Hysteresis modeling and compensation of a piezoelectric fast steering platform using multiple NARMA-L2 models

The piezoelectric fast steering platform (PFSP) enhances the scanning capabilities of lidar systems for autonomous vehicles. However, hysteresis nonlinearity degrades the scanning accuracy of the PFSP. To meet this challenge, this paper proposes a novel approach for hysteresis modeling and compensation using multiple nonlinear autoregressive moving average (NARMA)-L2 models. First, the hysteresis model is partitioned into a collection of submodels based on the K-means methodology, where the feature vector stems from the classical Bouc–Wen (CBW) model. Each submodel describes the dynamics of a specific hysteresis segment by a single NARMA-L2 model. The composite neural network (CNN), formed by combining two multilayer perceptron (MLP) networks, is trained to estimate the hysteresis output of the single NARMA-L2 model. Compared to the submodels obtained by evenly partitioning according to the input range, the submodels obtained by K-means partitioning offer higher hysteresis modeling accuracy. To compensate for the hysteresis nonlinearity, a novel adaptive Multi-NARMA-L2 (AMNL2) controller is then designed by online adjusting the parameters of the CNN. Furthermore, an adaptive filter is proposed to alleviate the oscillation caused by high-frequency disturbances during switching. Finally, experiments demonstrate that the AMNL2 controller outperforms the traditional MNL2 controller and the proportional–integral–derivative (PID) controller.