Adaptive rate-dependent feedforward control for piezoelectric actuator

Piezoelectric actuator is widely used in micro/nano applications due to advantages like high stiffness, rapid response and high resolution. However, the inherent hysteresis limits its performance in trajectory tracking. Moreover, the hysteresis nonlinearity is dependent of control input rate (which is called rate-dependent behavior). To make matters worse, it is also affected by environmental parameters like temperature, which increases the need for an adaptive controller. In addition, this rate-dependent relationship is generally nonlinear between the weights of the backlashes and input rate and complex in practice. In order to address this hysteresis nonlinearity with related problems, this paper proposes an adaptive feedforward controller which is built based on Prandtl-Ishlinskii (PI) model. Radial Basis Function Neural Network (RBFNN) is proposed in this paper to model the rate-dependent behavior. The adaptive RBFNN is then updated using recursive least square method. The controller is implemented and experiments with both periodic and non-periodic motions are conducted to verify the effectiveness and feasibility of the proposed method.