An Inversion-free Predictive Controller for Piezoelectric Actuators Based on A Dynamic Linearized Neural Network Model

Piezoelectric actuators (PEAs) are widely used in high-precision positioning applications. However, the inherent hysteresis nonlinearity seriously deteriorates the tracking performance of PEAs. To deal with it, the compensation of the hysteresis by using its inverse model (called inversion-based) is the popular method in the literature. One major disadvantage of this method is that the tracking performance of PEAs highly relies on its inverse model. Meanwhile, the computational burden of obtaining the inverse model is overwhelming. In addition, the physical constraints of the input voltage of PEAs is hardly handled by the inversion-based method. This paper proposes an inversion-free predictive controller, which is based on a dynamic linearized multilayer feedforward neural network (MFNN) model. By the proposed method, the inverse model of the inherent hysteresis is not required, and the control law can be obtained in an explicit form. By using the technique of constrained quadratic programming, the proposed method still works well when dealing with the physical constraints of PEAs. Moreover, an error compensation term is introduced to reduce the steady-state error if the dynamic linearized MFNN cannot approximate the PEA's dynamical model satisfactorily. To verify the effectiveness of the proposed method, experiments are conducted on a commercial PEA. The experiment results show that the proposed method has a satisfactory tracking performance even with high-frequency references. Comparisons demonstrate that the proposed method outperforms some existing results.