Improved adaptive control of X-ray beam stabilized piezoelectric platform based on Hammerstein model

Abstract The fourth-generation synchrotron light source has higher requirements for small-size beam precision than the previous three generations, making beam stability one of the most important factors constraining the experiments of the fourth-generation light source. In order to improve the control accuracy of the beam stabilisation system, we propose an improved adaptive control method based on the Least Mean Squares(LMS) algorithm and reference voltage, based on a piezoelectric drive platform. Firstly, a Hammerstein model is built by connecting the improved Prandtl-Ishlinskii(PI) model and Auto-Regressive with Extra Inputs(ARX) model in series to describe the hysteresis and rate dependence of the piezoelectric platform. Then its inverse model is used as a feedforward controller and Proportion Integration Differentiation(PID) feedback algorithm to form a feedforward PID control scheme. Finally, the reference voltage model is fitted on this basis and an improved adaptive control method is proposed to adaptively regulate the inverse model parameters. The experimental results show that the relative displacement error of the piezoelectric platform is reduced to less than 1.6% under the improved adaptive control method, which effectively compensates the tracking error caused by the hysteresis and rate dependence of the platform.