Electrostatic suspension system using bang-bang time optimal control and stability analysis

A cost-effective electrostatic suspension system is presented in this paper. In this system, an object is suspended stably at reference gap without any mechanical contacts in both atmospheric and vacuum environment. The position control is based on bang-bang time optimal control. It operates according to a relay feedback control and uses only two high-voltage power supplies to apply dc voltages of positive or negative polarity to the electrode unit instead of employing high voltage amplifiers that are costly and bulky. Therefore, the cost of the suspension system is reduced significantly. In addition, by using this bang-bang control, the amplitude of vibration of suspended object is decreased near zero in both two cases with and without damping forces. In this paper, the recoverable set has been found and the authors analysed stability of system by using the Lyapunov´s function. It is shown that despite the inherent limit cycle property of the relay feedback control, an excellent performance in vibration is attained. Experimental results presented for a 4-inchs silicon wafer show the effectiveness of the presented method. The silicon wafer has been suspended at a reference gap of about 300 mum. The system is expected to be applied for contactless handing of objects in the apparatus for spacecraft and semiconductor equipments where air does not exist.