Study on Analysis and Avoidance of Unstable Control for Flexible System Design

It is difficult to design the control law for flexible systems with multiple lightly damped modes. Particularly, when there exist parameter perturbations, for example, resonant frequency or damping ratio etc., the stability of the system cannot be guaranteed. Conventionally, the control design of the flexible system is only stabilization design, without considering the performance requirement of the system. For the H-infinity control, even the famous H-infinity loop shaping method proposed by McFarlaned, cannot improve further the performance of the system. Instead, the resulting controller is unstable, with is not easy to tune on in practice. In the proposed, the system bandwidth is chosen as the performance index for the H-infinity optimal control. The robustness of the system is further improved by considering the performance of the system. Furthermore, the controller is stable, i.e., the H-infinity strong stabilization problem is resolved. With this design, the control accuracy and the speed of response is improved, and also the controller can be tuned on easily. The proposed work is important for the application of flexible structures in the real world.