1. Three Axis Control Problem. The proposed attitude control problem discussed so far is limited to the pitch axis. However, the results can be extended to the three-axis control problem. From the orbital configuration, it can be seen that only the pitch attitude, subject to large angle rotation with respect to the orbital fixed frame, experiences large cyclic gravity gradient torque. The other two axes are practically fixed to the orbital frame, and, hence, with small attitude errors, the gravity gradient torques about the axes are relatively small. Their control may then be treated in a rather simpler way such as shown in Ref. 5. 2. Control Hardware Considerations. Sensors and actuators are basic control devices that need to be carefully assessed. Three-axis inertial sensors with star trackers placed at structural appropriate points will be required to make the system observable. Mass expelled actuators distributed along the long edges of the solar collector platform may be employed for the power-assisted control operations in the pitch axis. Momemtum wheels and CMG's may be used for the proportional control for the other two axes. 3. Assessment of Disturbance Effects. Although the energy sink approach (See Ref. 6) has been utilized in this paper to approximate the damping effects of the external and internal disturbances, their detailed effects such as the level of drag in orbit, the solar radiation pressure, the interaction of Earth magnetic field and the magnetic field on-board, the structural flexibility, the amount of drift for a given period of time, the frequency of correction maneuvers, the effectiveness of the algorithms, etc., must be investigated. Acknowledgements — This work was carried out at Martin Marietta Denver Aerospace under IR&D Program D39-R and at the Jet Propulsion Laboratory, California Institute of Technology, under NASA Contract No. NAS7-100. The authors are grateful to Dr. R. C. Ried and Dr. H. B. Hablani of the Johnson Space Center, and Professor R. W. Longman of Columbia University for their valuable suggestions and discussions. REFERENCES I. B.D. Elrod, A. Quasi-Inertial Attitude Mode for Orbiting Spacecraft, Journal of Spacecraft 9, 889-895, 1972. 2. T.M. Apostol, Mathematical Analysis: A Modern Approach to Advanced Calculus, Addison Wesley, Reading, Massachusetts, 1957. 3. A.D. Myskis, Advanced Mathematics for Engineers. English translation by V.M. Volosov and LG. Volosova, Mir Publishers, Moscow, USSR, 1975. 4. S.J. Wang, A Gradient Computational Technique for a Class of Optimal Control Problems Subject to Inequality Constraints, Ph.D. Dissertation, Michigan State University, East Lansing, Michigan, 1969. 5. C.T. Chen, Introduction to Linear System Theory, Holt, Rinehart and Winston, New York, 1970. 6. T.R. Kane and D.A. Levinson, Energy-Sink Analysis Containing Driven Rotors, in Proceedings of the Second VPI&SU/A1AA Symposium on Dynamics and Control of Large Flexible Spacecraft, held in Blacksburg, Virginia, and edited by L. Meirovitch, 1979.
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