A feedforward-feedback controller based on modified Prandtl–Ishlinskii model and submodel for tracking control the trajectories of piezoelectric actuator

Piezoelectric actuator (PEA) is widely applied in the field of micro/nano high precision positioning. However PEA has the phenomenon of hysteresis non-linearity between input voltage and output displacement, owing to the natural property of piezoelectric materials. The PEA hysteresis can be compensated by the hysteresis models and control methods, which make the input voltage and output displacement more linearity. The research work on tracking control of PEA trajectories by using various feedforward-feedback controller has been being a hot topic. This paper presents a feedforward-feedback controller based on the modified Prandtl–Ishlinskii (PI) (MPI) model and submodel and the incremental proportional-integral–differential(IPID) controller for tracking control the trajectories of PEA. The polynomial model is adopted as submodel, and parameters of MPI model and submodel are calculated by matlab optimization tool box. The proposed hybrid controller is compiled by C language in VC +  + environment. A series of comparative experiments are validated on a platform of commercial PEA. Comparing with the classical PI model, Bouc-Wen model, and other MPI models based IPID controller, the proposed hybrid controller has better control performance. According to the experimental results of the sinusoidal and triangular trajectories of different peaks and the mix sinusoidal and triangular trajectories, the proposed hybrid control method is feasible and effective in improving the tracking control accuracy of PEA trajectories.