Normal matrix design methodology of spacecraft robust attitude control

The attitude control problem for a flexible spacecraft with flywheels is addressed using the normal matrix control theory. The proposed control law is robust H_∞ optimal with respect to the nonlinear attitude dynamics with disturbances and uncertainties, and the associated Lyapunov function satisfies a Hamilton-Jacobi-Isaacs partial differential inequality. The control law includes three parts: three Proportional-Derivative controllers with same differential gains, the feedback of the dynamics parameters, and the inside-the-loop input shapers. The first part is for keeping the normality of the spacecraft dynamics, and the latter two is for the enhancement of the normality of the system. Furthermore, the normality and the system poles of the attitude dynamics, and the stability and design method of inside-the-loop input shapers are investigated. The system poles of flexible spacecraft with flywheels are determined by an odd-dimension eigenvalue problem of generalized gyroscopic system. The Linear Matrix Inequalities are established for the stability of inside-the-loop input shapers using free-weighting matrices. Numerical simulations are performed to demonstrate the validity and effectiveness of the proposed normal-matrix control law.