Abstract
This paper considers the application of the preview control method to the optimal tracking control problem for a class of continuous-time systems with state and input delays. First, through a transformation, the system is transformed into a nondelayed one. Then, the tracking problem of the time-delay system is transformed into one of a nondelayed system via processing of the reference signal. We then apply preview control theory to derive an augmented system for the nondelayed system and design a controller with preview function assuming that the reference signal is previewable. Finally, we obtain the optimal control law of the augmented error system and thus obtain that of the original system by letting the preview length of the reference signal go to zero. Numerical simulations are provided to illustrate the effectiveness and validity of our conclusions.
Highlights
As we all know, a time-delay phenomenon exists widely in practical engineering, and it is usually the main source of instability and performance degradation in various control systems
The contribution of this paper is to apply preview control theory to the optimal tracking control problem for continuous-time control systems that are subject to state and input delays
We have studied the optimal tracking control for a class of linear continuous-time control systems with state and input delays
Summary
A time-delay phenomenon exists widely in practical engineering, and it is usually the main source of instability and performance degradation in various control systems. It is a common practice to transform the time-delay system into a nondelayed system in research work of control theory. A preview control system will be a normal control system when the preview length goes to zero Based on these observations, the contribution of this paper is to apply preview control theory to the optimal tracking control problem for continuous-time control systems that are subject to state and input delays. Taking advantage of the methods of preview control theory to derive an augmented error system for the nondelayed system, a controller with preview action for the augmented error system can be obtained, assuming that the reference signal is previewable. We propose an optimal control law for the augmented error system when the preview length of the reference signal goes to zero and obtain the optimal control law of the original time-delay system.
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