Open AccessAdaptive gains of dual level to super‐twisting algorithm for sliding mode design
Author(s) -
Luo Dong,
Xiong Xiaogang,
Jin Shanghai,
Kamal Shyam
Publication year - 2018
Publication title -
iet control theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.059
H-Index - 108
eISSN - 1751-8652
pISSN - 1751-8644
DOI - 10.1049/iet-cta.2018.5380
Subject(s) - control theory (sociology) , sliding mode control , robustness (evolution) , perturbation (astronomy) , mode (computer interface) , mathematics , state observer , observer (physics) , adaptive control , computer science , control (management) , nonlinear system , physics , artificial intelligence , quantum mechanics , operating system , biochemistry , chemistry , gene
A gain‐adaption mechanism of a dual level to the super‐twisting algorithm (STA) for adaptive sliding mode design is studied. The proposed dual level method first tunes a third‐order sliding mode observer to exactly estimate the magnitude level of external disturbances, and then adjusts the two gains ( α , β ) of STA online simultaneously such that a second‐order sliding mode can take place with small rectifying gains. The gains of the third‐order sliding mode observer are adjusted by exploring the homogeneous property such that only one auxiliary parameter L is needed to be tuned. The magnitude of this parameter L increases until the error between the observer output and actual disturbance disappears. While driving the sliding variable to the sliding mode surface of STA, one gain β of the STA automatically converges to an adjacent area of the perturbation magnitude in finite time. The other gain α is adjusted by the gain β to guarantee the robustness of the STA. This method requires no intervention during adaptation. The usefulness is illustrated by an example of designing an equivalent control‐based sliding mode control with the proposed adaptive STA for a perturbed linear time‐invariant system.