Polytopic LPV modeling and gain scheduling [formula omitted] control of ball screw with position- and load-dependent variable dynamics

Abstract

Ball screw drive (BSD) is a precision transmission mechanism widely used in high-precision positioning or tracking systems. The dynamic behavior of BSD varies with position and load, which causes tracking errors and poor robustness. Therefore, this paper proposes a polytopic linear parameter varying (LPV) model to express the varying dynamic behavior of BSD. The parameters of the LPV model are identified by the closed-loop frequency domain method and Levenberg–Marquardt iterative algorithm. Based on the polytopic LPV model, an LPV gain scheduling (GS) H∞ controller is proposed for the BSD with varying dynamics. Specifically, the controller is designed through polytope-based GS representation and mixed sensitivity synthesis. The most significant part is the proposal of a GS H∞ control algorithm to implement controller parameters that change with changing dynamics. Moreover, the stability of the closed-loop system is achieved by quadratic stabilization with state feedback. Finally, identification experiments and trajectory-tracking comparative experiments are carried out. The experimental results demonstrate that the proposed polytopic LPV modeling and GS H∞ control synthesis are effective in achieving accurate trajectory tracking and excellent robustness.