Variable Gain Super-Twisting Sliding Mode Control

A multivariable super-twisting sliding mode approach

“…However in a succession of papers [6,16,14], Lyapunov methods were employed successfully for the first time to analyze the properties of the super-twisting algorithm for uncertain systems. This has opened the door for the integration of these ideas with other nonlinear tools including gain adaptation [13,10,7]. However in all these developments a single input control structure has essentially been considered.…”

“…In many situations it is possible by control input ⋆ A preliminary version of this paper was presented at the IFAC SAFEPROCESS workshop Mexico City, Mexico, September 2012. Contact email: c.edwards@exeter.ac.uk scaling to transform a multi-input control problem with m control inputs into a decoupled problem involving m single input control structures and so the approaches in [13,10,7] work satisfactorily. Instead, in this communique, a multi-variable super-twisting structure is proposed, which is then analyzed using an extension of the Lyapunov ideas from [14].…”

Integral sliding mode control for Markovian jump T–S fuzzy descriptor systems based on the super‐twisting algorithm

“…As in [44,45], the trajectories of the system (39) will cross and not stay on the subspace Ω 1 \ {0}. Thus, the stability of the system (39) can be guaranteed if the time derivative of V (s(t), ϖ(t)) in (40) along with the system (39) is negative definite for…”

An adaptive sliding mode differentiator for actuator oscillatory failure case reconstruction

“…However, recent theoretical developments described by Moreno and Osorio in [16] describe a Lyapunov approach. The use of Lyapunov based approaches has subsequently been investigated in [9], which proposes a variable gain formulation for the super-twisting algorithm, and [22] which proposes a super-twisting adaptive control formulation.…”

“…The work in [20] uses a sliding mode observer to estimate the sloshing effect and exploits this estimate as part of the control feedback loop to mitigate the effects on the structure. The adaptive differentiator proposed in this paper is also different to the ones in [9,21,22], since the latter papers consider a control design problem and seek to ensure the gains are as small as possible to avoid chattering. Although the work proposed in [21] considers an adaptive scheme which assumes an unknown bound on the disturbance (similar to the work proposed here), the adaptation rules and the Lyapunov analysis are quite different and the super-twisting gains continually adapt.…”