A Stable Autoregressive Moving Average Hysteresis Model in Flexure Fast Tool Servo Control

Abstract

Due to the excellent advantages of high speed and high precision, fast tool servo (FTS) system driven by piezoelectric actuators has great attraction for high-quality machining of microstructural array. However, its complex hysteresis nonlinearity at high speed will greatly affect the accuracy and stability of FTS system. Therefore, a stable autoregressive moving average (SARMA) model is proposed in this paper, which aims to describe the dynamic hysteresis nonlinearity accurately. First, a long autoregressive model residual calculation method is used to determine the order of the model and test the applicability of the model. Then, according to the Lyapunov stability theory, the strict stability analysis of the autoregressive moving average (ARMA) model is carried out in theory. By introducing the relaxation factor to transform the stability condition, the Lagrange multiplier and best square approximation method are applied to enhance the performance of the traditional ARMA model. Aiming at the difficulty of displacement sensor integration in FTS closed-loop controlling system, a hysteresis-compensated direct feedforward control strategy based on the proposed SARMA model is designed. Finally, a series of high-frequency trajectory tracking and comparing experiments has been carried out successfully with the traditional Prandtl-Ishlinskii (PI) and SARMA models to verify the effectiveness and superiority of the method. All results uniformly indicate that the SARMA model is nearly 20 times higher than the traditional PI model in terms of control accuracy and linearity, while the average linearity of FTS's dynamic tracking control is kept within 0.43% (265 nm), the stroke is 280 μm, and the positioning bandwidth is achieved up to 200 Hz.