Static shape control of structures using nonlinear piezoelectric actuators with energyconstraints

Abstract

Static shape control of composite plates with nonlinear piezoelectric actuators subject toenergy constraint is investigated in this paper. The optimal control voltages are determinedby using Lagrange multipliers so as to minimize a weighted generalized errorfunction at a given energy level. An eigenspace based algebraic equation of theunknown Lagrange multiplier is derived in order to reduce the computation load offinding the multipliers. Two methods, an iteration algorithm and a shape updatingalgorithm, are presented for iteratively finding the optimal control voltages forthe nonlinearly actuated composite plates. In the iteration algorithm, a controlvoltage vector is calculated after the Lagrange multipliers are solved for in eachiteration, and the iteration continues until an assigned precision is satisfied. Inthe shape updating algorithm, the actuated shape is calculated in each iterationand then the difference between the actuated and the desired shape is used asthe new desired shape in the next iteration. The control voltage vector will beupdated using new desired shapes repeatedly until convergence is reached. Finally, asimulation example is given to demonstrate the effectiveness of the present methods.