A new structure and identification method for Physical Guided Neural Network based pre-compensator of Piezoelectric actuators

Abstract

Piezoelectric actuators (PEAs) offer nanometer precision but are affected by various nonlinearities. This paper focuses on model-based pre-compensation of PEAs to achieve open-loop high motion precision. To this end, a novel Physical Guided Neural Network (PGNN)-based PEA model is proposed. The PGNN model adopts a parallel structure, with a Hammerstein hysteresis model-based physical model guiding the neural network output. This design helps the neural network achieve low complexity and robust performance, while also addressing the neural network’s inability to describe PEA’s multi-valued mapping hysteresis non-linearity due to its single-value mapping characteristic. Identification is crucial for the PGNN to realize its advantages, as over-competition between the physical model and neural network can lead to overfitting. In this paper, a novel Balanced Physics-Precision Identification Method (BPPIM) is proposed. This method mathematically describes the PGNN’s physical correctness and model precision and combines these to form a nonlinear objective function, strategically balancing the competition during identification. Based on the proposed PGNN model, an inverse model-based pre-compensator is established. Experimental tests were carried out on a PEA-actuated stage, performing an arbitrary third-order A-to-B trajectory to test performance. Results demonstrate the superior precision and performance robustness of the proposed PGNN model compared to existing physical models or neural network models. The PGNN model-based pre-compensator reduces peak-to-peak displacement error to within 51 nm, achieving an 82% reduction compared to the no-compensation scenario, a 62% reduction compared to the classic PI operator-based pre-compensator, and a 47% reduction compared to the PGNN-based pre-compensator proposed in the literature.