A feedforward controller with neural-network based rate-dependent model for piezoelectric-driven mechanism

Piezoelectric actuator is considered as the main device for the high precision positioning system due to its rapid response, high stiffness and ultra-high resolution. However, the intrinsic hysteresis behavior of piezoelectric actuator can seriously degrade the trajectory-tracking precision. Moreover, the model weights of the Prandtl-Ishlinskii (PI)'s play operator versus velocity are nonlinear which is hard to model when the bandwidth is relatively wide if the rate-dependent model is utilized to address the hysteresis. This will become more serious if the trajectory is non-periodic. Therefore, a neural-network (NN) based rate-dependent PI model is utilized to address the nonlinearity between model weights and corresponding rates since NN can be trained to learn the phenomena without any requirement of complex and difficult mathematical analysis. This method is verified by experiments and it is shown that this approach can effectively address the hysteresis nonlinearity under non-periodic input when the bandwidth is between 0-70 Hz.