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 ? 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.

Design and Implementation of an Accelerated Error Convergence Criterion for Norm Optimal Iterative Learning Controller

“…As mentioned above, the hysteresis effect makes the system complex in order to track the precise position. The proposed controller has satisfactory results compared to the typical PID [44], inverse system control [45] method and robust control [46] as well as sliding mode control [47]. A further experimental approach for the proposed controller can be adopted using any of the aforementioned models to verify this robust NOILC technique.…”

“…Electronics 2020, 9, x FOR PEER REVIEW 9 of 15 system control [45] method and robust control [46] as well as sliding mode control [47]. A further experimental approach for the proposed controller can be adopted using any of the aforementioned models to verify this robust NOILC technique.…”

High-frequency robust position control of a nonlinear piezoelectric bending actuator

“…In these conditions, piezoelectric nonlinearities such as “hysteresis” in high voltages and “creep” in low-frequency applications can degrade the control performance (Ghafarirad et al, 2014b; Rakotondrabe et al, 2010; Zhang and Xu, 2017). To cope with these issues, the nonlinearities should be taken into account in the actuator dynamic model and the corresponding controller design (Chao et al, 2011; Ghafarirad et al, 2014a). In some researches, the nonlinearities were assumed as a disturbance, and robust control methods were proposed for the position control (Jingang et al, 2009; Qingsong and Minping, 2014).…”

“…In some researches, the nonlinearities were assumed as a disturbance, and robust control methods were proposed for the position control (Jingang et al, 2009; Qingsong and Minping, 2014). In this regard, the authors used a linear dynamic model, which is coupled with nonlinear functions expressing hysteresis and creep phenomena (Chao et al, 2011; Ghafarirad et al, 2014a).…”

High-accuracy tracking of piezoelectric positioning stage by using iterative learning controller plus PI control

“…Many control methods have been used to implement motion control of the precision piezoelectric mechanical systems, such as PID control [12], robust control [13], inverse system methods [14] and sliding mode control [15]. A difficulty in achieving precise motion tracking control using PID method lies in the low gain margin of the piezoelectric mechanical systems.…”