Frequency Domain Analysis of the Extended Super-Twisting Algorithm

The Extended Super-Twisting Algorithm (ESTA) is a second order sliding mode controller generating continuous control signal. ESTA could be designed with arbitrary high homogeneity weight of output compensating theoretically exactly Lipschitz perturbations in the systems with relative degree one. In this paper to analyze fast-oscillations (chattering) caused by the presence of fast parasitic dynamics the Describing Function approach is used. The amplitude and frequency of self-excited oscillations, and the average power (power per each period) are parametrized in the terms of the actuator time-constant. Proposed analysis shows that ESTA allows to selecting desired accuracy of the output and desired power consumption by increasing homogeneity weight.