Natural frequency reducing method of anti-vibration apparatus using an idea of variable structure system

Abstract

In the field of precision positioning such as semiconductor exposure apparatus, vibration from the floor greatly influences the positioning accuracy. In order to prevent deterioration of accuracy, an anti-vibration apparatus is installed to isolate vibration. Along with high integration of semiconductor, the allowable value for disturbance vibration becomes severe, and improvement in the performance of the anti-vibration apparatus is required. The anti-vibration apparatus attenuates vibrations higher than natural frequency. Therefore, lowering the natural frequency is directly linked to performance improvement. Here we show stably lowering natural frequency by decreasing spring stiffness using variable structure system. We already proposed a method to decrease spring stiffness of the air spring. However, when trying to completely decrease the spring stiffness, excess or deficiency of decrease amount due to the uncertainty of the machine parameter occurs and it becomes unstable. This is because the polarity of the spring stiffness becomes positive, negative, and zero due to excess or deficiency, and the vibration characteristics greatly change. Therefore, the variable structure system aggressively switches the polarity of the spring stiffness on the phase plane. By geometrically designing the switching function on the phase plane under the vibration characteristics which change by switching, the equilibrium point becomes global asymptotically stable. In addition, the variable structure system has aspects of sliding mode control and converges to the equilibrium point without being affected by the uncertainty. The stability of the proposed method is guaranteed by the Lyapunov function. In addition, it was installed in an experimental apparatus to demonstrate the stability and effect on lowering natural frequency.

Keywords

• vibration isolation
• vibration control
• nonlinear control
• natural frequency