Prandtl–Ishlinskii model based event-triggered prescribed control: Design and application to piezoelectric-driven micropositioning stage

Abstract

Realization of micro-scale tracking accuracy and efficient utilization of the communication channel is crucial to the wide application of piezoelectric-driven micropositioning stages (PDMSs). In view of this, an event-triggered prescribed time output-feedback control method is proposed in this study. As a type of nonlinearity that severely deteriorates the tracking performance of the PDMS, the hysteresis behavior is investigated. To describe the hysteresis characteristics, a modified function-based Prandtl–Ishlinskii (MFPI) model is proposed. Subsequently, a three-order electromechanical model of the PDMS combined with the MFPI model is established, and an event-triggered prescribed time adaptive control (ETPTAC) scheme is developed. In the controller design process, a prescribed settling time regulator (PSTR) is innovatively designed. With the help of the PSTR, the tracking error can converge to a predefined accuracy in a prescribed time. To address the hysteresis nonlinearity, an auxiliary system based on the established MFPI model is introduced. In addition, an event-triggered mechanism is used to save the communication resources. Finally, the modeling and control performances of our proposed approaches are confirmed on the PDMS.