Analysis of chattering in homogenous sliding mode controllers using the locus of a perturbed relay system

Abstract

AbstractThis work investigates the use of the locus of a perturbed relay system (LPRS) method for the analysis of chattering and other possible oscillations in discontinuous homogenous Sliding Mode Controllers (SMC). Particularly these homogeneous SMCs are considered as linear input‐to‐state and nonlinear separable state‐to‐output dynamics of Wiener type. The existence of non‐vanishing oscillations in these sliding mode control systems, when parasitic dynamics are present, is shown. This supports the claim that the finite‐time convergence for homogenous SMCs only occurs in the absence of any parasitic dynamics which is an ideal and non‐realizable condition. We investigate the chattering and other possible oscillations using the LPRS for the controllers proposed in the study by Ding et al. The undertaken analysis reveals multiple periodic solutions for the plants of relative degrees 2 through 4. The LPRS, originally developed for linear plants, is extended to linear input‐to‐state and nonlinear separable state‐to‐output dynamics. To investigate chattering, the parasitic dynamics are included in this analysis through a second‐order actuator model. The proposed approach to analysis provides exact values of the frequency and amplitude of chattering, as well as categorization of the obtained periodic solutions into orbitally stable and orbitally unstable. The analytical results are supported by simulations.