LPRS Analysis of Super Twisting Sliding Mode Control System

In this work, we analyze the chattering phenomenon in Supertwisting (ST) Sliding Mode Control (SMC) system, using the Locus of a Perturbed Relay System (LPRS) method. Due to the nonlinear nature of system dynamics, we adopt a numerical approach to compute both the real and imaginary parts of the LPRS. We address unmodeled dynamics by incorporating a second-order actuator model. Our analysis focuses on how changes in the actuator parameter influence the chattering characteristics of the system’s output. The ST control loop is re-structured to a standard form of relay feedback system. This enables us to employ the LPRS to compute, for the first time, periodic solutions of the ST SMC system, that provide insights about its average dynamics and the existence of chattering in its practical implementation.