Stability Analysis of a Proximate Time Optimal Controlled Electrostatic Suspension System Using Piezo Actuator via Lyapunov Functional Approach

Abstract

An electrostatic suspension of silicon wafer using proximate time optimal control has been successfully developed. In this system, the movable electrodes which are supplied by constant voltage and actuated by the piezoelectric (PZT) actuator are used instead of stationary electrodes like previous systems. The changing of the gap length between movable electrodes and the suspended object will create varying capacitances that can control the electrostatic forces. To overcome the problem of actuator saturation of the piezo actuator, a proximate time optimal control is used to stabilize the system. The system stability is theoretically investigated using Lyapunov’s function. The constant voltage supplying to the electrode is an important parameter, and it is also determined. The paper presents series of the simulation and experimental results that prove completely suspension of 4-inch silicon wafer without any mechanical contact.