Abstract
AbstractThe robust preview control problem of uncertain discrete-time systems satisfying matching conditions is considered. First, for the nominal system, we use the difference between a system state and its steady-state value, instead of the usual difference between system states, to derive an augmented error system that includes the future information on the reference signal and disturbance signal to transform the tracking problem into a regulator problem. Then, the robust controller design problem based on the optimal controller of the augmented error system is proposed for uncertain system. And the proposed robust preview control law is obtained in terms of the linear matrix inequality (LMI) technique and the Lyapunov stability theory. Bringing the resulting controller back to the original system, a controller with preview actions achieving robust tracking performance is presented. The numerical simulation example also illustrates the effectiveness of the results presented in the paper.
Highlights
The research question of preview control theory is as follows: when the reference signal or exogenous disturbance can be previewable, how can we take full advantage of the known future reference signal or disturbance signal to improve the tracking performance of a closed-loop system? Sheridan (1966) proposed the concept of preview control via three models
In this paper, the robust preview control problem has been proposed for a class of uncertain discretetime systems
The optimal controller is obtained for an augmented error system (i.e. system (15)) applying optimal control theory
Summary
The research question of preview control theory is as follows: when the reference signal or exogenous disturbance can be previewable, how can we take full advantage of the known future reference signal or disturbance signal to improve the tracking performance of a closed-loop system? Sheridan (1966) proposed the concept of preview control via three models. The tracking problem was transformed into a regulator problem, and the optimal control law for the augmented error system was obtained using optimal control theory. Liao, Takaba, Katayama, and Katsuura (2003) investigated the optimal preview control problem for multirate systems via a research study on the working mechanism of the chemical fractionation tower control system, and solved the problem well. Research has made possible a breakthrough (Liao, Lu, & Liu, 2016; Wu, Liao, & Tomizuka, 2016; Zhang, Bae, & Tomizuka, 2015; Zhao, Sun, Ren, & Li, 2016) via preview control for multi-agent systems, descriptor systems, the variable coefficient of control systems, stochastic control systems, and so on
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