Predefined–Time Adaptive Control of a Piezoelectric–Driven Motion System With Time–Varying Output Constraint

This brief investigates the output feedback adaptive tracking control of a piezoelectric–driven motion (PDM) system with time–varying output constraint. The key features of the developed predefined–time adaptive neural control (PTANC) method are as follows. i) A broad learning system with recurrent enhancement node (RENBLS) is used to construct an RENBLS–based observer such that state information can be estimated; ii) we incorporate a performance regulator and time–varying barrier Lyapunov function (TVBLF) into the controller design. The proposed method can then achieve the control effect in a predefined time without violating the output constraint. Stability analysis of the PTANC strategy is demonstrated in theory. Furthermore, the effectiveness of the proposed control scheme is experimentally verified via the PDM system.

I. Introduction

By virtue of their rapid response and nanometer resolution, piezoelectric–driven motion (PDM) systems have emerged as popular devices in the fields of high–precision positioning [1], [2]. However, the hysteresis nonlinearity induced by piezoelectric actuation is a dominant effect that degrades the positioning accuracy. Different control strategies with or without considering the hysteresis model have been developed (see [3], [4], and the references therein). To improve the tracking accuracy of the PDM systems, adaptive pseudo inverse control [5], iterative learning control [6], and sliding mode control [7] have been investigated and attained certain control effects. The backstepping control method, which is an effective recursive design technique, is applicable in dealing with the control problems of nonlinear systems [8], [9]. Considering that hysteresis models are always subject to modeling errors, this brief investigates a robust adaptive backstepping control design without the use of hysteresis model.