Two techniques are presented for the synthesis of suboptimal systems using motor-driven inertia wheels as the source of torque for three-dimensional attitude control. These techniques approximately minimize the integral of a quadratic function of system error and control effort, and both procedures compensate for non-linear inter-axis coupling. The techniques developed in this paper are applied to the design of attitude control systems for two typical artificial satellites. The resulting control laws are in feedback form. In a computer simulation, systems designed on the basis of the procedures developed are shown to respond faster and more accurately than those designed by optimization procedures based on linearized approximations of the equations of motion or by conventional transform methods.
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1. INTRODUCTION MANY studies concerning the application of mathematical optimization techniques to the design of spacecraft attitude control systems have appeared in recent years. Most research in this area has been focused on time-and fuel-optimal, gas-jet control about a single axis \[1-4\]. Optimization of attitude control systems using inertia wheels as the source of control torque has been treated in considerably less detail. FLUGGE-LOTZ and M~a~-BACH \[1\a] nd SCHWARTZ \[5\h] ave proposed minimum-time and minimum-energy systems for inertia-wheel control about a single axis. KALMAN, ENGLAR and Bucv \[6\] have presented a three- * This work was partially supported by NASA Grant NAS8-18120 and NSF Grant GK-3273. Received 18 February 1969; revised 30 June 1969. The original version of this paper was presented at the 4th IFAC Congress which was held in Warsaw, Poland during June 1969. It was recommended for publication in revised form by associate editor B. Morgan. t Department of Aeronautics and Engineering Mechanics, University of Minnesota, Minneapolis, Minnesota, USA. :~ Department of Engineering Mechanics, University of Texas, Austin, Texas, USA.