Controlling chaos in Josephson-Junction using nonlinear backstepping controller

IEEE Transactions on Applied Superconductivity

Volumn 16, Issue 4, 2006, Pages 1988-1998

  Harb, Ahmad M ^a,b   Harb, Bassam A ^c  

^a IEEE   (Jordan)

^b JORDAN UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Jordan)

^c YARMOUK UNIVERSITY   (Jordan)

Author keywords

Chaos theory; Josephson junction; Nonlinear backstepping controller

Indexed keywords

EXTERNAL DIRECT CURRENTS; HOPF BIFURCATION POINTS; NONLINEAR BACKSTEPPING CONTROLLERS; STABLE PERIODIC SOLUTION REGION;

BIFURCATION (MATHEMATICS); CHAOS THEORY; ELECTRIC CURRENTS; NONLINEAR CONTROL SYSTEMS;

JOSEPHSON JUNCTION DEVICES;

EID: 33845548377     PISSN: 10518223     EISSN: None     Source Type: Journal    
DOI: 10.1109/TASC.2006.881811     Document Type: Article

References (23)

1. F. M. Salam and S. S. Sastry, "Dynamics of the forced Josephson junction circuit: The region of chaos," IEEE Trans. Circuits Syst., vol. 32, no. 8, pp. 784-796, Aug. 1985.
2. C. B. Whan and C. J. Lobb, "Complex dynamical behaviour in RLC-shunted Josephson tunnel junctions," Phys. Rev. B, vol. 53, no. 1, pp. 405-413, Jan. 1996.
3. S. K. Dana, D. C. Sengupta, and K. D. Edoh, "Chaotic dynamics in Josephson junction," IEEE Trans. Circuit Syst. I, vol. 48, no. 8, pp. 405-413, Aug. 2001.
4. A. C. Scott and A. Petraglia, "Flux interactions on stacked josephson junctions," Phys. Lett. A, vol. 211, pp. 161-167, 1996.
5. E. Ott, C. Grebogi, and J. A. York, "Controlling chaos," Phys. Rev. Lett., vol. 64, pp. 1196-1199, 1990.
6. E. R. Hunt, "Stabilizing high-period orbits in a chaotic system: The diode resonator," Phys. Rev. Lett., vol. 67, no. 15, pp. 1953-1957, 1991.
7. T. H. Yang, S. F. Chen, and Y. S. Gou, "Efficient strategy for the occasional proportional feedback method in controlling chaos," Phys. Rev. E, vol. 59, no. 5, pp. 5393-5399, 1999.
8. I. L. Atkin and E. Abraham, "Control of chaos in discrete josephson transmission lines," IEEE Trans. Appl. Supercond., vol. 7, no. 2, pp. 2894-2896, Jun. 1997.
9. O. H. Olsen and M. R. Samuelsen, "Control of chaotic patterns in a josephson junction model," Phys. Lett. A, vol. 266, pp. 123-133, 2000.
10. E. Abraham, I. L. Atkin, and A. Wilson, "Josephson voltage standard by controlling chaos," IEEE Trans. Appl. Supercond., vol. 9, no. 2, pp. 4166-4169, Jun. 1999.
11. K. Pyragas, "Continuous control of chaos by self-controlling feedback," Phys. Lett. A, vol. 170, pp. 421-428, 1992.
12. H. Khalil, Nonlinear Systems, 2nd ed. New York: Prentice Hall, 1996.
13. M. Krstic, "Ioannis Kanellakopoulus and Peter Kokotovic," in Non-linear and Adaptive Control Design. New York: Wiley, 1995.
14. A. Zaher and M. Zohdy, "Robust Control of Biped Robots," in Proc. ACC, Chicago, IL, Jun. 2000, pp. 405-413.
15. A. Zaher, M. Zohdy, F. Areed, and K. Soliman, "Real-time model-reference control of non-linear processes," presented at the 2nd Int. Conf. On Computers in Industry, Bahrain, Nov. 2000.
16. A. Zaher, M. Zohdy, F. Areed, and K. Soliman, "Robust model-reference control for a class of non-linear and piece-wise linear systems," in Proc. ACC, Arlington, VA, Jun. 2001, pp. 405-413.
17. F. Ikhouane and M. Krstic, "Robustness of the tuning functions adaptive backstepping design for linear systems," IEEE Trans. Autom. Control, vol. 43, no. 3, pp. 431-437, Mar. 1998.
18. A. Al Qaisia, A. Harb, A. Zaher, and M. Zohdy, "Robust estimation-based control of chaotic behavior in an oscillators with inertial elastic symmetric nonlinearities," J. Vibration Control, vol. 9, pp. 665-684, 2003.
19. A. M. Harb and B. A. Harb, "Chaos control of third-order phase-locked loops using backstepping nonlinear controller," Int. J.Chaos, Solitons Fractals, vol. 20, pp. 719-723, 2004.
20. A. M. Harb and N. Abed-Jabbar, "Controlling Hopf bifurcation and chaos in a small power system," Int. J. Chaos, Solitons Fructals, vol. 18, pp. 055-1063, 2003.
21. _, "Nonlinear chaos control in a permanent magnet reluctance machine," Int. J. Chaos, Salitons Fractals, vol. 19, pp. 1217-1224, 2004.
22. C. B. Whan, C. J. Lobb, and M. G. Forester, "Effect of inductance in externally shunted Josephson tunnel junction," J. Appl. Phys. Rev., vol. 77, no. 1, pp. 382-389, 1995.
23. A. B. Cawthorne, C. B. Whan, and C. J. Lobb, "Complex dynamics of esistively and inductively shunted Josephson junction," J. Appl. Phys., vol. 84, no. 2, pp. 1126-1132, 1998.