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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

Huang, J. , 2004, Nonlinear Output Regulation: Theory and Applications, SIAM, Philadelphia, PA.
Chen, H. , Zhang, B. , Zhao, T. , Wang, T. , and Li, K. , 2016, “ Finite-Time Tracking Control for Extended Nonholonomic Chained-Form Systems With Parametric Uncertainty and External Disturbance,” J. Vib. Control, epub.
Lu, M. , and Haung, J. , 2015, “ Robust Output Regulation Problem for Linear Time-Delay Systems,” Int. J. Control, 88(6), pp. 1236–1245. [CrossRef]
Mobayen, S. , 2016, “ Finite-Time Robust-Tracking and Model-Following Controller for Uncertain Dynamical Systems,” J. Vib. Control, 22(4), pp. 1117–1127. [CrossRef]
Feng, G. , and Zhang, T. J. , 2006, “ Output Regulation of Discrete-Time Piecewise-Linear Systems With Application to Controlling Chaos,” IEEE Trans. Circuits Syst. II, 53(4), pp. 249–253. [CrossRef]
Chu, X. , and Lan, W. , 2014, “ Composite Nonlinear Feedback Control for Output Regulation Problem of Linear Discrete-Time Systems With Input Saturation,” J. Syst. Eng. Electron., 25(6), pp. 1043–1055. [CrossRef]
Huang, J. , and Lin, C. F. , 1994, “ A Stability Property and Its Application to Discrete-Time Nonlinear System Control,” IEEE Trans. Autom. Control, 39(11), pp. 2307–2311. [CrossRef]
Hakimi, A. R. , and Binazadeh, T. , 2017, “ Robust Generation of Limit Cycles in Nonlinear Systems: Application on Two Mechanical Systems,” ASME J. Comput. Nonlinear Dyn., 12(4), p. 041013. [CrossRef]
Binazadeh, T. , and Bahmani, M. , 2017, “ Design of Robust Controller for a Class of Uncertain Discrete-Time Systems Subject to Actuator Saturation,” IEEE Trans. Autom. Control, 62(3), pp. 1505–1510. [CrossRef]
Binazadeh, T. , and Shafiei, M. H. , 2014, “ Robust Stabilization of Uncertain Nonlinear Slowly-Varying Systems: Application in a Time-Varying Inertia Pendulum,” ISA Trans., 53(2), pp. 373–379. [CrossRef] [PubMed]
Mobayen, S. , 2015, “ An Adaptive Fast Terminal Sliding Mode Control Combined With Global Sliding Mode Scheme for Tracking Control of Uncertain Nonlinear Third-Order Systems,” Nonlinear Dyn., 82(1–2), pp. 599–610. [CrossRef]
Binazadeh, T. , and Yousefi, M. , 2017, “ Designing a Cascade-Control Structure Using Fractional-Order Controllers: Time Delay Fractional-Order Proportional-Derivative Controller and Fractional-Order Sliding-Mode Controller,” ASCE J. Eng. Mech., 143(7).
Shafiei, M. H. , and Binazadeh, T. , 2013, “ Application of Partial Sliding Mode in Guidance Problem,” ISA Trans., 52(2), pp. 192–197. [CrossRef] [PubMed]
Yousefi, M. , and Binazadeh, T. , 2016, “ Delay-Independent Sliding Mode Control of Time-Delay Linear Fractional Order Systems,” Trans. Inst. Meas. Control., epub.
Mobayen, S. , Baleanu, D. , and Tchier, F. , 2016, “ Second-Order Fast Terminal Sliding Mode Control Design Based on LMI for a Class of Non-Linear Uncertain Systems and Its Application to Chaotic Systems,” J. Vib. Control, epub.
Binazadeh, T. , 2016, “ Finite-Time Tracker Design for Uncertain Nonlinear Fractional-Order Systems,” ASME J. Comput. Nonlinear Dyn., 11(4), p. 041028. [CrossRef]
Mobayen, S. , 2015, “ Finite-Time Tracking Control of Chained-Form Nonholonomic Systems With External Disturbances Based on Recursive Terminal Sliding Mode Method,” Nonlinear Dyn., 80(1–2), pp. 669–683. [CrossRef]
Wei, X. J. , Zhang, G. F. , and Guo, L. , 2009, “ Composite Disturbance-Observer Based Control and Terminal Sliding Mode Control for Uncertain Structural Systems,” Int. J. Syst. Sci., 40(10), pp. 1009–1017. [CrossRef]
Wu, S. N. , Sun, X. Y. , Sun, Z. W. , and Wu, X. D. , 2010, “ Sliding-Mode Control for Staring-Mode Spacecraft Using a Disturbance Observer,” Proc. Inst. Mech. Eng. Part G, 224(2), pp. 215–224. [CrossRef]
Yang, J. , Li, S. , and Yu, X. , 2013, “ Sliding-Mode Control for Systems With Mismatched Uncertainties Via a Disturbance Observer,” IEEE Trans. Ind. Electron., 60(1), pp. 160–169. [CrossRef]
Binazadeh, T. , and Shafiei, M. H. , 2014, “ A Novel Approach in the Finite-Time Controller Design,” Syst. Sci. Control Eng., 2(1), pp. 119–124. [CrossRef]
Khalil, H. K. , 2002, Nonlinear Systems, 3rd ed., Prentice Hall, Upper Saddle River, NJ.
Bhat, S. P. , and Bernstein, D. S. , 2000, “ Finite-Time Stability of Continuous Autonomous Systems,” SIAM J. Control Optim., 38(3), pp. 751–766. [CrossRef]
Chen, W. H. , 2004, “ Disturbance Observer Based Control for Nonlinear Systems,” IEEE/ASME Trans. Mechatronics., 9(4), pp. 706–710. [CrossRef]
Isidori, A. , 1995, Nonlinear Control Systems, Springer-Verlag, London.
Guo, L. , and Chen, W. H. , 2005, “ Disturbance Attenuation and Rejection for Systems With Nonlinearity via DOBC Approach,” Int. J. Robust Nonlinear Control, 15(3), pp. 109–125. [CrossRef]
Sun, H. , and Guo, L. , 2014, “ Output Regulation Control for MIMO Nonlinear System With Mismatched Disturbances and Its Application to BTT Missiles,” 11th World Congress on Intelligent Control and Automation (WCICA), Shenyang, China, June 29–July 4, pp. 1130–1136.
Chenarani, H. , and Binazadeh, T. , 2017, “ Flexible Structure Control of Unmatched Uncertain Nonlinear Systems Via Passivity-Based Sliding Mode Technique,” Iran. J. Sci. Technol., epub.
Vaidyanathan, S. , 2015, “ Adaptive Chaotic Synchronization of Enzymes-Substrates System With Ferroelectric Behaviour in Brain Waves,” Int. J. PharmTech Res., 8(5), pp. 964–973.
Adhami-Mirhosseini, A. , Yazdanpanah, M. J. , and Khaki-Sedigh, A. , 2012, “ Robust Tracking of a Class of Perturbed Nonlinear Systems Via Multivariable Nested Sliding Mode Control,” ASME J. Dyn. Syst. Meas. Control, 134(3), p. 031004. [CrossRef]

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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