Anti-Control of Chaos of Single Time Scale Brushless DC Motor System with Unknown Parameters Using Adaptive Control

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Abstract:

In this paper, an adaptive feedback control method is proposed for the anti-control of chaos of single time scale brushless DC motor system with unknown parameters based on model-matching. The well-known Rössler chaotic system is considered as the reference system. The chaotification is achieved choosing an appropriate control law and a parametric updating law using Lyapunov stability theory, which provides the stability of the resulting adaptive system and the convergence of the tracking errors to zero. The numerical simulation results show the effectiveness of the proposed method.

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Periodical:

Advanced Materials Research (Volumes 211-212)

Pages:

736-741

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Online since:

February 2011

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[1] X. Wu, J. Lu, H. Iu and S. Wong, Suppression and generation of chaos for a three-dimensional autonomous system using parametric perturbations, Chaos Solitons Fractals, 31: 811–819, (2007).

DOI: 10.1016/j.chaos.2005.10.050

Google Scholar

[2] Z. M. Ge , C. M. Chang and Y. S. Chen, Anti-control of chaos of single time-scale brushless dc motors and chaos synchronization of different order systems, Chaos, Solitons and Fractals, 27, 1298–1315, (2006).

DOI: 10.1016/j.chaos.2005.04.095

Google Scholar

[3] R. T. Yang, Y. G. Hong, H. S. Qin and G. R. Chen, Anticontrol of chaos for dynamic systems in p-normal form: a homogeneity-based approach, Chaos Solitons Fractals, 25: 687–697, (2005).

DOI: 10.1016/j.chaos.2004.11.090

Google Scholar

[4] H. Huijberts, H. Nijmeijer and R. Willems, System identification in communication with chaotic systems, IEEE Trans. Circuits Syst I, 47(6): 800–808, (2000).

DOI: 10.1109/81.852932

Google Scholar

[5] S. Sinha and W. L. Ditto, Computing with distributed chaos, Phys Rev E, 60(1): 363–376, (1999).

Google Scholar

[6] S. J. Schiff, K. D. Jerger, H. Duong, T. Chang, M. L. Spano and W. L. Ditto, Controlling chaos in the brain, Nature, 370: 615–620, (1994).

DOI: 10.1038/370615a0

Google Scholar

[7] W. Yang, M. Ding, A. J. Mandell and E. Ott, Preserving chaos: control strategies to preserve complex dynamics with potential relevance to biological disorders, Phys Rev E, 51: 102–110, (1995).

DOI: 10.1103/physreve.51.102

Google Scholar

[8] G. Chen, J. Q. Fang, Y. Hong and H. S. Qin, Introduction to chaos control and anti-control, In: Leung TP, Qin HS (eds) Advanced topics in nonlinear control systems, Chap 6. World Scientific, Singapore, p.193–245, (2001).

DOI: 10.1142/9789812798541_0006

Google Scholar

[9] G. Chen and X. Dong, From chaos to order: methodologies, perspectives and applications, Singapore: World Scientific, (1998).

Google Scholar

[10] I. T. Georgiou and I. B. Schwartz, Dynamics of large scale coupled structural/mechanical systems: A singular perturbation/proper orthogonal decomposition approach, SIAM J. Appl. Math., 59: 1178–1207, (1999).

DOI: 10.1137/s0036139997299802

Google Scholar

[11] X. F. Wang, G. R. Chen and K. F. Man, Making a continuous-time minimum-phase system chaotic by using time-delay feedback, IEEE Trans Circuits Syst I, 48: 641–645, (2001).

DOI: 10.1109/81.922469

Google Scholar

[12] L. Yang, Z. Liu and G. R. Chen, Chaotifying a continuous-time system via impulsive input, Int J Bifurc Chaos, 12: 1121–1128, (2002).

DOI: 10.1142/s0218127402004954

Google Scholar

[13] H. G. Zhang, Z. L. Wang and D. Liu, Chaotifying fuzzy hyperbolic model using impulsive and nonlinear feedback control approaches, Int J Bifurc Chaos, 15: 2603–2610, (2005).

DOI: 10.1142/s021812740501354x

Google Scholar

[14] D. Chen, H. Wang and G. Chen, Anti-control of Hopf bifurcation, IEEE Trans Circuits Syst I, 48: 661–672, (2001).

DOI: 10.1109/81.928149

Google Scholar

[15] J. G. Lu, Chaotic behavior in sampled-data control systems with saturating control, Chaos Solitons Fractals, 30: 147–155, (2006).

DOI: 10.1016/j.chaos.2005.08.191

Google Scholar

[16] Q. F. Chen, Q. H. Zhong, Y. G. Hong and G. R. Chen, Generation and control of spherical circular attractors using switching schemes, Int J Bifurc Chaos, 17: 243–253, (2007).

DOI: 10.1142/s021812740701729x

Google Scholar

[17] Z. Li, J. B. Park, G. R. Chen, Y. H. Joo and Y. H. Choi, Generating chaos via feedback control from a stable TS fuzzy system through a sinusoidal nonlinearity, Int J Bifurc Chaos, 12: 2283–2291, (2002).

DOI: 10.1142/s0218127402005844

Google Scholar

[18] H. Asada and K. Youcef-Toumi, Direct drive robots: theory and practice, Cambridge, MA: MIT Press; (1987).

DOI: 10.7551/mitpress/2438.001.0001

Google Scholar

[19] S. Murugesan, An overview of electric motors for space applications, IEEE Trans Ind Electr Control Instrum, (1981) ; IECI-28(4).

DOI: 10.1109/tieci.1981.351050

Google Scholar

[20] Z. M. Ge, C. M. Chang and Y. S. Chen, Anti-control of chaos of single time-scale brushless DC motor, Phil. Trans. R. Soc. A, (2006) 364, 2449-2462.

DOI: 10.1098/rsta.2006.1834

Google Scholar

[21] N. Hemati, Strange attractors in brushless dc motors, IEEE Trans Circ Syst, (1994) ; 41(1): 40–5.

DOI: 10.1109/81.260218

Google Scholar

[22] N. Hemati, Dynamic analysis of brushless motors based on compact representations of the equations of motion, IEEE Trans Ind Appl Social Annual Meeting, (1993) ; 1: 51–8.

DOI: 10.1109/ias.1993.298903

Google Scholar