As the hysteresis of piezoelectric ceramics is multi-valued mapping, and traditional neural networks can only address one-to-one mappings, a Duhem-BP model is proposed to expand the input of the neural network by converting the multi-valued relationships into one-to-one mapping. Firstly, the Northern Eagle algorithm is used to identify the Duhem model with α, f(.), and g(.). Then, the Duhem-BP rate-dependent hysteresis model is established using the spatial expansion method, which achieves an accurate prediction of the rate-dependent hysteresis nonlinearity of the piezoelectric drive system, and the root-mean-square error of the hysteresis modeling is only 26.437 nm at 160 Hz. Secondly, the Duhem model’s inverse model is solved, the model is then merged with a BP neural network and a feedforward controller to adjust the system. Finally, a compound control method of feedback linearization sliding mode combined with inverse model compensation is proposed. The experimental results show that, compared with the feedforward control, the compound control method proposed has good tracking performance under both single-frequency and composite-frequency tracking signals, which verifies the effectiveness of the compound control method.
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