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

• Published in: Journal of China universities of posts and telecommunications Vol. 23; no. 1; pp. 55 - 59
• Main Authors: Hongbo, Kang, Yu, Shen
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.02.2016
• Subjects: chattering parameters; Control systems; describing function approach; Describing functions; Initial conditions; Intervals; Mathematical analysis; multiple limit cycle analysis; Sampling; sampling interval; Simulation; Vibration; 估计精度; 图形计算; 存在性条件; 抖振; 描述函数法; 极限环; 滑模控制系统; 采样间隔; describing function approach; sampling interval; multiple limit cycle analysis; chattering parameters
• ISSN: 1005-8885
• DOI: 10.1016/S1005-8885(16)60008-0

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.