Energy optimization in local shape control of structures with nonlinear piezoelectric actuators

Shape control of a local part of a structure rather than the entire structure is often encountered in engineering practice using as less control energy as possible. Energy optimization for local shape control of structures integrated with nonlinear piezoelectric actuators is investigated. The local shape is maintained by assigning the generalized displacements to the desired ones at some given points. The distortion of the residual shape is also limited to a given range. This optimal control voltage distribution is solved by using elimination and the Lagrange multiplier method. A unique solution scheme based on Cholesky decomposition and eigenvalue problem is given to reduce the computational load for finding the Lagrange multipliers from an algebraic equation. The final optimal control voltage distribution for the nonlinear system is obtained by an iteration procedure. Finally, an example is given to illustrate the present method, and the results show that proper relaxation of the error tolerance of the residual shape can significantly reduce the control energy requested for the local shape control of the designated area.