Adaptive variable structure and commanding shaped vibration control of flexible spacecraft

In this paper, a new approach for vibration control of flexible spacecraft during attitude maneuvering is proposed. This control strategy integrates the command input shaping and the technique of dynamic variable structure output feedback control. More precisely, the input shaper is implemented outside of the feedback loop, which is designed for the reference model to achieve the exact elimination of residual vibration by modifying the existing command; whereas for the feedback loop, the controller is designed to make the closed-loop system follow the reference model with input shaper and eliminate the residual vibrations in the presence of parametric uncertainty and external disturbances. An attractive feature of this proposed dynamic variable structure output feedback control algorithm is that the parametric uncertainties of the system are not necessarily to satisfy the so-called matching condition or invariance conditions, provided that certain bounds are known. Furthermore, an adaptive version of the proposed controller is achieved through releasing the limitation of knowing the bounds of the uncertainties and perturbations in advance. The adaptive control law results in substantially simpler stability analysis and improves overall response. Compared with conventional methods, the developed control scheme guarantees not only the stability of the closed-loop system, but also yields better performance and robustness in the presence of parametric uncertainties and external disturbance. Simulation results are presented for the spacecraft model to show the effectiveness of the proposed control techniques.