Adaptive gains of dual level to super-twisting algorithm for sliding mode design

Abstract

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. © The Institution of Engineering and Technology 2018