A controllability index for optimal design of piezoelectric actuators in vibration control of beam structures

This paper addresses the controllability aspect in vibration control of beam structures with piezoelectric actuators. First, we model the beam structure with piezoelectric actuators and establish the corresponding state-coupled equation. Based on the state equation, we propose a controllability index to quantify the controllability factor. This index allows one to estimate the amount of control energy by the piezoelectric actuators to the beam for a given control input. So it can be used as an objective function to determine the optimal locations of piezoelectric actuators for vibration control of beam structures. Some numerical simulations are carried out to illustrate the use of this newly proposed controllability index in seeking out the optimal locations of actuators in simply supported and cantilevered beams with one and two actuators. The index is shown to be adequately sensitive for determining the optimal locations of the actuators.