Abstract
This paper presents theoretical and experimental studies ofH∞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. AnH∞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.
Highlights
In dynamic modeling and active control of structures, errors may occur in the modeling process due to uncertainty of physical properties and boundary conditions of the structure, and signal noise and external disturbance may affect control effectiveness at control implementation
Robust control method is robust to the variance of structural intrinsic parameters and external disturbance, and has been getting more and attention in the active control of structures [1,2,3,4,5,6,7,8]
Time delay problems are mainly investigated in mathematics and control systems, and most studies are focused on stability or the maximum allowable time delay to maintain time-delay systems stable
Summary
In dynamic modeling and active control of structures, errors may occur in the modeling process due to uncertainty of physical properties and boundary conditions of the structure, and signal noise and external disturbance may affect control effectiveness at control implementation. For active control of structures, some treating methods were proposed to deal with time delay, such as the Taylor series [10], the technique of phase shift [11], the advance estimation of state variables [12], etc. These methods are only applicable for systems with very small time delay, and work awkwardly for systems with large delays. The proposed method in [13,14] is applicable for both small time delay and large time delay problems, which is experimentally verified by working on different flexible structures [15,16].
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