Chattering analysis of uniform fixed-time convergent Sliding Mode Control

In this paper, chattering in systems controlled by a super-twisting based fixed-time convergent controller is analyzed. The analysis is performed by introducing dynamical perturbations into the system driven by the fixed-time convergent controller that yields self-sustained oscillations with a finite frequency and a finite amplitude. Describing Function-Harmonic Balance technique is used to estimate the amplitude and the frequency of those self-sustained oscillations. Then, the stability of the self-sustained oscillations is analyzed. Furthermore, considering a DC motor as a case study, chattering of super-twisting based fixed-time convergent controller is compared with chattering of the traditional super-twisting controller having the same gains.