Analysis of the sub-optimal second-order sliding-mode control algorithm in the frequency domain

The frequency-domain characteristics of the sub-optimal second-order sliding mode control (2-SMC) algorithm are analyzed making reference to the feedback control of linear plants. We show that if the plant is stable and its relative degree is greater than two then a stable periodic solution may exist. Two methods for computing the amplitude and frequency of the limit cycle are proposed. The dependence of the frequency and amplitude of the periodic solution from the tuning parameters of the 2-SMC algorithm is investigated.