Step-test based procedure for Super-Twisting Algorithm gains adjustment

Super-Twisting Algorithms (STA) is a non-linear PI-like continuous Sliding Mode (SM) algorithm designed to substitute discontinuous control to continuous and to realise a second-order SM for systems with relative degree one. It is able to compensate the Lipschitz disturbances theoretically exactly and ensures finite-time convergence. However, due to the finite-time convergence of STA and the presence of non-idealities in the system, chattering occurs. This paper proposes a step-test based procedure for adjusting the STA gains to minimize chattering amplitude. We assume that system non-idealities can be modeled as a specific first-order system, namely, with time delay, time constant and system gain. The procedure consists of two steps: on the first stage, identifying the parameters of system; on the second step, predicting the amplitude and frequency of the chattering based on the Describing Function approach and the Harmonic Balance equation, then obtaining expressions of the chattering amplitude and frequency as functions of STA gains and, finally, adjusting the STA parameters based on predicted chattering behavior. This approach is verified on both simulations and experiments on a Maxon RE50 DC Motor.