Shape Control of Distributed Parameter Reflectors Using Sliding Mode Control

摘要

Sliding mode control has become one of the most powerful control methods for variable structure systems, a set of continuous systems with an appropriate switching logic. Its robustness properties and order reduction capability have made sliding mode control one of the most efficient tools for relatively higher order nonlinear plants operating under uncertain conditions. Piezo-electric materials possess the property of creating a charge when subjected to a mechanical strain, and of generating a strain when subjected to an electric field. Piezo-electric actuators are known to have a hysteresis due to the thermal motion and Coulomb interaction of Weiss domains. Because of the thermal effect the hysteresis of piezo-electric actuators is reproducible only with some uncertainty in experiments. The robustness of sliding mode control under uncertain conditions has an advantage in handling the hysteresis of piezo-electric actuators. In this research sliding mode control is used to control the shape of one- and two-dimensionally curved adaptive reflectors with piezo-electric actuators. Four discrete linear actuators for the one-dimensionally curved reflector and eight actuators for the two-dimensionally curved reflector are assumed.