Journal Article

Lyapunov-based settling time estimate and tuning for twisting controller

Harshal B. Oza, Yury V. Orlov and Sarah K. Spurgeon

in IMA Journal of Mathematical Control and Information

Published on behalf of Institute of Mathematics and its Applications

Volume 29, issue 4, pages 471-490
Published in print December 2012 | ISSN: 0265-0754
Published online December 2012 | e-ISSN: 1471-6887 | DOI: http://dx.doi.org/10.1093/imamci/dnr037
Lyapunov-based settling time estimate and tuning for twisting controller

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A novel switched control synthesis is developed and an upper bound on the settling time is obtained for a robust second-order sliding mode controller. The framework is based on step-by-step application of classical linear feedback design and the well-known ‘twisting’ controller. The underlying philosophy is to utilize globally exponentially stable linear feedback so that the trajectories enter an arbitrarily defined domain of attraction in finite time and then switch to the ‘twisting’ controller so that the trajectories settle at the origin in finite time. The proposed method is applied to the linear inverted pendulum to obtain an upper bound on the settling time of the closed-loop system in a full-state feedback setting in the presence of disturbances. Tuning rules to achieve the desired settling time are explicitly derived without recourse to the differential inequality of the Lyapunov function.

Keywords: finite time stability; variable structure control; settling time estimate; twisting controller

Journal Article.  0 words. 

Subjects: Mathematics

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