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

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 $\mu \text{m}$ , and the positioning bandwidth is achieved up to 200 Hz. Note to Practitioners—With the purpose to effectively improve the positioning accuracy for the piezoelectric-actuated fast tool servo mechanism, a hysteresis model with accurate description performance should be established for the further motion control. Therefore, a stable autoregressive moving average model is proposed in this paper. The strict stability analysis of the autoregressive moving average (ARMA) model is carried out using the Lyapunov stability theory. A relaxation factor is introduced to transform the stability condition, the best square approximation method is applied to enhance the performance of the traditional ARMA model. Combining with the established hysteresis model, a series of tracking control tests is successfully conducted. Comparing to the traditional Prandtl–Ishlinskii model, the FTS’s motion accuracy is greatly improved by 20 times. The fast tool servo system has the capability to achieve millimeter stroke and nanometer scale precision, since its performance can be further improved by using other actuators and sensors with larger travel range and higher resolution. In summary, its potential applications will be promising.