Multiple-input multiple-output robust vibration control for constrained gyroelastic solar panel considering parametric and un-modeled dynamic uncertainties

Abstract

Gyroelastic solar panel is a kind of flexible solar panel structure with variable-speed control moment gyroscopes distributed inside. The torque generated by these variable-speed control moment gyroscopes can be used for active vibration suppression. This paper addresses the vibration suppression problem of gyroelastic solar panel in the presence of parametric uncertainties and un-modeled dynamic uncertainties. A novel μ-synthesis method based on analytical multiple-input multiple-output weights design is proposed, which relates 2-norm of the vector of regulated outputs, closed-loop modal damping, and relative control ability of actuators to each mode to the weights. Based on the idea of collocated control, the full order state-space model of the constrained gyroelastic plate with angle gyros as measuring devices is derived. After model reduction, modeling of un-modeled dynamic, and designing the multiple-input multiple-output weights, μ-controller is solved by the DK-iteration method. Furthermore, a comparative study of the μ-controller designed by the proposed procedure and the Positive Position Feedback (PPF) controller designed by the non-smooth H∞ synthesis method is also presented. The control methods are compared for their vibration attenuation, energy utilization, robustness performance characteristics, and robustness stability characteristics. Results for both time domain and frequency domain simulations are presented. Simulation results show that the designed μ-controller has better vibration attenuation effect and robustness performance characteristics than the PPF controller, and can achieve a better robust vibration suppression of the constrained gyroelastic solar panel in presence of parametric and un-modeled dynamic uncertainties.