Active piezoelectric vibration control for a Timoshenko beam

Abstract

Optimal piezoelectric vibration control problem for a Timoshenko beam is considered. The performance index function to be minimized by using the minimum level of the control voltage consists of a weighted quadratic function of displacement and velocity of the beam and also includes a quadratic functional of the control voltage function as a penalty term. The optimal control function is derived by means of a maximum principle which transforms the control problem to an initial-boundary-terminal value problem. In order to show the effectiveness of the control actuation, numerical results are given by MATLAB in table and graphical forms. (C) 2015 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.