H-infinity feedback for attitude control of liquid-filled spacecraft

An H-infinity, that is, Hardy infinity, feedback controller for the attitud e control problem of a liquid-filled spacecraft is presented. The spacecraf t is modeled as a main rigid body filled with an ideal liquid in uniform vo rtex motion and three control torques and disturbances. Quaternions are use d to describe the evolution of liquid-filled spacecraft orientation to elim inate the singularities due to Euler angle representations for the kinemati cs motions. The H-infinity feedback controller is formulated by solving the Hamilton-Jacobi-Issacs inequality associated with the H-infinity suboptima l control problem on state manifolds according to Van der Schaft's theory ( Van der Schaft, A. J., "On a State Space Approach to Non-Linear H-infinity Control," Systems and Control Letters, Vol. 16, No. 1, 1991, pp. 1-8 and Va n der Schaft, A. J., "L-2-Gain Analysis of Non-Linear Systems and Non-Linea r State Feedback N-infinity Control," IEEE Transactions on Automatic Contro l, Vol. 37, No. 6, 1992, pp. 770-784). The orientation and angular velociti es of the liquid-filled spacecraft are stabilized by appropriately choosing the feedback coefficients. The determination of the coefficients is given explicitly. The numerical simulations show that the designed feedback laws can be effectively applied to stabilize the attitude of liquid-filled space craft with energy dissipation and external disturbances.