Stability analysis of a time-optimally controlled electrostatic suspension system and suspension experiments in a vacuum

Abstract

Electrostatic suspension permits conductive, semiconductive, and dielectric materials to be supported without mechanical contact, in contrast to electromagnetic levitation by which only ferromagnetic materials can be levitated. To expand applications of electrostatic suspension systems, a low-cost electrostatic suspension system using a time optimal bang—bang control scheme where linear analogue high-voltage amplifiers that are costly and bulky are not employed has already been implemented. In this article, a time optimal bang—bang control scheme is used to stabilize the system like the previous work. First, the process to find the recoverable set for all the states in which a time optimal bang—bang control exists is described in detail. Then, the switching criterion for the suspension system is derived by using a backward integration technique and the system stability is theoretically investigated using Lyapunov's function as well. To experimentally verify the system stability in vacuum, suspension experiments are carried out with 3.5 in aluminium discs in a vacuum environment. Experiments in the atmosphere are also conducted for comparison with the results in the vacuum. The experimental results show that an aluminium disc has been stably suspended at a reference gap length of 300 μm in a vacuum environment.