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Technical Brief

A Terminal Sliding Mode Control of Disturbed Nonlinear Second-Order Dynamical Systems

[+] Author and Article Information
Pawel Skruch

Department of Automatics and Biomedical Engineering,
AGH University of Science and Technology,
al. A. Mickiewicza 30/B1,
Krakow 30-059, Poland
e-mail: pawel.skruch@agh.edu.pl

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received December 24, 2015; final manuscript received December 29, 2015; published online February 3, 2016. Assoc. Editor: Sotirios Natsiavas.

J. Comput. Nonlinear Dynam 11(5), 054501 (Feb 03, 2016) (5 pages) Paper No: CND-15-1450; doi: 10.1115/1.4032503 History: Received December 24, 2015; Revised December 29, 2015

The paper presents a terminal sliding mode controller for a certain class of disturbed nonlinear dynamical systems. The class of such systems is described by nonlinear second-order differential equations with an unknown and bounded disturbance. A sliding surface is defined by the system state and the desired trajectory. The control law is designed to force the trajectory of the system from any initial condition to the sliding surface within a finite time. The trajectory of the system after reaching the sliding surface remains on it. A computer simulation is included as an example to verify the approach and to demonstrate its effectiveness.

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Figures

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Fig. 1

RLC circuit with nonlinear elements and a noise signal

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Fig. 2

Comparison of the closed-loop trajectories for a small amplitude (A = 0.1) of the disturbance signal

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Fig. 3

Control signals u for A = 0.1

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Fig. 4

Comparison of the closed-loop trajectories for a medium amplitude (A = 1) of the disturbance signal

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Fig. 5

Control signals u for A = 1

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Fig. 6

Comparison of the closed-loop trajectories for a high amplitude (A = 5) of the disturbance signal

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Fig. 7

Control signals u for A = 5

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Fig. 8

Comparison of the closed-loop trajectories for a band-limited white noise disturbance of power 0.1

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Fig. 9

Control signals u for a band-limited white noise disturbance of power 0.1

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