Robust Adaptive Attitude Tracking Control With $L2$-Gain Performance and Vibration Reduction of an Orbiting Flexible Spacecraft

This paper presents a dual-stage control system design method for flexible spacecraft attitude tracking control and active vibration suppression by an embedded smart material as sensors/actuators. More specifically, a conventional sliding mode controller with the assumption of knowing system parameters is first designed that ensures asymptotical convergence of attitude tracking error described by error quaternion and its derivative in the presence of bounded parameter variation/disturbance. Then it is redesigned, such that the need for knowing the system parameters in advance is eliminated by using an adaptive updating law. For the synthesis of the controller, to achieve the prescribed $L2$-gain performance criterion, the control gains are designed by solving a linear matrix inequality problem. Indeed, external torque disturbances/parametric error attenuations with respect to the performance measurement along with the control input penalty are ensured in the $L2$-gain sense. Even if this controller has the ability to reject the disturbance and deal with actuator constraint, it excites the elastic modes of flexible appendages, which will deteriorate the pointing performance. Then the undesirable vibration is actively suppressed by applying feedback control voltages to the piezoceramic actuator, in which the modal velocity feedback control method is employed for determining the control voltages. Numerical simulations are performed to show that attitude tracking and vibration suppression are accomplished, in spite of the presence of disturbances/parameter uncertainties and even control input constraint.