Optimal shape control of thin plate using laminated piezoelectric actuators with genetic algorithm

This paper deals with the shape control of a cantilever thin plate structure by using laminated piezoelectric actuators (LPA). The shape control equation of the cantilever thin plate partially covered with LPA is derived based on the constitutive relations of the elastic material and piezoelectric material and the thin plate deformation theory. The actuating forces produced by LPA are formulated as well. It reveals how the actuating forces depend on the number of piezoelectric layers, the thickness of piezoelectric layers. The driving voltages of LPAs are then determined by a genetic optimization algorithm. The shape control of the cantilever thin plate applying the optimal voltage to LPAs is simulated. The simulation results show that the increasing of LPA layer number can significantly improve the control performance as the acting forces of LPA are a quadratic function of the LPA layer number. Consequently, the LPA of large layer number is able to diminish effectively the pre-deflection of the thin plate under low control voltage. And with the same control voltage, the LPA can obtain better control performance than the conventional single layer piezoelectric actuator.