Repetitive Control Design Based on Two-dimensional Hybrid Model and State Observer

Abstract

This paper presents a method of designing a repetitive control system for a class of regular linear systems. The method is based on a state observer and a two-dimensional(2D)hybrid model.First,a state observer is constructed to reconstruct system states and a linear control law is established based on the reconstructed states.Next,by describing the continuous control and discrete learning actions of repetitive control system independently,a continuous-discrete 2D hybrid model is established based on the state observer and the reconstructed state feedback.In the light of the 2D Lyapunov function,a sufficient condition is given in the form of linear matrix inequality(LMI)for the existence of the state observer and the repetitive controller for the repetitive control system.The condition can be resolved conveniently by using the Matlab toolbox.A numerical example is provided to demonstrate the effectiveness of the proposed controller design procedures.