Table of Contents Author Guidelines Submit a Manuscript
Journal of Control Science and Engineering
Volume 2011, Article ID 169848, 11 pages
http://dx.doi.org/10.1155/2011/169848
Research Article

Limit Cycle Predictions of Nonlinear Multivariable Feedback Control Systems with Large Transportation Lags

Department of Aeronautical Engineering, National Formosa University, 64, Wen Hua Road, Huwei, Yunlin 63208, Taiwan

Received 4 September 2010; Revised 1 February 2011; Accepted 6 April 2011

Academic Editor: Peilin Fu

Copyright © 2011 Tain-Sou Tsay. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. K. C. Patra and Y. P. Singh, “Graphical method of prediction of limit cycle for multivariable nonlinear systems,” IEE Proceedings: Control Theory and Applications, vol. 143, no. 5, pp. 423–428, 1996. View at Google Scholar
  2. J. O. Gray and P. M. Taylor, “Computer aided design of multivariable nonlinear control systems using frequency domain techniques,” Automatica, vol. 15, no. 3, pp. 281–297, 1979. View at Google Scholar · View at Scopus
  3. J. O. Gray and N. B. Nakhla, “Prediction of limit cycles in multivariable nonlinear systems,” IEE Proceedings D: Control Theory and Applications, vol. 128, no. 5, pp. 233–241, 1981. View at Google Scholar · View at Scopus
  4. H. C. Chang, C. T. Pan, C. L. Huang, and C. C. Wei, “General approach for constructing the limit cycle loci of multiple-nonlinearity systems,” IEEE Transactions on Automatic Control, vol. 32, no. 9, pp. 845–848, 1987. View at Google Scholar · View at Scopus
  5. F. Paoletti, A. Landi, and M. Innocenti, “A CAD tool for limit cycle prediction in nonlinear systems,” IEEE Transactions on Education, vol. 39, no. 4, pp. 505–511, 1996. View at Google Scholar · View at Scopus
  6. S. D. Katebi and M. R. Katebi, “Control design for multivariable multivalued nonlinear systems,” Systems Analysis Modelling Simulation, vol. 15, no. 1, pp. 13–37, 1994. View at Google Scholar
  7. D. P. Atherton, Nonlinear Control Engineering, D. Van Nostrand Reinhold Company, London, UK, 1982.
  8. J. H. Taylor, Describing Functions, in Electrical Engineering Encyclopedia, John Wiley & Sons, New York, NY, USA, 1999.
  9. D. P. Atherton and S. Spurgeon, Nonlinear Control Systems, Analytical Methods, Electrical Engineering Encyclopedia, John Wiley & Sons, New York, NY, USA, 1999.
  10. H. Khalil, Nonlinear Systems, Prentice Hall, Upper Saddle River, NJ, USA, 3rd edition, 2002.
  11. M. Basso, R. Genesio, and A. Tesi, “A frequency method for predicting limit cycle bifurcations,” Nonlinear Dynamics, vol. 13, no. 4, pp. 339–360, 1997. View at Google Scholar · View at Scopus
  12. B. F. Wu and S. M. Chang, “A stabilized analysis of a front-wheel-steered vehicle with simulated trajectories,” WSEAS Transactions on Systems, vol. 6, no. 6, pp. 1138–1146, 2007. View at Google Scholar · View at Scopus
  13. P. S. V. Nataraj and J. J. Brav, “Reliable and accurate algorithm to computer the limit cycle locus for uncertain nonlinear system,” IEE Proceedings on Control Theory and Applications, vol. 150, no. 5, pp. 457–466, 2003. View at Google Scholar
  14. Y. J. Sun, “Existence and uniqueness of limit cycle for a class of nonlinear discrete-time systems,” Chaos, Solitons and Fractals, vol. 38, no. 1, pp. 89–96, 2008. View at Publisher · View at Google Scholar · View at Scopus
  15. V. K. Pillai and H. D. Nelson, “New algorithm for limit cycle analysis of nonlinear control systems,” Journal of Dynamic Systems, Measurement and Control, vol. 110, no. 3, pp. 272–277, 1988. View at Google Scholar · View at Scopus
  16. B. F. Wu, H. I. Chin, and J. W. Perng, “Gain-phase margin analysis of nonlinear perturbed vehicle control systems for limit cycle prediction,” WSEAS Transaction on System, vol. 3, no. 5, pp. 1881–1886, 2004. View at Google Scholar
  17. Y. J. Wang, “Robust prevention of limit cycle for nonlinear control systems with parametric uncertainties both in the linear plant and nonlinearity,” ISA Transactions, vol. 46, no. 4, pp. 479–491, 2007. View at Publisher · View at Google Scholar · View at PubMed · View at Scopus
  18. T. S. Tsay and K. W. Han, “Limit cycle analysis of nonlinear multivariable feedback control systems,” Journal of the Franklin Institute, vol. 325, no. 6, pp. 721–730, 1988. View at Google Scholar · View at Scopus
  19. Y. J. Sun, “Existence and uniqueness of limit cycle for a class of nonlinear discrete-time systems,” Chaos, Solitons and Fractals, vol. 38, no. 1, pp. 89–96, 2008. View at Publisher · View at Google Scholar · View at Scopus
  20. C. Lin and Q. G. Wang, “On uniqueness of solutions to relay feedback systems,” Automatica, vol. 38, no. 1, pp. 177–180, 2002. View at Publisher · View at Google Scholar · View at Scopus
  21. S. Engelberg, “Limitations of the describing function for limit cycle prediction,” IEEE Transactions on Automatic Control, vol. 47, no. 11, pp. 1887–1890, 2002. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  22. C. F. Lu, C. C. Liu, and C. J. Wu, “Effect of battery energy storage system on load frequency control considering governor deadband and generation rate constraint,” IEEE Transaction on Energy Conversion, vol. 10, no. 3, pp. 555–561, 1995. View at Google Scholar
  23. Q. G. Wang, Y. U. Zhang, and M. S. Chiu, “Decoupling internal model control for multivariable systems with multiple time delays,” Chemical Engineering Science, vol. 57, no. 1, pp. 115–124, 2002. View at Publisher · View at Google Scholar · View at Scopus
  24. Q. Xiong, W. J. Cai, and M. J. He, “A practical loop pairing criterion for multivariable processes,” Journal of Process Control, vol. 15, no. 7, pp. 741–747, 2005. View at Publisher · View at Google Scholar · View at Scopus
  25. Q. G. Wang, C. C. Hang, and B. Zou, “A frequency response approach to autotuning of multivariable controllers,” Chemical Engineering Research and Design, vol. 75, no. 8, pp. 797–806, 1997. View at Google Scholar · View at Scopus