Robust momentum management and attitude control system for the Space Station

A game theoretic controller is synthesized for momentum management and attitude control of the Space Station in the presence of uncertainties in the moments of inertia. Full state information is assumed since attitude and attitude rates are assumed to be very accurately measured. By an input-output decomposition of the uncertainty in the system matrices, the parameter uncertainties in the dynamic system are represented as an unknown gain associated with an internal feedback loop (IFL). The input and output matrices associated with the IFL form directions through which the uncertain parameters affect system response. If the quadratic form of the IFL output augments the cost criterion, then enhanced parameter robustness is anticipated. By considering the input and the input disturbance from the IFL as two noncooperative players, a linear-quadratic differential game is constructed. The solution in the form of a linear controller is used for synthesis. Inclusion of the external disturbance torques results in a dynamic feedback controller that consists of conventional proportional-integralderivative control and cyclic disturbance rejection filters. It is shown that the game theoretic design allows large variations in the inertias in directions of importance. GAME theoretic controller developed in Refs. 1 and 22 is applied to the attitude/momentum control for the Space Station that uses control moment gyros (CMGs) as the primary actuating devices and gravity gradient torque to manage momentum stored in CMGs. The moments of inertia of the Space Station are assumed to be constant but uncertain. In Refs. 2 and 3 the linear quadratic regulator (LQR) design procedure has been used to control the attitude/momentum of the Space Station. Full state information is assumed since the attitude and attitude rate are assumed to be very accurately measured. In Ref. 2 disturbance rejection filters are augmented to the system to handle the external cyclic disturbance torque, and the LQR design and pole assignment procedures for pitch control and roll-yaw control, respectively, are applied to the augmented system. In this paper the system equation is differentiated until the external disturbance torque term disappears in the resulting equation to apply the design procedure developed in Sec. II. The resulting controller consists of conventional proportional-integral-derivative (PID) control and the cyclic disturbance rejection filter as in Ref. 2. The application of the game theoretic approach combined with the internal feedback loop decomposition for describing parameter uncertainty allows very large variation in the inertia of the Space Station with little deterioration in performance. In Ref. 4, a differential game approach to developing synthesis techniques was taken where the parameter uncertainty was not decomposed and only the uncertainty in the system matrix is considered. In Refs. 5-7, Lyapunov stability theory has been used to design a control law for a system with uncertainty. This approach is similar to that used here in that a particular algebraic Riccati equation (ARE) must be solved. In Ref. 8, by adopting an input-output decomposition of the parameter uncertainty, the uncertain system is represented as an internal