Experimental Study of H∞ Control of Flexible Plate with Time Delay

Abstract

This paper presents theoretical and experimental studies of H∞ control of a flexible plate with time delay. A matrix inequality used for stability analysis is proposed and proved by using the Lyapunov-Krasovskii functional and free-weighting matrix. An H∞ controller is designed based on the matrix inequality and by using the parameter-adjusting method. Three control scenarios are discussed in detail by transforming the problem into parameters optimization: (i) controller design when maximum time delay of the system is known; (ii) allowable time delay when controller is known; (iii) the biggest allowable time delay to guarantee system stability when controller is unknown. Numerical simulations and experiments are also given to demonstrate the validity and feasibility of the proposed methods in this paper.