Chattering analysis for Lipschitz continuous sliding‐mode controllers

Abstract

SummaryIn this article, an analysis of chattering in systems driven by Lipschitz continuous sliding‐mode controllers (LCSMC) is performed using the describing function approach. Two kinds of LCSMC are considered: the first one is based on a linear sliding variable (LSV) and the second one on a terminal sliding variable (TSV). Predictions of amplitude, frequency, and average power of self‐excited oscillations, are used to compare such LCSMC respect to the supertwisting controller (STC) in systems with fast‐actuators. Theoretical predictions and simulations allow the following conclusions: (i) LCSMC still may induce fast‐oscillations (chattering) of smaller amplitude and average power, than ones caused by the STC in the absence of the measurement noises. (ii) The level of chattering with LSV‐LCSMC could be smaller than one produced by TSV‐LCSMC. (iii) The zero (sliding) dynamics of the LSV‐LCSMC cannot be arbitrarily fast or the closed‐loop system may lose even practical stability, unlike the TSV‐LCSMC whose trajectories are finally bounded.