data acquisition system allows great ac- curacy in the measurement and control of the sensors and actuators. For example, the ac- curacy of the present thruster control has im- proved by a factor of 100 over a previous version.

Daisy’s hub positions are determined eas- ily by simple polling of the 16 signals from each absolute encoder. Daisy’s hub veloci-

tation of the functional partitioning and dis- tributed control concepts.

Functional partitioning should not be con- fused with parallelization, where a single code stream is divided into multiple code streams and executed on a single computer with multiple processors. In functional par- titioning, each task is written separately and executed in parallel on separate SBCs. As in any multitask environment, the tasks must communicate information among each other; if the computer system is not built for mul- titasking, this can lead to substantial over- head. In traditional multiprocessor systems, where one processor is the bus master and the others are slaves, information must al- ways be passed to and from the master. This degrades the overall system performance so that additional processors do not increase the system performance proportionally. Fortu- nately, the Multibus I1 system is built for the demands of multiprocessing [ 131 and, thus, eliminates the data bottlenecks seen in other computer systems.

Some other advantages of an open archi- tecture such as the Multibus I1 are versatil- ity, expandability, and adaptability; for ex- ample, the real-time computer is being used

in the control of a two-link flexible manip- ulator called Radius [ 141. Our system has 20 SBC slots; currently, we are using only nine. Assuming processor technology does not in- crease, we can at least double our current performance. By the addition or replacement of SBCs, the system can incorporate new board technologies and adapt to new sensor and actuator requirements. However, the system is complex and requires that each SBC be configured into the computer system and then programmed for a specific task.

We have distributed the control of Daisy onto five SBCs. The control task uses the iRMX I1 real-time operating system and re- sides on an Intel 80386B0287 SBC. The hub position and velocity measurement task and the thruster control task run on two 96-chan- ne1 digital input/output (I/O) SBCs. The ac- celerometer measurement task runs on a 64- channel analog input SBC. A task running on a general-purpose prototype SBC com- bines with the embedded controllers to con- trol hub torques. Four other SBCs complete the real-time computer: a peripheral con- troller to control the floppy drive, hard disk, and tape drives; a central service module to synchronize the interconnecting bus; a ter-

IEEE Control Systems Magazine 6

Table Acknowledgments Typical Control Execution Times (msec)

The Daisy facility has been funded in part System PDP 11/73 Intel 80287 Intel 80387 bv the Soace Mechanics Directorate of the

Department of Communications, in part by the Natural Sciences and Engineering Re- search Council, and in part by the Institute

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ties are calculated by setting up three timers to determine the periods between interrupts generated by the incremental encoder pulses, and then the periods are inverted and scaled. Again, some internal interrupts are used to generate the duty cycle of the 10-Hz P W M thruster control signal. The rib analog ac- celeration signals are simply converted by the analog input SBC into digital numbers that can be used by the control computer. The prototyping SBC and the embedded con- troller form a second distributed control net- work linked together by a twisted pair of lines. The prototyping SBC transmits to the embedded controller the required reaction- wheel velocities, which are generated by in- tegrating the control toques.

Figure 4 shows the interface circuits used to connect the sensors and actuators to the control computer: the embedded controllers and power amplifiers control the reaction wheels, the transmitter and receiver circuits cany the transistor-transistor logic signals across the 10 m separating the structure and the control computer, and a circuit that con- verts the digital thruster control signals into signals that can drive the thruster valves.

Sample Results

For simple demonstrations, a “baseline” controller, consisted of a simple integral-de- rivative feedback control on the position of the hub. No proportional term is needed be- cause the pitch and roll modes of Daisy are slightly pendulous. The gains have been tuned manually through observation of the hub response ta an initial velocity disturb- ance. For ease of implementation, control is based on a timed loop rather than a system clock interrupt. This controller is limited only to effective control of the rigid modes of Daisy and is not designed to take into ac- count the controller “spillover” effect of the flexible modes. Figure 5 illustrates the closed-loop response of Daisy’s hub to an initial roll rate with low gain control. The ribs were locked, rendering the test bed a purely rigid structure for this run.

To aid in controller code design and anal- ysis, a model of Daisy has been developed using Matrix,. This software package, resi- dent on our Apollo workstation, allows the simulation of both the ideal dynamic equa-

for Space and Terrestrial Science.

tions and the introduction of nonlinear ef- fects such as frictional losses and sensor lim- itations. The inclusion of some practical test- [l] L. W. Taylor, Jr., Proc. 4th Annual SCOLE bed limitations can greatly enhance the pro- Workshop, Hampton, VA, Oct. 1988. duction of usable controllers. Figure 6 shows [21 George c. SChameL and Raphael T. comparisons among three control algo- Haftka, “LQG and Direct Rate Feedback

Control with Model Reduction on a Flexible rithms: classical PID, madem LQ, and LQG. Control Grid Structure,” Seventh VPI&SU/ Depicted are the time responses to a self- AIM Symp. on Llynamics and Control of Large Structures, Blacksburg, VA, May generated velocity disturbance at time zero.

1989. The simulation has a controller sampling rate Of lo HZ and friction in [3] D. W. Sparfcs, Jr., G. C. Homer, J. Juang, the hub bearings and controller output quan- and G. Klose, “A Survey of Experiments tization. The effects of improved algorithms and Experimental Facilities for Active Con- are clearly evident with the modem LQ con- trol of Flexible Structures,” Third NASA/ troller outperforming the classical PID and DOD CSI Technology Conf., San Diego, with the LQG controller outperforming the CA, Jan. 1989.

W. Martin, and Paul T. Kotnik, “Labora- being self-generated, this improved control- tory Facility for Flexible Structure Control Experiments,” Sixth VPI&SU/AIAA Symp. ler response can be seen both before and after

time zero. on Llynamics and Control of Large Struc- tures, June 1987.

[5] F. C. Moon et al., “Nonlinear Dynamics and Control of Flexible Structures,” An- nual Report to AFOSR, Cornel1 Univ., Ith- aca, NY, Sept. 1988.

[6] Kenneth R. Lorell, Jean-NoEl Aubmn, Donald F. Zacharie, and Ernest0 Perez, “Control Technology Test Bed for Large Segmented Reflectors,” IEEE Contr. Syst. Mag., vol. 9, no. 6, pp. 13-20, Oct. 1989.

[7] G. B. Sincarsin and W. G. Sincarsin, “Lab- oratory Demonstntion of Control Tech- niques for Third Generation Spacecraft: Daisy Design Model,” Dywcon Enter- prises Ltd., Rept. Daisy-8, Feb. 1984

Fig. 5. Closed-loop impulse response Of [8] H. C. Vivan et al., “Flexible StNCtUE hub. Control Laboratory Development and Tech-

Referepces

simpler LQ controller. With the dism&ace [41 OZ@ner, Stephen Yurkovich, Joseph

Time [DOC-CR-84-009].

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January 1990 7

nology Demonstration,” Jet Propulsion [15] K. A. Carroll and W. G. Sincarsin, “Ex- Peter C. Hughes re- Lab., Pasadena, CA, Pub. 88-29, Oct. periment Research on the Control of Flex- ceived the Ph.D. degree 1987. ible Structures,” Dynacon Enterprises Ltd., in aerospace engineering

[9] S. S. Welch, “Optical Distributed Sensing Rept. 28-901/0201, Mar. 1989. from the University of and Computation for a Proposed Flexible Toronto in 1966. His Beam Experiment,” Seventh VPI&SU/AIAA areas of research interest Symp. on Dynamics and Control of Large include modeling, dy- Structures, Blacksburg, VA, May 1989. namics, and control of ro-

[IO] D. Laurin, “Development of Optical Sen- botic systems and flexible son for Space Structures,” Ph.D. Thesis, structures. Dr. Hughes is Univ. of Toronto, Institute for Aerospace a Fellow of the Canadian Studies (in preparation). Aeronautics and Space In-

[ l l ] W. G. Sincarsin, “Development of the stitute, and he reviews regularly for U.S. aero- Daisy Facility: Thruster Installation,” Dy- nacon Enterprises Ltd., Rept. 28-607/0302, Dec. 1989 [DOC-CR-SP-86-0381.

space journals.

B. Mack and M. M. Bayoumi, “Analysis of Sensing and Control Algorithms Using the Robot Controller Test Station,” Fifth CAS1 Conf. on Astronautics, Ottawa, On- tario, Canada, Nov. 1988. Francois Hubuenin, “Multibus I1 Simplifies Partitioning of a Complex Design,” Intel Application Note 43 1, Mar. 1989. K. S. Buchan, J. Carusone, and G. M. T. D’Eleuterio, “Radius-A Laboratoly Fa- cility for the Study of the Dynamics and Control of Structurally Flexible Manipula- tors,’’ Seventh VPI&SU/AIAA Symp. on

Gary W. Crocker was born in 1965 in Vancou- ver, British Columbia, Canada. He received the B.A.Sc. degree in engi- neering physics from the University of British Co- lumbia in 1987. He is cur- rently finishing work on the M.A.Sc. degree in aerospace engineering at the University of To-

ronto. His areas of research include real-time con-

Tony Hong was born in 1965 in Sudbuly, On- tario, Canada. He re- ceived the honors B.A.Sc. degree in engineering sci- ence from the University of Toronto in 1987. He is currently finishing work on the M.A.Sc. degree in aerospace engineering at the University of To- ronto. His areas of re-

Dynamics and Control of Large Structures, Blacksburg, VA, May 1989. flexible structures. tation of flexible structures.

trol, microprocessor-based data acquisition, and search interest include the control and instrumen-

Out of Control

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“This here is called ‘Preparation H-Infinity ’, recently approved f o r over-the-counter sale. It’s guaranteed to cure all your control ills!”

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