Disturbance compensation in minimum operator based sliding mode control

Abstract

This paper proposes an advanced disturbance-compensated sliding mode control framework based on a minimum-operator reaching law for discrete-time uncertain systems. By integrating a difference-based disturbance compensation mechanism with a finite-time minima-based reaching strategy, the original matched disturbance is effectively transformed into its increment, which is typically much smaller in magnitude. As a result, the proposed approach significantly reduces the quasi-sliding mode band width, while preserving rapid finite-time convergence of the switching function. Rigorous analysis establishes explicit settling-time bounds and guarantees finite-time convergence of system trajectories to a compact invariant set determined by the disturbance variation. Simulation studies on a perturbed mechatronic actuator demonstrate improved disturbance compensation, reduced steady-state error, and suppressed chattering compared to conventional discrete-time sliding mode controllers.