Output Delay Systems Tracking Using System Centre Approach and Sliding Mode Control

Gang Liu1 — Alan S.I. Zinober1 — Yuri B. Shtessel2

1 Department of Applied Mathematics University of Sheffield Sheffield, United Kingdom {app03gl,a.zinober}@sheffield.ac.uk

2 Department of Electrical and Computer Engineering University of Alabama in Huntsville Huntsville, AL, USA shtessel@ece.uah.edu

ABSTRACT. Output tracking in SISO fully linearizable nonlinear systems with an output time delay is considered using sliding mode control and the system centre approach. Using Padé approximations for the delay, the problem is reduced to the tracking of a nonminimum phase control system. This system is transformed into a corresponding state tracking problem, where the state tracking profiles are generated by the equations of the stable system centre. The sliding mode control approach is developed and numerical examples are presented. Also the describing function is used to evaluate the limit cycle generated by the feedback of the actual delayed output and these results agree very closely with the system simulations.

KEYWORDS: Stable system centre, sliding mode control, output delay

1. Introduction

Output time delay is a common feature in many systems and must be taken into account when designing a controller. The output tracking of a real-time reference profile in nonlinear systems with output delay by sliding mode control was addressed in the paper [SHT 03a]. In addition to the first order Padé approximation, ...

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