Robust synchronization of a chaotic mechanical system with nonlinearities in control inputs

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• 作者：Mohammad Pourmahmood Aghababa (1)
  Hasan Pourmahmood Aghababa (2) (3)
  
• 关键词：Finite ; time synchronization ; Non ; autonomous centrifugal governor ; Adaptive law ; Unknown parameter ; Input nonlinearity
• 刊名：Nonlinear Dynamics
• 出版年：2013
• 出版时间：2 - July 2013
• 年：2013
• 卷：73
• 期：1
• 页码：363-376
• 全文大小：689KB
• 参考文献：1. Pecora, L.M., Carroll, T.L.: Synchronization in chaotic systems. Phys. Rev. Lett. 64, 821鈥?24 (1990) CrossRef
  2. Kwon, O.M., Park, J.H., Lee, S.M.: Secure communication based on chaotic synchronization via interval time-varying delay feedback control. Nonlinear Dyn. 63, 239鈥?52 (2011) CrossRef
  3. Lee, S.M., Choi, S.J., Ji, D.H., Park, J.H., Won, S.C.: Synchronization for chaotic Lur鈥檈 systems with sector鈥搑estricted nonlinearities via delayed feedback control. Nonlinear Dyn. 59, 277鈥?88 (2010) CrossRef
  4. Aghababa, M.P., Khanmohammadi, S., Alizadeh, G.: Finite-time synchronization of two different chaotic systems with unknown parameters via sliding mode technique. Appl. Math. Model. 35, 3080鈥?091 (2011) CrossRef
  5. Aghababa, M.P., Heydari, A.: Chaos synchronization between two different chaotic systems with uncertainties, external disturbances, unknown parameters and input nonlinearities. Appl. Math. Model. 36, 1639鈥?652 (2012) CrossRef
  6. Aghababa, M.P., Akbari, M.E.: A chattering-free robust adaptive sliding mode controller for synchronization of two different chaotic systems with unknown uncertainties and external disturbances. Appl. Math. Comput. 218, 5757鈥?768 (2012) CrossRef
  7. Aghababa, M.P., Feizi, H.: Nonsingular terminal sliding mode approach applied to synchronize chaotic systems with unknown parameters and nonlinear inputs. Chin. Phys. B 21, 060506 (2012) CrossRef
  8. Aghababa, M.P., Aghababa, H.P.: Chaos suppression of a class of unknown uncertain chaotic systems via single input. Commun. Nonlinear Sci. Numer. Simul. 17, 3533鈥?538 (2012) CrossRef
  9. Aghababa, M.P., Feizi, H.: Design of a sliding mode controller for synchronizing chaotic systems with parameter and model uncertainties and external disturbances. Trans. Inst. Meas. Control (2012). doi:10.1177/0142331211434657
  10. Aghababa, M.P., Aghababa, H.P.: A novel finite-time sliding mode controller applied to synchronize chaotic systems with input nonlinearity. Arab. J. Sci. Eng. (2012). doi:10.1007/s13369-012-0459-z
  11. Aghababa, M.P.: A novel adaptive finite-time controller for synchronizing chaotic gyros with nonlinear inputs. Chin. Phys. B 20, 090505 (2011) CrossRef
  12. Aghababa, M.P., Aghababa, H.P.: Finite-time stabilization of uncertain non-autonomous chaotic gyroscopes with nonlinear inputs. Appl. Math. Mech. 33, 155鈥?64 (2012) CrossRef
  13. Aghababa, M.P., Aghababa, H.P.: Chaos suppression of uncertain gyros in a given finite time. Chin. Phys. B 21, 110505 (2012) CrossRef
  14. Aghababa, M.P., Aghababa, H.P.: Synchronization of nonlinear chaotic electromechanical gyrostat systems with uncertainties. Nonlinear Dyn. 67, 2689鈥?701 (2012) CrossRef
  15. Aghababa, M.P., Aghababa, H.P.: Adaptive finite-time stabilization of uncertain non-autonomous chaotic electromechanical gyrostat systems with unknown parameters. Mech. Res. Commun. 38, 500鈥?05 (2011) CrossRef
  16. Aghababa, M.P., Aghabab, H.P.: Synchronization of mechanical horizontal platform systems in finite time. Appl. Math. Model. 36, 4579鈥?591 (2012) CrossRef
  17. Aghababa, M.P., Aghababa, H.P.: Finite-time stabilization of a non-autonomous chaotic rotating mechanical system. J. Franklin Inst. 349, 2875鈥?888 (2012) CrossRef
  18. Aghababa, M.P., Aghababa, H.P.: A general nonlinear adaptive control scheme for finite-time synchronization of chaotic systems with uncertain parameters and nonlinear inputs. Nonlinear Dyn. 69, 1903鈥?914 (2012) CrossRef
  19. Aghababa, M.P., Aghababa, H.P.: Adaptive finite-time synchronization of non-autonomous chaotic systems with uncertainty. J. Comput. Nonlinear Dyn. 8, 031006 (2013) CrossRef
  20. Aghababa, M.P.: Robust finite-time stabilization of fractional-order chaotic systems based on fractional Lyapunov stability theory. J. Comput. Nonlinear Dyn. 7, 021010 (2012) CrossRef
  21. Aghababa, M.P.: Robust stabilization and synchronization of a class of fractional-order chaotic systems via a novel fractional sliding mode controller. Commun. Nonlinear Sci. Numer. Simul. 17, 2670鈥?681 (2012) CrossRef
  22. Aghababa, M.P.: Finite-time chaos control and synchronization of fractional-order chaotic (hyperchaotic) systems via fractional nonsingular terminal sliding mode technique. Nonlinear Dyn. 69, 247鈥?61 (2012) CrossRef
  23. Beltrami, E.: Mathematics for Dynamic Modeling. Academic Press, Boston (1987)
  24. Chu, Y.D., Zhang, J.G., Li, X.F., Chang, Y.X., Luo, G.W.: Chaos and chaos synchronization for a non-autonomous rotational machine systems. Nonlinear Anal., Real World Appl. 9, 1378鈥?393 (2008) CrossRef
  25. Ge, Z.M., Yang, H.S., Chen, H.H., Chen, H.K.: Regular and chaotic dynamics of a rotational machine with a centrifugal governor. Int. J. Eng. Sci. 37, 921鈥?43 (1999) CrossRef
  26. Zhang, J.G., Li, X.F., Chu, Y.D., Yu, J.N., Chang, Y.X.: Hopf bifurcations, Lyapunov exponents and control of chaos for a class of centrifugal flywheel governor system. Chaos Solitons Fractals 39, 2150鈥?168 (2009) CrossRef
  27. Zhang, J.G., Yu, J.N., Chu, Y.D., Li, X.F., Chang, Y.X.: Bifurcation and chaos of a non-autonomous rotational machine systems. Simul. Model. Pract. Theory 16, 1588鈥?605 (2008) CrossRef
  28. Sotomayor, J., Mello, L.F., Braga, D.C.: Stability and Hopf bifurcation in an hexagonal governor system. Nonlinear Anal., Real World Appl. 9, 889鈥?98 (2008) CrossRef
  29. Ge, Z.M., Jhuang, W.R.: Chaos, control and synchronization of a fractional order rotational mechanical system with a centrifugal governor. Chaos Solitons Fractals 33, 270鈥?89 (2007) CrossRef
  30. Ge, Z.M., Lee, C.I.: Non-linear dynamics and control of chaos for a rotational machine with a hexagonal centrifugal governor with a spring. J. Sound Vib. 262, 845鈥?64 (2003) CrossRef
  31. Ge, Z.M., Lee, C.I.: Anticontrol and synchronization of chaos for an autonomous rotational machine system with a hexagonal centrifugal governor. J. Sound Vib. 282, 635鈥?48 (2005) CrossRef
  32. Ge, Z.M., Lee, C.I.: Control, anticontrol and synchronization of chaos for an autonomous rotational machine system with time-delay. Chaos Solitons Fractals 23, 1855鈥?864 (2005)
  33. Aghababa, M.P., Aghababa, H.P.: Chaos suppression of rotational machine systems via finite-time control method. Nonlinear Dyn. 69, 1881鈥?888 (2012) CrossRef
  34. Aghababa, M.P., Aghababa, H.P.: Finite-time stabilization of non-autonomous uncertain chaotic centrifugal flywheel governor systems with input nonlinearities. J. Vib. Control (2012). doi:10.1177/1077546312463715
  35. Aghababa, M.P.: Design of an adaptive finite-time controller for synchronization of two identical/different non-autonomous chaotic flywheel governor systems. Chin. Phys. B 21, 030502 (2012) CrossRef
  36. Curran, P.F., Chua, L.O.: Absolute stability theory and the synchronization problem. Int. J. Bifurc. Chaos 7, 1357鈥?382 (1997)
  37. Zhang, H., Huang, W., Wang, Z., Chai, T.: Adaptive synchronization between two different chaotic systems with unknown parameters. Phys. Lett. A 350, 363鈥?66 (2006) CrossRef
  
• 作者单位：Mohammad Pourmahmood Aghababa (1)
  Hasan Pourmahmood Aghababa (2) (3)
  
  1. Electrical Engineering Department, Urmia University of Technology, Urmia, Iran
  2. Department of Mathematics, University of Tabriz, Tabriz, Iran
  3. Research Center for Industrial Mathematics of University of Tabriz, Tabriz, Iran
  

文摘

Centrifugal flywheel governors are known as chaotic non-autonomous mechanical devices used for automatic control of the speed of engines. The main characteristic of them is avoiding the damage caused by sudden change of the load torques. In this paper, the problem of robust finite-time synchronization of centrifugal flywheel governor systems is studied. The effects of unknown parameters, model uncertainties, external noises, and input nonlinearities are fully taken into account. We propose some adaptive laws to overcome the side effects of the unknown parameters of the system on the synchronization performance. Then, a robust adaptive switching controller is introduced to synchronize centrifugal flywheel governors with nonlinear control inputs in a given finite time. The finite-time fast convergence property of the proposed scheme is analytically proved and numerically illustrated.