Model-Free Adaptive Positioning Control of the Bidirectional Stick–Slip Piezoelectric Actuator with Coupled Asymmetric Flexure-Hinge Mechanisms

Abstract

A model-free adaptive positioning control strategy for piezoelectric stick–slip actuators (PSSAs) with uncertain disturbance is proposed. The designed controller consists of a data-driven self-learning feedforward controller and a model-free adaptive feedback controller with a radial basis function neural network (RBFNN)-based observer. Unlike the traditional model-based control methods, the model-free adaptive control (MFAC) strategy avoids the complicated modeling process. First, the nonlinear system of the PSSA is dynamically linearized into a data model. Then, the model-free adaptive feedback controller based on a data model is designed to avoid the complicated modeling process and enhance the robustness of the control system. Simultaneously, the data-driven self-learning feedforward controller is improved to realize the high-precision control performance. Additionally, the convergence of the tracking error and the boundedness of the control output signal are proved. Finally, the experimentally obtained results illustrate the advantages and effectiveness of the developed control methodology on the bidirectional stick–slip piezoelectric actuator with coupled asymmetric flexure-hinge mechanisms. The positioning error through the proposed controller reaches 30 nm under the low-frequency condition and 200 nm under the high-frequency condition when the target position is set to 100 μm. In addition, the target position can be accurately tracked in less than 0.5 s in the presence of a 100 Hz frequency.

Keywords

• piezoelectric stick–slip actuators (PSSAs)
• positioning control
• model-free adaptive control (MFAC)
• radial basis function neural network (RBFNN)-based disturbance estimator
• uncertain disturbance