A Lyapunov approach to second-order sliding mode controllers and observers

This paper develops a unified adaptive second order sliding mode (ASOSM) control method. By using the proposed control structure, the upper bounds of uncertainties are not required, the over-estimation of the control gains are avoided, and the chattering of the conventional sliding mode controllers can be attenuated. It should be noted that the adaptive gains are obtained based on the switching function and its derivative; as a result, the gains keep updating before and after the practical sliding mode is established. Meanwhile, the finite time convergence is proved based on a quadratic Lyapunov approach. Finally, to illustrate the performance of the presented method, an ASOSM controller is designed for a pendulum system and several simulations are performed.

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Hybrid-Impulsive Second Order Sliding Mode Control: Lyapunov Approach

IFAC Proceedings Volumes ◽

10.3182/20130204-3-fr-2033.00187 ◽

2013 ◽

Vol 46 (2) ◽

pp. 397-402 ◽

Cited By ~ 2

Author(s):

Yuri Shtessel ◽

Alain Glumineau ◽

Franck Plestan ◽

Martin Weiss

Keyword(s):

Sliding Mode Control ◽

Sliding Mode ◽

Second Order ◽

Lyapunov Approach ◽

Mode Control ◽

Second Order Sliding Mode

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The Lyapunov Function Design for the Stability Analysis of the “Italian Version” of the Second Order Sliding Mode Controllers

IFAC Proceedings Volumes ◽

10.3182/20110828-6-it-1002.00109 ◽

2011 ◽

Vol 44 (1) ◽

pp. 5866-5871

Author(s):

Andrey Polyakov ◽

Alexander Poznyak

Keyword(s):

Stability Analysis ◽

Lyapunov Function ◽

Sliding Mode ◽

Second Order ◽

Italian Version ◽

Function Design ◽

Sliding Mode Controllers ◽

The Stability ◽

Second Order Sliding Mode

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Second Order Sliding Mode Control of the Coupled Tanks System

Mathematical Problems in Engineering ◽

10.1155/2015/167852 ◽

2015 ◽

Vol 2015 ◽

pp. 1-9 ◽

Cited By ~ 5

Author(s):

Fayiz Abu Khadra ◽

Jaber Abu Qudeiri

Keyword(s):

Performance Measures ◽

Sliding Mode ◽

Absolute Error ◽

Second Order ◽

Liquid Level ◽

First Order ◽

Sliding Mode Controllers ◽

The Time Domain ◽

Domain Performance ◽

Second Order Sliding Mode

Four classes of second order sliding mode controllers (2-SMC) have been successfully applied to regulate the liquid level in the second tank of a coupled tanks system. The robustness of these classes of 2-SMC is investigated and their performances are compared with a first order controller to show the merits of these controllers. The effectiveness of these controllers is verified through computer simulations. Comparison between the controllers is based on the time domain performance measures such as rise time, settling time, and the integral absolute error. Results showed that controllers are able to regulate the liquid level with small differences in their performance.

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