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Research Papers

A Novel Global Sliding Mode Control Based on Exponential Reaching Law for a Class of Underactuated Systems With External Disturbances

[+] Author and Article Information
Saleh Mobayen

Department of Electrical Engineering,
Faculty of Engineering,
University of Zanjan,
P.O. Box 38791-45371,
Zanjan 38791-45371, Iran
e-mail: mobayen@znu.ac.ir

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received May 8, 2015; final manuscript received July 7, 2015; published online August 26, 2015. Assoc. Editor: Haiyan Hu.

J. Comput. Nonlinear Dynam 11(2), 021011 (Aug 26, 2015) (9 pages) Paper No: CND-15-1125; doi: 10.1115/1.4031087 History: Received May 08, 2015

This paper is concerned with the control of underactuated systems with external disturbances. Using the global sliding mode control (GSMC) technique, a new robust controller is presented to improve the robustness and stability of the system. The conditions of asymptotic stability are presented by linear matrix inequalities (LMIs). Our purpose is to build a control law so that it would enforce the states of the system to exponentially verge the sliding surface. The suggested controller has a simple structure because it is derived from the associated first-order differential equation and is able to handle the external disturbances and system nonlinearities. The efficiency of the proposed scheme is observed through simulations in an illustrative example. Simulation results demonstrate the considerable performance of the suggested technique.

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Figures

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Fig. 1

TORA system schematic configuration

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Fig. 3

The states trajectories of the system without the presence of noise

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Fig. 4

Control performances without the presence of noise: (a) the control input and (b) the sliding surface

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Fig. 5

The states trajectories of the system with noise and disturbances d1=d3=0 and d2=11ɛx3

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Fig. 6

Control performances with noise and disturbances d1=d3=0 and d2=11ɛx3: (a) the control input and (b) the sliding surface

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Fig. 7

The states trajectories with noise and disturbances d1=0.04 cos(2t), d2=11ɛx3, and d3=0.3 sin(t)

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Fig. 8

Control performances with noise and disturbances d1=0.04 cos(2t), d2=11ɛx3, and d3=0.3 sin(t)

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