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Summary It is commonly believed that reduced‐order observers, including reduced‐order Kalman filters, cannot be used in the loop transfer recovery (LTR) design of the plant output side. In contrast to common understanding, we show that, at least for nonminimum‐phase plants, the reduced‐order Kalman filter can be used in the linear‐quadratic‐Gaussian (LQG)/LTR design of the plant output side with clear meaning in systems theory. The key concept is to regard a reduced‐order Kalman filter as a high‐gain full‐order Kalman filter. For the reduced‐order LQG controller, we examine the asymptotic property achieved by applying the recovery procedure used in the full‐order LQG/LTR design. Using the equivalent full‐order Kalman filter, we find that the sensitivity property of the reduced‐order LQG controller is asymptotically equivalent to that of a high‐gain partial output injection system. Motivated by this result, we propose the reduced‐order LQG/LTR procedure taking the high‐gain partial output injection system as a target. Some target properties are discussed to clarify the difference from the full‐order design. A multivariable design example is presented to show that the procedure provides a systematic design of a reduced‐order controller with optimality consideration.

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.

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In this article, a mixed robust/optimal control approach is proposed to treat the active vibration control (or active vibration suppression) problems of flexible structural systems under the effects of mode truncation, linear time-varying parameter perturbations and nonlinear actuators. A new robust stability condition is derived for the flexible structural system which is controlled by an observer-based controller and is subject to mode truncation, nonlinear actuators and linear structured time-varying parameter perturbations simultaneously. Based on the robust stability constraint and the minimization of a de2ned H 2 performance, a hybrid Taguchi-genetic algorithm (HTGA) is employed to find the optimal state feedback gain matrix and observer gain matrix for uncertain flexible structural systems. A design example of the optimal observer-based controller for a simply supported beam is given to demonstrate the combined application of the presented sufficient condition and the HTGA.