Observer Design for Chaos Synchronization of Time-delayed Power Systems
The global chaos synchronization for a class of time-delayed power systems is investigated via observer-based approach. By employing the concepts of quadratic stability theory and generalized system model, a new sufficient criterion for constructing an observer is deduced. In contrast to the previous works, this paper proposes a theoretical and systematic design procedure to realize chaos synchronization for master-slave power systems. Finally, an illustrative example is given to show the applicability of the obtained scheme.
[1] L. M. Pecora and T. L. Carroll, "Synchronization in chaotic systems,"
Phys. Rev. Lett., vol.64, pp.821-824, 1990.
[2] H. Salarieh, A. Alasty, "Adaptive synchronization of two chaotic systems
with stochastic unknown parameters," Communications in Nonlinear
Science and Numerical Simulation, vol.14, pp.508-519, 2009.
[3] G. S. M. Ngueuteu, R. Yamapi, P. Woafo, "Effects of higher nonlinearity
on the dynamics and synchronization of two coupled electromechanical
devices," Communications in Nonlinear Science and Numerical
Simulation, vol.13, pp.1213-1240, 2008.
[4] S.L.T. de Souza, I.L. Caldas, R.L. Viana, J.M. Balthazar and R.M.L.R.F.
Brasil, "A simple feedback control for a chaotic oscillator with limited
power supply," Journal of Sound and Vibration, vol.299, pp.664-671,
2007.
[5] X. Wu, J. Cai and M. Wang, "Robust synchronization of chaotic horizontal
platform systems with phase difference," Journal of Sound and Vibration,
vol.305, pp.481-491, 2007.
[6] S. Bowong, "Adaptive synchronization between two different chaotic
dynamical systems," Communications in Nonlinear Science and
Numerical Simulation, vol.12, pp.976-985, 2007.
[7] A. Si-Ammour, S. Djennoune, M. Bettayed, "A sliding mode control for
linear fractional systems with input and state delays," Communications in
Nonlinear Science and Numerical Simulation, vol.14, pp.2310-2318, 2009.
[8] M. Chen, D. Zhou and Y. Shang, "A new observer-based synchronization
scheme for private communication," Chaos Solitons & Fractals, vol.24
pp.1025-1030, 2005.
[9] S.H. Chen, Q. Yang, C.P. wang, "Impulsive control and synchronization of
unified chaotic system," Chaos Solitons & Fractals, vol.20 pp. 751-758,
2004.
[10] J. T. Sun, Y. P. Zhang, Q.D. Wu, "Impulsive control for the stabilization
and synchronization of Lorenz systems," Phys. Lett. A., vol.298,
pp.153-160, 2002.
[11] M. Rafikov, José Manoel Balthazar, "On control and synchronization in
chaotic and hyperchaotic systems via linear feedback control,"
Communications in Nonlinear Science and Numerical Simulation, vol.13,
pp.1246-1255, 2008.
[12] X. Yu and Y. Song, "Chaos synchronization via controlling partial state of
chaotic systems," Int. J. Bifurcation and Chaos, vol.11, pp.1737-1741,
2001.
[13] H. T. Yau, C. L. Kuo, J. J. Yan, "Fuzzy sliding mode control for a class of
chaos synchronization with uncertainties," International Journal of
Nonlinear Sciences and Numerical Simulation, vol.7, pp.333-338, 2006.
[14] J. J. Yan, M. L. Hung and T. L. Liao, "Adaptive sliding mode control for
synchronization of chaotic gyros with fully unknown parameters," Journal
of Sound and Vibration, vol.298, pp.298-306, 2006.
[15] Y. P. Tian and X. Yu, "Stabilization unstable periodic orbits of chaotic
systems via an optimal principle," Journal of the Franklin Institute, vol.337,
pp.771-779, 2000.
[16] S. M. Guo, L. S. Shieh, G. Chen and C. F. Lin, "Effective chaotic orbit
tracker: a prediction-based digital redesign approach," IEEE Trans.
Circuits syst. I, vol.47, pp.1557-1560, 2000.
[17] T. Wu and M. S. Chen, "Chaos control of the modified Chua-s circuit
system," Physica D, vol.164, pp.53-58, 2002.
[18] J. Zhang, C. Li, H. Zhang and J. Yu, "Chaos synchronization using single
variable feedback based on backstepping method," Chaos Solitons &
Fractals, vol.21, pp.1183-1193, 2004.
[19] N. Kopell and R.B. Washburn, Chaotic motions in the
two-degree-of-freedom swing equations, IEEE Trans Circ Syst. CAS-29,
pp.738-746, 1982.
[20] E. H. Abed and P. P. Varaiya, Nonlinear oscillations in power systems. Int
J Electr Power Energy Syst., vol.6, pp.37-43, 1984.
[21] H. K. Chen, T. N. Lin and J. H. Chen, "Dynamic analysis, controlling
chaos and chaotification of a SMIB power system," Chaos Solitons &
Fractals,vol. 24, pp.1307-1315, 2005.
[22] E. M. Shahverdiev, L. H. Hashimova and N. T. Hashimova, "Chaos
synchronization in some power systems," Chaos Solitons & Fractals,
vol.37, pp.829-834, 2008.
[23] J. C. Doyle, K. Glover, P.P. Khargonekar, B.A. Francis, "State-space
solutions to standard 2 H and ∞ H control problem," IEEE Trans
Automat Contr., vol.34, pp.831-846, 1989.
[24] S. D. Brierley, J. N. Chiasson, E. B. Lee and S. H. Zak, "On the stability
independent of delay for linear systems," IEEE Trans Automat Contr.,
vol.27, pp.252-254, 1982.
[1] L. M. Pecora and T. L. Carroll, "Synchronization in chaotic systems,"
Phys. Rev. Lett., vol.64, pp.821-824, 1990.
[2] H. Salarieh, A. Alasty, "Adaptive synchronization of two chaotic systems
with stochastic unknown parameters," Communications in Nonlinear
Science and Numerical Simulation, vol.14, pp.508-519, 2009.
[3] G. S. M. Ngueuteu, R. Yamapi, P. Woafo, "Effects of higher nonlinearity
on the dynamics and synchronization of two coupled electromechanical
devices," Communications in Nonlinear Science and Numerical
Simulation, vol.13, pp.1213-1240, 2008.
[4] S.L.T. de Souza, I.L. Caldas, R.L. Viana, J.M. Balthazar and R.M.L.R.F.
Brasil, "A simple feedback control for a chaotic oscillator with limited
power supply," Journal of Sound and Vibration, vol.299, pp.664-671,
2007.
[5] X. Wu, J. Cai and M. Wang, "Robust synchronization of chaotic horizontal
platform systems with phase difference," Journal of Sound and Vibration,
vol.305, pp.481-491, 2007.
[6] S. Bowong, "Adaptive synchronization between two different chaotic
dynamical systems," Communications in Nonlinear Science and
Numerical Simulation, vol.12, pp.976-985, 2007.
[7] A. Si-Ammour, S. Djennoune, M. Bettayed, "A sliding mode control for
linear fractional systems with input and state delays," Communications in
Nonlinear Science and Numerical Simulation, vol.14, pp.2310-2318, 2009.
[8] M. Chen, D. Zhou and Y. Shang, "A new observer-based synchronization
scheme for private communication," Chaos Solitons & Fractals, vol.24
pp.1025-1030, 2005.
[9] S.H. Chen, Q. Yang, C.P. wang, "Impulsive control and synchronization of
unified chaotic system," Chaos Solitons & Fractals, vol.20 pp. 751-758,
2004.
[10] J. T. Sun, Y. P. Zhang, Q.D. Wu, "Impulsive control for the stabilization
and synchronization of Lorenz systems," Phys. Lett. A., vol.298,
pp.153-160, 2002.
[11] M. Rafikov, José Manoel Balthazar, "On control and synchronization in
chaotic and hyperchaotic systems via linear feedback control,"
Communications in Nonlinear Science and Numerical Simulation, vol.13,
pp.1246-1255, 2008.
[12] X. Yu and Y. Song, "Chaos synchronization via controlling partial state of
chaotic systems," Int. J. Bifurcation and Chaos, vol.11, pp.1737-1741,
2001.
[13] H. T. Yau, C. L. Kuo, J. J. Yan, "Fuzzy sliding mode control for a class of
chaos synchronization with uncertainties," International Journal of
Nonlinear Sciences and Numerical Simulation, vol.7, pp.333-338, 2006.
[14] J. J. Yan, M. L. Hung and T. L. Liao, "Adaptive sliding mode control for
synchronization of chaotic gyros with fully unknown parameters," Journal
of Sound and Vibration, vol.298, pp.298-306, 2006.
[15] Y. P. Tian and X. Yu, "Stabilization unstable periodic orbits of chaotic
systems via an optimal principle," Journal of the Franklin Institute, vol.337,
pp.771-779, 2000.
[16] S. M. Guo, L. S. Shieh, G. Chen and C. F. Lin, "Effective chaotic orbit
tracker: a prediction-based digital redesign approach," IEEE Trans.
Circuits syst. I, vol.47, pp.1557-1560, 2000.
[17] T. Wu and M. S. Chen, "Chaos control of the modified Chua-s circuit
system," Physica D, vol.164, pp.53-58, 2002.
[18] J. Zhang, C. Li, H. Zhang and J. Yu, "Chaos synchronization using single
variable feedback based on backstepping method," Chaos Solitons &
Fractals, vol.21, pp.1183-1193, 2004.
[19] N. Kopell and R.B. Washburn, Chaotic motions in the
two-degree-of-freedom swing equations, IEEE Trans Circ Syst. CAS-29,
pp.738-746, 1982.
[20] E. H. Abed and P. P. Varaiya, Nonlinear oscillations in power systems. Int
J Electr Power Energy Syst., vol.6, pp.37-43, 1984.
[21] H. K. Chen, T. N. Lin and J. H. Chen, "Dynamic analysis, controlling
chaos and chaotification of a SMIB power system," Chaos Solitons &
Fractals,vol. 24, pp.1307-1315, 2005.
[22] E. M. Shahverdiev, L. H. Hashimova and N. T. Hashimova, "Chaos
synchronization in some power systems," Chaos Solitons & Fractals,
vol.37, pp.829-834, 2008.
[23] J. C. Doyle, K. Glover, P.P. Khargonekar, B.A. Francis, "State-space
solutions to standard 2 H and ∞ H control problem," IEEE Trans
Automat Contr., vol.34, pp.831-846, 1989.
[24] S. D. Brierley, J. N. Chiasson, E. B. Lee and S. H. Zak, "On the stability
independent of delay for linear systems," IEEE Trans Automat Contr.,
vol.27, pp.252-254, 1982.
@article{"International Journal of Electrical, Electronic and Communication Sciences:58322", author = "Jui-Sheng Lin and Yi-Sung Yang and Meei-Ling Hung and Teh-Lu Liao and Jun-Juh Yan", title = "Observer Design for Chaos Synchronization of Time-delayed Power Systems", abstract = "The global chaos synchronization for a class of time-delayed power systems is investigated via observer-based approach. By employing the concepts of quadratic stability theory and generalized system model, a new sufficient criterion for constructing an observer is deduced. In contrast to the previous works, this paper proposes a theoretical and systematic design procedure to realize chaos synchronization for master-slave power systems. Finally, an illustrative example is given to show the applicability of the obtained scheme.
", keywords = "Chaos, Synchronization, Quadratic stability theory, Observer", volume = "4", number = "5", pages = "832-4", }
