On limit cycle chattering in sliding mode control systems under the influence of sampling intervals based on describing function approach

In this paper, the influence of sampling intervals on the chattering in sliding mode (SM) control systems is considered. The describing function (DF) approach is employed to analyze the chattering characteristics in the sampling SM control. By the DF calculations and limit cycle existence conditions, an unstable limit cycle and two stable limit cycles are found in the SM control system. The frequencies and amplitudes of the two limit cycles can also be estimated by graphical calculations. The estimation accuracy of chattering parameters is evaluated by the simulations. The results of simulations show that the system could converge to a large and a small limit cycle from different initial conditions.