Robust Kalman-Filter-Based Frequency-Shaping Optimal Active Vibration Control of Uncertain Flexible Mechanical Systems

Abstract

This paper presents a time-domain control methodology, which is named as the robust Kalman-filter-based frequency-shaping optimal feedback (KFBFSOF) control method, to treat the active vibration control (or active vibration suppression) problem of flexible mechanical systems under simultaneously high frequencies unmodelled dynamics, residual modes, linear time-varying parameter perturbations in both the controlled and residual parts, noises (input noise and measurement noise), and noise uncertainties. Two robust stability conditions are proposed for the flexible mechanical system, which is controlled by a KFBFSOF controller and subject to mode truncation, noise uncertainties, and linear structured time-varying parameter perturbations simultaneously. The advantage of the presented KFBFSOF control methodology is that it can make the controlled closed-loop system to obtain both good robustness at high frequencies and good performance at low frequencies. Besides, the proposed robust stability criteria guarantee that the designed KFBFSOF controller can make the controlled flexible mechanical system to avoid the possibilities of both spillover-induced instability and time-varying-parameter-perturbation-induced instability. Two examples are given to illustrate the application of the presented control methodology to the active vibration control problems of a simply supported flexible beam and of a flexible rotor system.

A Mixed Robust/Optimal Active Vibration Control for Uncertain Flexible Structural Systems with Nonlinear Actuators Using Genetic Algorithm

“…To the authors' best knowledge, only a few articles (Lin et al, 19901 Khot andHeise, 19941 Khot andOz, 19971 Chou et al, 1998a1 Chen et al, 20001 Zheng et al, 2002) have addressed the problem of stabilization of flexible structural systems under mode truncation and parameter perturbations. Note that the results proposed by Lin et al (1990), Chou et al (1998a), Chen et al (2000) and Zheng et al (2002) are valid for linear structured time-varying parameter perturbations, whereas the results given by Khot and Heise (1994) and Khot and Oz (1997) are applicable only to linear structured time-invariant parameter perturbations. It is well known that any analysis used for the time-varying case can be applied to the time-invariant case (but not vice versa).…”

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

“…In our recent paper (Chen et al, 2000), we have proposed a robust Kalman-filter-based frequency-shaping controller for flexible mechanical systems with time-varying perturbations. However, the case considered in Chou et al (1998) and Chen et al (2000) is a standard LQG control problem with white noise, such that the resulting control system cannot suppress the persistent excitations. Until now, to the best of our knowledge, disturbance rejection for flexible systems with timevarying parameter perturbations under persistent excitation has not yet been discussed.…”

“…Active vibration control of flexible mechanical systems with time-varying parameter perturbations has been widely discussed by using the LQG control method recently (e.g., Chou et al, 1998;Chen et al, 2000). Chou et al (1998) have discussed the robust stabilization of flexible mechanical systems with time-varying parameter perturbations and derived a robust stability condition for the controller design.…”

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.…”

“…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.…”