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Research Papers

Robust Output Regulation Via Sliding Mode Control and Disturbance Observer: Application in a Forced Van Der Pol Chaotic Oscillator

[+] Author and Article Information
F. Shiravani

Department of Electrical and
Electronic Engineering,
Shiraz University of Technology,
Modares Boulevard,
Shiraz 7155713876, Iran
e-mail: f.shiravani@sutech.ac.ir

M. H. Shafiei

Department of Electrical and
Electronic Engineering,
Shiraz University of Technology,
Modares Boulevard,
Shiraz 7155713876, Iran
e-mail: shafiei@sutech.ac.ir

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received September 3, 2016; final manuscript received February 18, 2017; published online June 5, 2017. Assoc. Editor: Hashem Ashrafiuon.

J. Dyn. Sys., Meas., Control 139(9), 091015 (Jun 05, 2017) (6 pages) Paper No: DS-16-1430; doi: 10.1115/1.4036235 History: Received September 03, 2016; Revised February 18, 2017

This paper considers the problem of robust output regulation of nonlinear systems in semi strict-feedback form in the presence of model uncertainties and nonvanishing disturbances. In the proposed procedure, two exosystems are considered to generate the disturbance and reference signals. In order to reduce both the conservatism of the control law and the chattering phenomena, a disturbance observer is designed for disturbance estimation instead of assuming the known upper bound for the disturbance. Moreover, a novel sliding surface is designed based on the tracking error to guarantee that the output of the system tracks the output of the exosystem. In this regard, some theorems are given and according to the Lyapunov approach, it is proved that the robust output regulation is guaranteed in the presence of model uncertainties and external disturbances. Finally, in order to show the applicability of the proposed controller, it is applied to the Van der Pol chaotic oscillator. Computer simulations verify the theoretical results and also show the effective performance of the proposed controller.

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References

Figures

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Fig. 1

Phase portrait of the FVPCO

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Fig. 2

Time response of real value and estimated value of external disturbance d,d̂

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Fig. 3

Time response of the error of DO, ed

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Fig. 4

Time response of the tracking yd by y

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Fig. 5

Time response of the tracking error (e) by using the proposed method in this paper and the presented method in Ref. [30]

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Fig. 6

Time response of the control signal u by using the proposed method in this paper and the presented method in Ref. [30]

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