Smith predictor-based time delay compensation for attitude control of pneumatic anti-vibration apparatuses with two degrees-of-freedom

Abstract

Pneumatic anti-vibration apparatuses (AVAs), which have air springs, are needed for the precision positioning of wafer stages in lithography equipment. However, the difference of time delays in the response of the air springs causes the undesirable rotational motion of an isolated table. This paper considers the attitude control of the AVA including difference time delays. To avoid the rotation of the isolated table, a Smith predictor is employed. It is verified that this approach can be used for the AVAs with mode control, which is often used in vibration isolation systems for semiconductor manufacturing. The overshoot of the rotational angle of the isolated table can be further reduced by shaping the reference trajectory.

Stability analysis and fuzzy smith compensation control for semi-active suspension systems with time delay

“…Based on the Lyapunov stability analysis [24,27], the necessary and sufficient condition of the time-delay system is that all the roots of the characteristic Equation (5) is negative real part or the conjugate complex root with negative real part. Therefore, the critical condition of suspension instability is that there is only a purely imaginary eigenvalue represented by λ in Equation (5).…”

“…Recently, intensive research has been conducted on addressing the problem of the smith predictor [16,25,27] and time delay compensation control [19,21,24,26]. The authors in [17] investigated the effect of the time delay on stability and investigated a method to compensate for the time delay effect in order to ensure galloping suppression.…”

“…In [19], the authors designed a human-simulation intelligent control (HSIC) strategy to compensate for the time delay of the MR suspension system in the time domain. In [24] and [26], the authors adopted the Smith predictor to achieve time delay compensation and presented a stability analysis. In addition, the authors in [21] established a closed-loop stability of the resulting infinite-dimensional nonlinear system for a general non-negative-valued delay function of the state and local asymptotic stability for locally stabilizable systems in the absence of the delay.…”