A Modified Prandtl-Ishlinskii Model and its Applications to Inverse Control of Piezoelectric Actuators

Abstract

Piezoelectric actuators based motion-producing devices are widely used in precision machining, deformable mirrors, micropumps and piezoelectric injec- tion systems. However, because of their hysteresis nonlinear property, the piezo- electric actuators can not provide absolutely precise displacements. To solve this problem, researchers applied inverse control method to compensate the nonlinear- ity of piezoelectric actuators, and the inverse models are mainly based on tradi- tional hysteresis models such as the Preiasch model or Prandtl-Ishlinskii model. In this paper, a new approach for inverse control of piezoelectric actuators is pre- sented. The new method utilize a modified Prandtl-Ishlinskii model which is based on a combination of two asymmetric hysteresis operators, and the two operators can independently model ascending branches and descending branches of hystere- sis loops. Based on the inversion of the proposed model, an open-loop inverse controller and an adaptive inverse controller are designed and implemented in a real-time control system. The performances of the two controllers are tested and assessed. The experimental results show that the open-loop inverse controller can suppress the hysteresis nonlinearity to 2.31% and the adaptive inverse controller can reduce the hysteresis nonlinearity to 2.02%.