Robust control design for precision positioning of a generic piezoelectric system with consideration of microscopic hysteresis effects

Abstract

This study performs precision positioning of a generic piezoelectric structure against hysteresis effects by finite elements, microscopic hysteresis cancellation and robust H? compensation. The designed control algorithm is expected to be effective in enhancing servo performance of hard disk drives. The precision positioning is accomplished by adding a polarization term into the linear constitutive equations of piezoelectric materials. This polarization term is then described by the well-known Preisach model. Applying basic principles of finite elements and Hamilton's thoery, the macroscopic governing equations of an arbitrary piezoelectric system in finite elements are obtained. Based on the macro-model, a controller consisting of two parts is designed to perform the precision positioning of a generic piezo-structure. The first part is responsible for direct hysteresis cancellation at the microscopic level, while the second one is a robust H(infinity) controller to overcome inevitable cancellation errors. In this way, the control effort is then more effective than the conventional PI and double-lead controller without microscopic hysteresis cancellation. A simple piezoelectric structure of a bender-bimorph cantilever beam is considered for designs and experimental validation. Based on experimental results, the proposed control design is found effective to suppress hysteresis effects as opposed to conventional controllers.