Skip to main content
SpringerLink
Log in

Robust pole assignment for linear control systems in a circular region using novel global harmony search algorithm

  • Published:
International Journal of Control, Automation and Systems Aims and scope Submit manuscript

Abstract

This paper presents a new approach to the problem of robust pole assignment in a circular region using novel global harmony search (NGHS) algorithm. Based on geometric principles, the position information of poles in the circular region is depicted and the rules of dynamic selection of poles from the circular region are determined. This ensures the algorithm select poles dynamically from the circular region. In order to get a set of poles and the state feedback controller which allow the system to have a maximum allowable perturbation or uncertainty, the upper bound of perturbation or uncertainty is optimized by the NGHS algorithm for the poles in the circular region. In contrast to most existing methods, an optimization method using NGHS algorithm for the dynamic selection of poles, makes the closed-loop system show better robustness. Finally, the simulation results demonstrate the effectiveness of the proposed approach.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. J. Kautsky, N. K. Nichols, and P. Van Dooren, “Robust pole assignment in linear state feedback,” International Journal of Control, vol. 41, no. 5, pp. 1129–1155, May 1985.

    Article  MathSciNet  MATH  Google Scholar 

  2. X. Le and J. Wang, “Robust pole assignment for synthesizing feedback control systems using recurrent neural networks,” IEEE Trans. on Neural Networks and Learning Systems, vol. 25, no. 2, pp. 383–393, February 2014. [click]

    Article  Google Scholar 

  3. R. Byers and S. G. Nash, “Approaches to robust pole assignment,” International Journal of Control, vol. 49, no. 3, pp. 97–117, January 1989.

    Article  MathSciNet  MATH  Google Scholar 

  4. J. Lam and W. Y. Van, “A gradient flow approach to the robust pole-placement problem,” International Journal of Robust and Nonlinear Control, vol. 5, no. 3, pp. 175–185, March 1995.

    Article  MathSciNet  MATH  Google Scholar 

  5. J. Wang and G. Wu, “A multilayer recurrent neural network for on-line synthesis of minimum-norm linear feedback control systems via pole assignment,” Automatica, vol. 32, no. 3, pp. 435–442, March 1996.

    Article  MathSciNet  MATH  Google Scholar 

  6. D. W. C. Ho, J. Lam, J. Xu, and H. K. Tam, “Neural computation for robust approximate pole assignment,” Neurocomputing, vol. 25, no. 1, pp. 191–211, April 1999. [click]

    Article  MATH  Google Scholar 

  7. S. Hu and J. Wang, “A gradient flow approach to on-line robust pole assignment for synthesizing output feedback control systems,” Automatica, vol. 38, no. 11, pp. 1959–1968, November 2002. [click]

    Article  MathSciNet  MATH  Google Scholar 

  8. D. Jiang and J. Wang, “Augmented gradient flows for online robust pole assignment via state and output feedback,” Automatica, vol. 38, no. 2, pp. 279–286, February 2002. [click]

    Article  MATH  Google Scholar 

  9. A. L. Tits and Y. Yang, “Globally convergent algorithms for robust pole assignment by state feedback,” IEEE Trans. on Automatic Control, vol. 41, no. 10, pp. 1432–1452, October 1996. [click]

    Article  MathSciNet  MATH  Google Scholar 

  10. Y. C. Soh, R. J. Evans, I. R. Petersen, and R. E. Betz, “Robust pole assignment,” Automatica, vol. 23, no. 5, pp. 601–610, September 1987. [click]

    Article  MathSciNet  MATH  Google Scholar 

  11. P. S. Rao and I. Sen, “Robust pole placement stabilizer design using linear matrix inequalities,” IEEE Trans. on Power Systems, vol. 15, no. 1, pp. 313–319. February 2000. [click]

    Article  Google Scholar 

  12. M. Ait Rami, S. El Faiz, A. Benzaouia, and F. Tadeo, “Robust exact pole placement via an LMI-based algorithm,” IEEE Trans. on Automatic Control, vol. 54, no. 2, pp. 394–398, February 2009. [click]

    Article  MathSciNet  Google Scholar 

  13. E. K. Chu, “Pole assignment via the Schur form,” Systems & control letters, vol. 56, no. 4, pp. 303–314, April 2007. [click]

    Article  MathSciNet  MATH  Google Scholar 

  14. G. Garcia and J. Bernussou, “Pole assignment for uncertain systems in a specified disk by state feedback,” IEEE Trans. on Automatic Control, vol. 40, no. 1, pp. 184–190, January 1995. [click]

    Article  MathSciNet  MATH  Google Scholar 

  15. M. Chilali, P. Gahinet, and P. Apkarian, “Robust pole placement in LMI regions,” IEEE Trans. on Automatic Control, vol. 44, no. 12, pp. 2257–2270, December 1999. [click]

    Article  MathSciNet  MATH  Google Scholar 

  16. G. Garcia, J. Bernussou, and D. Arzelier. “An LMI solution for disk pole location with H2 guaranteed cost,” European Journal of Control, vol. 1, no. 1, pp. 54–61, 1995. [click]

    Article  MATH  Google Scholar 

  17. K. Furuta and S. Kim, “Pole assignment in a specified disk,” IEEE Trans. on Automatic Control vol. 32, no. 5, pp. 423–427, May 1987. [click]

    Article  MATH  Google Scholar 

  18. A. AbdulL-Wahab, “Pole assignment in a specified circular region using a bilinear transformation onto the unit circle,” International Journal of Systems Science, vol. 25, no. 7, pp. 1113–1125, July 1994.

    Article  MathSciNet  MATH  Google Scholar 

  19. J. L. Wu and T. T. Lee, “A new approach to optimal regional pole placement,” Automatica, vol. 33, no. 10, pp. 1917–1921, October 1997. [click]

    Article  MathSciNet  MATH  Google Scholar 

  20. N. Maamri, O. Bachelier, and D. Mehdi, “Pole placement in a union of regions with prespecified subregion allocation,” Mathematics and Computers in Simulation, vol. 72, no. 1, pp. 38–46, July 2006. [click]

    Article  MathSciNet  MATH  Google Scholar 

  21. Z. W. Geem, J. H. Kim, and G. V. Loganathan, “A new heuristic optimization algorithm: harmony search,” Simulation, vol. 76, no. 2, pp. 60–68, February 2001. [click]

    Article  Google Scholar 

  22. K. S. Lee and Z. W. Geem, “A new meta-heuristic algorithm for continuous engineering optimization: harmony search theory and practice,” Computer Methods in Applied Mechanics and Engineering, vol. 194, no. 36, pp. 3902–3933, September 2005. [click]

    Article  MATH  Google Scholar 

  23. S. S. Shreem, S. Abdullah, and M. Z. A. Nazri, “Hybridising harmony search with a Markov blanket for gene selection problems,” Information Sciences, vol. 258, pp. 108–121, February 2014. [click]

    Article  MathSciNet  Google Scholar 

  24. D. Zou, L. Gao and J. Wu, S. Li, and Y. Li, “A novel global harmony search algorithm for reliability problems,” Computers & Industrial Engineering, vol. 58, no. 2, pp. 307–316, March 2010. [click]

    Article  Google Scholar 

  25. D. Manjarres, I. Landa-Torres and S. Gil-Lopez, et al, “A survey on applications of the harmony search algorithm,” Engineering Applications of Artificial Intelligence, vol. 26, no. 8, pp. 1818–1831, September 2013. [click]

    Article  Google Scholar 

  26. R. A. Horn and C. R. Johnson, Matrix Analysis, Cambridge University Press, Cambridge, 1990.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Information Science and Technology, Bohai University, Jinzhou, Liaoning, 121013, P. R. China

    Junchang Zhai

  2. College of Information Science and Engineering, Northeastern University, Shenyang, Liaoning, 110819, P. R. China

    Junchang Zhai

  3. College of Information Science and Engineering, Northeastern University, Shenyang, Liaoning, 110819, P. R. China

    Liqun Gao

  4. Graduate School of Business and Law, RMIT University, Melbourne, VIC, 3000, Australia

    Steven Li

Authors
  1. Junchang Zhai
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Liqun Gao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Steven Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Junchang Zhai.

Additional information

Recommended by Associate Editor Shengyuan Xu under the direction of Editor Myotaeg Lim. This work is partially supported by the Funds of National Science of China (Grant nos. 61104106 and 61104029), the Natural Science Foundation of Liaoning Province (Grant nos. 201202156 and 2013020144).

Junchang Zhai received the B.S. degree in mathematics from Bohai University in 2002, and he obtained his M.S. degree in computer software and theory from Bohai University, Jinzhou, China in 2009. He is currently working towards Ph.D. degree in the field of control theory & control Engineering at Northeastern University. His current research interests are robust control and evolutionary algorithms.

Liqun Gao received the M.S. and Ph.D. degrees in automatic control from Northeastern University, Shenyang, China, in 1985 and 1991, respectively. Currently, he is a professor in the control theory and navigation technology department, Northeastern University. His current research interests are artificial intelligence, control theory and control methods, and pattern recognition.

Steven Li is a Professor of Finance in RMIT University, Melbourne, Australia. He holds a PhD in applied mathematics from Delft University of Technology, The Netherlands, an MBA from Melbourne Business School and a Bachelor of Science degree from Tsinghua University, China. He has previously taught at University of South Australia, Queensland University of Technology, Edith Cowan University and Tsinghua University. His current research interests are mainly in Quantitative Finance and Financial Management. He has published extensively in both finance and applied mathematics.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhai, J., Gao, L. & Li, S. Robust pole assignment for linear control systems in a circular region using novel global harmony search algorithm. Int. J. Control Autom. Syst. 14, 713–722 (2016). https://doi.org/10.1007/s12555-014-0302-2

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12555-014-0302-2

Keywords

Search

Navigation