Static shape control of structures using nonlinear piezoelectric actuators with energy constraints

摘要

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