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

Piezoelectric actuators based motion-producing devices are widely used in precision machining, deformable mirrors, micropumps and piezoelectric injection systems. However, because of their hysteresis nonlinear property, the piezoelectric actuators can not provide absolutely precise displacements. To solve this problem, researchers applied inverse control method to compensate the nonlinearity of piezoelectric actuators, and the inverse models are mainly based on traditional hysteresis models such as the Preiasch model or Prandtl-Ishlinskii model. In this paper, a new approach for inverse control of piezoelectric actuators is presented. 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 hysteresis 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%.