Tuning Methods of a Smith Predictor for Pneumatic Active Anti-Vibration Apparatuses

Abstract

Pneumatic active anti-vibration apparatuses (AVAs) are widely employed for the highprecision positioning of wafer stages in semiconductor lithography equipment. However, there exists delay of transmission of air supplied to air springs. In this paper, we consider the suppression of vibration caused by the time delay (i.e., dead-time) of AVAs. The dead-time is compensated by using a Smith predictor, which is well-known as a control method for time delay systems. In the implementation of the predictor, the plant model and the dead-time are needed. For this reason, this paper focuses on the tuning of Smith predictor effective for the control of AVAs. To improve the model accuracy of AVAs, the approximation model of pipe resonance is utilized. Moreover, to determine suitable time delay in the Smith predictor, our methods utilize the resonance frequency of the control system and the tracking error of the isolated table. Conventionally, the nominal value of the dead-time can be obtained by using step response of the control system. On the other hand, it is difficult to exactly estimate the dead-time of AVAs due to position sensor noise. Therefore, the time delay is precisely tuned by proposed methods instead of the step response approach in order to improve the performance of the Smith predictor. Experimental results show that when the error of the time delay in the predictor is zero, the resonance frequency and the time integral become minimized.

Keywords

• anti-vibration apparatus
• smith predictor
• resonance frequency
• time integral