Vibration optimal control of a smart plate with input voltage constraint of piezoelectric actuators

A nonlinear optimal control of a plate vibration is developed. Three pairs of piezoelectric patches with limited voltages input are used as a source of applying an active forcing function to control the vibration of the plate. The dynamic model of the plate with piezoelectric actuators is applied for the purpose of analyzing the coupling between piezoelectric actuators and a plate. The model is based on discrete assumed mode shapes of different beams. To keep the voltages of any pair of actuators in their allowable limits, the optimal control procedure presented in this paper shows that the voltage of other piezoelectric actuators that are in the allowable limit would also be affected. Therefore, the Pontryogan minimum principle is not enough for systems with multi inequality constrained of control inputs.