Stability condition for flexible structure control with mode residualization

Abstract

Chun-Liang Lin* and Fei-Bin Hsiaoj National Cheng Kung University, Tainan, Taiwan, Republic of China and Bor-Sen Chen J National Tsing Hua University, Hsinchu, Taiwan, Republic of China accommodated in controller design. One of the methods for obtaining a reduced-order controller is to use the formalism of mode residualization. This is extensively applied in the flutter suppression and structural control' problems. This formulation of the reduced-order model is obtained by assuming that the residual modal states of the system quickly reach steady state values. The reduced-order controller design is then based on this simplified model. Although such a controller usually works well on the reduced-order system, it may not stabilize the actual closed-loop system. This is, of course, the most important evaluation criterion for a control law selection. In this Note, we develop the general idea of mode residualization for a high-order, flexible structure and obtain results for the operation of an observer-based controller, based on the reduced-order model, in closed-loop with the actual system. By applying the perturbation theory, we derive a new stability condition on the basis of the frequency domain representation, which guarantees the stability of the overall closedloop system even when the sensors and actuators are not collocated. In the flutter suppression or other structural control problems, the natural frequency, mode shape, and damping characteristics of modes are all known imprecisely. Thus, parameter uncertainty may cause the system to be unstable. Addressing this issue, we also present a simple robust stability condition, which insures the overall stability so that the controlled system will not be destabilized by parametric perturbations.