Development of a Neural Network-Based Compensatory Enhanced-Hammerstein Modeling Strategy for Piezoelectric System With Hysteresis

The accurate modeling of the piezoelectric actuator (PEA) is fundamental to guarantee the rapidity and accuracy of positioning control for micro-nano manipulation. Nevertheless, the high-accuracy modeling of input voltage and driving displacement is difficult because the PEA has creep, vibration dynamics, nonlinear hysteresis, and system uncertainty. In this article, a compensatory nonlinear-linear-linear Hammerstein (CNLLH) modeling strategy considering creep, vibration dynamics, hysteretic nonlinearity, and uncertainty compensation for piezoelectric system is proposed to achieve an accurate input-output model for control design, where the input is voltage signal and the output is driving displacement. This model structure is a nonlinear-linear-linear-nonlinear block, where the first nonlinear model is used to describe hysteretic nonlinear behavior, the two linear models are used to describe creep and vibration characteristics, and the second nonlinear model with a neural network is used to compensate the system uncertainty. The corresponding CNLLH model identification algorithm is developed based on the singular value decomposition, regularized least-squares method, and gradient descent method. The proposed CNLLH strategy can realize the simultaneous identification of four different characteristics only based on a set of experimental data without the decoupled experiment design. Experiments are conducted on the piezoelectric system to show the correctness of the proposed CNLLH strategy.