Closed Loop Finite Element Modeling of Piezoelectric Smart Structures

Abstract

The objective of this paper is to develop a general design and analysis scheme for actively controlled piezoelectric smart structures. The scheme involves dynamic modeling of a smart structure, designing control laws and closed-loop simulation in a finite element environment. Based on the structure responses determined by finite element method, a modern system identification technique known as Observer/Kalman filter Identification (OKID) technique is used to determine the system Markov parameters. The Eigensystem Realization Algorithm (ERA) is then employed to develop an explicit state space model of the equivalent linear system for control law design. The Linear Quadratic Gaussian (LQG) control law design technique is employed to design a control law. By using ANSYS parametric design language (APDL), the control law is incorporated into the ANSYS finite element model to perform closed loop simulations. Therefore, the control law performance can be evaluated in the context of a finite element environment. Finally, numerical examples have demonstrated the validity and efficiency of the proposed design scheme. Without any further modifications, the design scheme can be readily applied to other complex smart structures.