General attitude control and stability of spacecraft with flexible structures

The method of input-output feedback linearizar tion incorporating the Lyapunov stability analysis was applied in this study for the simultaneous multiaxis reorientation of a rigid spacecraft with flexible structures. Only three attitude torque actuators in the hub are required for the proposed control law. Mathematical modeling of the system gives a set of coupled ordinary and partial differential equations, which includes the attitude dynamics of the spacecraft and the dynamics of the flexible structures. To simplify the system equations for controller design, the deformations of the flexible structures were assumed small and the mode-shape functions were applied first. Furthermore, the set of nonlinear equations governing the attitude motions was transformed into Euler parameters representation. Through the method of feedback linearization and vector subtraction in the Euler parameters space, the dynamics of the attitude errors was formulated as a set of stable second-order ordinary differential equations with constant coefficients, from which the attitude feedback control law can be derived. Vibration control of the flexible structures iri the form of adaptive damping was also derived from the procedure of Lyapunov stability analysis and become a part of the attitude feedback control law. The stability of the overall dynamic system can also be achieved by tuning the selected control gains in the Lyapunov analysis. Attitude maneuver of a model spacecraft was tested using the proposed control law and the simulation results were compared for the cases with and without adaptive structural damping. For a given set of attitude gains, the study shows by selecting the adaptive damping coefficients the relative optimal time and torque maneuver of the flexible spacecraft can be determined.