Event-triggered fixed-time sliding mode control for Euler–Lagrange systems with experimental validation

This paper presents an event-triggered fixed-time sliding mode control scheme for trajectory tracking of Euler–Lagrange (EL) systems under matched disturbances. A nonlinear sliding manifold to guarantee fixed-time reaching and sliding phases. In order to ensure that the control is free from singularity, a weighted sampling error with a switched triggering mechanism is designed. Moreover, the proposed triggering law exhibits a strictly positive inter-event interval globally. Using Lyapunov stability analysis, we demonstrate the existence of a practical sliding mode band (PSMB) in a fixed time. Using the results of fixed time practical sliding mode, we further show the existence of fixed time practical stability for the closed-loop dynamics. Moreover, we explicitly show that the PSMB and inter-event time can be tuned by the event design parameter with a trade-off. Numerical simulation of a two-link manipulator and experimental results obtained through real-time validation on a single-link manipulator validate the proposed theory. The controller achieves convergence within the calculated fixed-time bound, with reduced control updates relative to periodic SMC, and maintains robust tracking under unmodeled friction.