Robust Backstepping Sliding Mode Attitude Tracking and Vibration Damping of Flexible Spacecraft with Actuator Dynamics

This paper presents a dual-stage control system design method for the attitude tracking control and vibration stabilization of a spacecraft with flexible appendages embedded with piezoceramics as sensor and actuator. In this design approach, attitude control system and vibration suppression were designed separately using a lower order model. Based on the sliding mode control (SMC) and backstepping technique, a new attitude controller in the form of the input voltage of the reaction wheel is derived to control the attitude motion of a spacecraft, in which the reaction wheel dynamics is also considered from the real applications point of view. Here the sliding mode technique is used to achieve an asymptotic convergence of the attitude and angular velocity tracking errors in the presence of parameter variation and disturbance by providing a virtual torque input at the rigid body while the backstepping technique is used to regulate the input voltage of the actuator to provide the required torque. The asymptotic stability is shown using a Lyapunov analysis. Furthermore, an adaptive version of the proposed attitude control law is also designed for adapting the unknown upper bounds of the lumped disturbance so that the limitation of knowing the bound of the disturbance in advance is released. For actively suppressing the induced vibration, strain rate feedback control methods are presented by using piezoelectric materials as additional sensors and actuators bonded on the surface of the flexible appendages. The performances of the hybrid control schemes are assessed in terms of attitude tracking and level of vibration reduction in comparison to the proportional-derivative and conventional SMC. Both analytical and numerical results are presented to show the theoretical and practical merit of this hybrid approach.