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The hysteresis nonlinearity and rate dependence of piezoelectric actuators seriously affect their positioning accuracy in precise positioning. Proper compensation needs to be given to improve the positioning accuracy of the actuator. In this paper, the static hysteresis characteristics are described by improving the BP neural network model based on the adaptive particle swarm optimization algorithm, and the PI model is used as the hysteresis factor by the extended space method to realize the multi-valued mapping of hysteresis nonlinearity. And input three types of voltage signals, compare and analyze the experimental data and model prediction output, and use the maximum relative error and root mean square error as the evaluation indicators to prove the accuracy of the built model. Based on the improved BP neural network model, a second-order low-pass analog filter is introduced to construct a rate-dependent hysteresis model. Comparing and analyzing the rate-dependent hysteresis model and the static hysteresis model, the experimental results show that when the signal frequency is 10 Hz, 40 Hz, and 100 Hz, the predicted output of the rate-dependent hysteresis model is compared with that of the static hysteresis model, and the root mean square error decreases by 46.3%. %, 59.6%, and 65.1%, the model can more accurately describe the hysteresis characteristics of piezoelectric actuators. Finally, a rate-dependent hysteresis inverse model is established, and the rate-dependent hysteresis inverse model is used as a feedforward combined with a single neuron network PID control to form a composite controller, and the experimental verification is carried out. The results show that the maximum error between the composite controller and the actual expectation is only 2.15%. Therefore, the established model can accurately express the rate-dependent hysteresis characteristics of piezoelectric actuators, and the use of a composite controller can effectively reduce the accuracy error caused by the hysteresis nonlinear characteristics of piezoelectric actuators.

Modeling and control of rate-dependent hysteresis characteristics of piezoelectric actuators based on analog filters