Optimum Control Voltage Design for Constrained Static Shape Control of Piezoelectric Structures

Abstract

Design optimization of control voltage distribution for constrained static shape control of structures using piezoelectric actuators is investigated. Two cases are studied. In the first case, a scheme is developed to find the optimal control voltage distribution minimizing the square error between the desired and actuated shapes subject to a given control electric energy. The optimal control voltage constrained by control energy can be found after solving an algebraic equation in terms of the Lagrangian multiplier. An alternative form for this algebraic equation is derived by taking advantage of an eigenvalue problem of a real symmetrical matrix, which significantly reduces the computational cost for finding its roots. A procedure for finding the optimal control energy is also given. In the second case, a process of seeking the control voltage distribution with least control energy for any given square error tolerance between the actuated and desired shapes is presented. Finally, illustrative examples for the constrained shape control of thin plates are given to demonstrate the presented methods.