Networked <inline-formula> <tex-math notation="LaTeX">$H_\infty$</tex-math> </inline-formula> Controller Design for a Direct-Drive Linear Motion Control System

This paper focuses on the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> state feedback control method for networked control systems and its application to the discrete-time direct-drive linear motion control system over a communication network with external disturbances and network-induced random time delay. The unavoidable network-induced random delay is modeled by a Markov chain with the uncertain transition probability. In this paper, the experimental linear motion control system is a double-sided linear switched reluctance machine (DLSRM). To tackle the external disturbances in the DLSRM, an H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> control strategy is designed by using Lyapunov stability theory and linear matrix inequalities technique. A mode-dependent state feedback H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> controller is designed for the closed-loop discrete-time direct-drive linear motion control system over a network to achieve a high-precision position control performance with antidisturbance capability. The experimental tests on the networked DLSRM system are presented to verify the effectiveness and practicability of the proposed H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> control method for industrial applications of networked control systems.