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On phase deficit of the super‐twisting second‐order sliding mode control algorithm
Author(s) -
Boiko Igor
Publication year - 2020
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.5054
Subject(s) - convergence (economics) , control theory (sociology) , phase (matter) , nonlinear system , mathematics , relay , sliding mode control , perspective (graphical) , algorithm , computer science , control (management) , physics , quantum mechanics , power (physics) , artificial intelligence , economics , economic growth , geometry
Summary The notion of phase deficit was introduced in [12], which allows one to determine if a nonlinear system can reveal finite‐time or asymptotic convergence. Twisting and suboptimal second‐order sliding mode control algorithms and a conventional relay feedback system were analyzed from the perspective of the phase deficit. However, phase deficit for the super‐twisting algorithm was not determined at that time due to the complexity of the problem. Therefore, although it is known that the super‐twisting algorithm reveals finite‐time convergence (when no parasitic dynamics are present), it was not supported by the criterion based on the phase deficit. In the current article this problem has been solved through an open‐loop interpretation of the phase deficit, which is proposed in the article. Another problem addressed in the article is the relationship between the frequency characteristics of the system and the type of convergence (finite‐time or asymptotic). The mechanism of convergence is analyzed through considering time‐varying frequency of self‐excited oscillations and phase lag of the linear part of the system.