Chattering analysis of second order sliding mode algorithms for linear plants with disturbance

An analysis of second-order sliding-mode algorithms, specially of super-twisting and twisting as a filter algorithm is performed in frequency domain with the use of the describing function method, and is shown that periodic motion happens and the parameters of this periodic motion is intended. The analysis is done via utilization of the concept of equivalent gain of nonlinear function. The equivalent gain is used as a model of propagation of averaged values of signals through nonlinear elements of system. By exerting External disturbance to the system, the output of the system was evaluated. By means of a simulation example, results are presented.