The Application of Predictor Feedback in Designing a Preview Controller for Discrete-Time Systems with Input Delay

Abstract

This paper presents a method for designing a type one servomechanism for a discrete-time linear system with input delay subject to a previewable desired output and a nonmeasurable constant disturbance. The tracking problem of a delay system is transformed into a regulation problem of a delay-free system via constructing an augmented error system and a variable substitution. A controller is obtained with delay compensation and preview compensation based on preview control theory and the predictor method. When the state vector is not directly measurable, a full-dimensional observer is offered. The effectiveness of the design method is demonstrated by numerical simulations.

A Predictor-preview Controller for Discrete-time Systems with Input Delay and External Interference

“…Equation (14) shows that the future state vector () X k f + is determined by the current state vector () Xk , the past control input () u k l f  + − ( 0, , 1 lf =− ), and the difference () w k l + ( 0, , 1 lf =− ) of the future interference signal. The predictor method used above is a generalization of the predictor feedback method [22,25].…”

“…In recent years, more and more scholars have employed various control strategies to eliminate time delay, a commonplace in practical systems, aiming to ensure the control effect and protect system stability [13][14][15][16][17][18][19][20][21][22]. For instance, Reference [23] relies on discrete lifting technique to transform the delay system into a system without delay.…”

“…For instance, Reference [23] relies on discrete lifting technique to transform the delay system into a system without delay. Reference [22] proposes a predictive method for discrete-time systems, and, on this basis, designs a preview controller for discrete-time systems with input delay. Reference [24] creates a preview controller through a lifting-predictor method, applies the controller in discrete-time linear systems with state delay and input delay, and effectively reduces the dimension of the augmented system.…”