Sliding Mode Fixed‐Time Control With Exact Cancellation of Mismatched Disturbances

ABSTRACT Sliding Mode Control (SMC) theory allows the design of algorithms that can adequately deal with matched perturbations in dynamic systems. However, its employment is less direct when mismatched perturbations are under study, yielding in most cases to only ultimate boundedness instead of a complete rejection of the disturbance. Some of the reasons for this decrease in the performance are the possible presence of singularities or discontinuities at the origin introduced through the definition of the sliding variable. This work proposes an innovative solution by designing a fixed‐time singularity‐free SMC approach to fully reject both matched and mismatched disturbances for a class of nonlinear systems by means of a new differentiator. Fixed‐time stability provides a stronger result than most SMC approaches in the sense that errors can be yielded to zero in a finite time independent of the system's initial conditions, which allows a faster transient response. A complete analysis is presented to show the closed‐loop stability of the controller and the differentiator together. It is shown that the scheme is robust in the presence of noisy measurements in the sense that it can fully reject the perturbations, while the effect of the noise mainly prevents reaching the origin exactly. To validate the theory, some simulations have been carried out, including an example of a marine surface vessel (MSV).