Second‐order sliding mode controller design subject to mismatched unbounded perturbations

• Published in: International journal of robust and nonlinear control Vol. 27; no. 18; pp. 4706 - 4722
• Main Authors: Liu, Lu, Ding, Shihong
• Format: Journal Article
• Language: English
• Published: Bognor Regis Wiley Subscription Services, Inc 01.12.2017
• Subjects: backstepping; Control systems design; Dynamics; finite‐time control; Perturbation methods; sliding mode; Sliding mode control; Uncertainty
• ISSN: 1049-8923; 1099-1239
• DOI: 10.1002/rnc.3828

Summary The dynamics of the second‐order sliding mode (SOSM) can be obtained by directly taking the second derivative on the sliding variable when it has a relative degree of 2 with respect to the control input. However, there will always appear some state‐dependent certain or uncertain terms in the first derivative of the sliding variable, and the derivative directly imposed on these terms could enlarge the uncertainties in the control channel. One method to reduce the uncertainties in the control channel is to hold this information in the dynamics of the first derivative of the sliding variable, while the original SOSM dynamics could be transformed to be a SOSM system with a mismatched unbounded perturbation. This paper focuses on the controller design problem for SOSM dynamics subject to mismatched unbounded perturbation. By using Lyapunov analysis, a novel backstepping‐like design methodology will be proposed. The rigorous mathematical proof will show that under the derived SOSM controller, the closed‐loop sliding mode dynamics is globally finite‐time stable. Meanwhile, the frequently used constant upper bound assumptions for the standard SOSM system can also be extended to the state‐dependent hypotheses in this paper. An academic example is illustrated to verify the effectiveness of the proposed method. Copyright © 2017 John Wiley & Sons, Ltd.