Robust variable structure attitude control with L₂-gain performance for a flexible spacecraft including input saturation

This paper presents the design of a robust controller, based on variable structure control, for the rotational manoeuvring and vibration reduction of a flexible spacecraft with input saturation. The dynamic equations of motion are formulated as a finite dimensional mathematical model, but accounting for the infinite number of natural vibration modes of the flexible appendages. Based on this model, a variable structure controller is designed for rotational manoeuvres and vibration suppression, and its exponential stability is demonstrated. The synthesis of the control system assumes that only the pitch angle and its derivative are accessible for feedback, and that the flexible modes are not measured. Saturation limits are introduced into the controller design to cope with the actuation limitations, and the stability of the modified control solution is verified. The prescribed robust performance is obtained by ensuring that the L₂-gain synthesis, from a torque disturbance to the penalty output, is less than a specified level. Simulation results are presented for the attitude manoeuvring and elastic mode stabilization of an orbiting flexible spacecraft; these results demonstrate the excellent performance of the proposed controller and illustrate its robustness to external disturbances.