Friction-Tracker-Embedded Discrete Finite-Time Sliding Mode Control Algorithm for Precise Motion Control of Worm-Gear Reducers Under Unknown Switched Assistive/Resistive Loading

Abstract

This paper proposes a novel method for simultaneous estimation of unknown switched external disturbance and precise position control of dynamical systems which employ worm gear drive reducers. This algorithm is based on an improved discrete sliding mode control (DSMC) design which ensures convergence to the desired sliding set without introducing chattering effects to the dynamical system. In order to improve the performance of DSMC and to obtain an accurate estimation of gearbox model, a new method for incorporation of switched friction is proposed in the presence of external disturbance. To this end, the dynamical response of worm gear drive reducer is investigated in distinct switched disturbance modes of resistive disturbances, assistive disturbances and no disturbance to obtain approximate functions describing system dynamics in aforementioned configurations. In comparison with the feedback data, the obtained models permit appropriate incorporation of friction into the improved DSMC scheme. Based on multiple common Lyapunov functions and calculation of virtual reference signals for armature currents, the feasibility of control algorithm is ensured in all modes of switched dynamics. The effectiveness of the proposed estimation and control schemes has been verified using an experimental setup employing a worm gear drive reducer on which multiple permanent magnet DC motors are installed, and improvements resulted from incorporation of friction estimation algorithm are analyzed.