A Robust Disturbance Rejection Method for Uncertain Flexible Mechanical Vibrating Systems Under Persistent Excitation

Abstract

6546) This paper presents a robust disturbance rejection method for a class of flexible mechanical vibrating systems with time-varying parameter perturbations subject to persistent excitation. The control input is split into two parts as a common strategy: one is obtained from the regulator design that is responsible for primary stabilization; the other is assigned to cancel the effect of the persistent excitation. The states of controlled dynamics and excitation dynamics are estimated by a Kalman filter. Then, taking into account plant variations, a robust stability condition is proposed to ensure the stability of the resulting closed system. It is shown that, using the proposed stability condition, the designed controller can effectively suppress the persistent excitation and keep the flexible mechanical system from the possibility of instability caused by spillover and time-varying parameter perturbations. Finally, two examples are given to demonstrate the use of the design method.2 *95) Flexible mechanical systems, robust disturbance rejection, persistent excitation, time-varying parameter perturbations +9584 9 ,(54698 48 98659 10:

Design of robust-stable and quadratic finite-horizon optimal active vibration controllers with low trajectory sensitivity for the uncertain flexible rotor systems via the orthogonal-functions approach and the hybrid Taguchi-genetic algorithm

“…Thus, it is impractical or impossible to implement the infinite-dimensional feedback controllers based on complete models of the flexible rotor system. Hence, instead of using the original infinite-dimensional distributed parameter model, many researchers used the finite-dimensional model to approximate the original infinite-dimensional model for designing the vibration controllers (see, for example, Balas, 1978a,b, 1982; Balas et al, 1988; Chen, 2003; Chen et al, 2000; Chou et al, 1998; Khot and Heise, 1994; Lin et al, 1990; Nonami et al, 1992; Zheng, 2004). Those researchers divided the finite-dimensional model into two parts: the controlled part and the residual part.…”

“…However, the problem of parameter perturbations in the active control design of a flexible rotor system has not received as much attention as the spillover problem. Thus, recently, some articles (Chen, 2003; Chou et al, 1998; Khot and Heise, 1994; Lin et al, 1990; Zheng, 2004) have discussed the robustness analysis of active vibration control of flexible rotor system with both the residual modes and the linear elemental parameter perturbations. On the other hand, the plant parameters may deviate from their nominal values and the system designed to be optimal for one set of parameter values no longer remains optimal for a different set of values.…”

“…Besides, for some practical problems, we need to deal with the finite-horizon (i.e., finite-time) optimal control problems (Friedland, 1986). Most of the LQ-based and related optimal control methods of active vibration control (see, for example, Balas, 1978a,b, 1982; Balas et al, 1988; Chen, 2003; Chen et al, 2000; Chou et al, 1998; Khot and Heise, 1994; Lin et al, 1990; Nonami et al, 1992; Zheng, 2004) belong to quadratic-infinite-horizon-optimal control approaches, and thus can only guarantee the steady-state performance. But the quadratic-finite-horizon-optimal control approaches can ensure both transient and steady-state performances.…”

Reduced Model inH∞Vibration Control Using Linear Matrix Inequalities

“…Experimental difficulties can also be responsible for uncertainties due to measurements limitations. Although robust controllers are designed using a reduced model (nominal model) of the structure, it should be able to control the real structure under parametric and dynamic uncertainties [3,21,26,31] ensuring stability and a good performance.…”