Optimal time-delayed boundary control of beams using wavelets


Kucuk I. , SADEK I.

JOURNAL OF VIBRATION AND CONTROL, vol.19, no.14, pp.2083-2091, 2013 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 19 Issue: 14
  • Publication Date: 2013
  • Doi Number: 10.1177/1077546312455678
  • Title of Journal : JOURNAL OF VIBRATION AND CONTROL
  • Page Numbers: pp.2083-2091

Abstract

Time delays exist in active control systems. Although a time delay in most cases is small, it results in the actuator applying energy to the control system with a time delay. This might cause instability of the dynamic systems and degrade the performance of the control systems. The objective of the present work is to propose a feasible methodology that can achieve good control performance for a dynamic beam structure system by time-delayed boundary torque actuators. The control problem is to determine optimal time-delayed boundary control by minimizing a given performance criterion. The performance criterion is specified as a weighted quadratic functional of the dynamic responses of the beam which is to be minimized at a specified terminal time using continuous time-delayed torque actuators. The modal expansion approach is used to convert the optimal control problem of a distributed parameter system into the optimal control problem of a linear lumped parameter system (LPS). A direct state-control parameterization approach is proposed where wavelets are employed to solve time-delayed LPS. The operational matrices of integration and delay are utilized to reduce the solution of linear time-varying delayed systems to the solution of algebraic equations. A numerical simulation is presented to illustrate the efficiency of the proposed control algorithm.