Wednesday , December 19 2018

Lead-lag Controller Design for Time Delay Systems Using Genetic Algorithms

Nidhal BEN HASSEN1, Karim SAADAOUI1,2, Mohamed BENREJEB1
1Université de Tunis El Manar, Ecole Nationale d’Ingénieurs de Tunis,
Laboratoire de Recherche en Automatique (LARA),
B.P. 37, 1002 Tunis, Le Belvédère, Tunisia.
2 Computer Engineering Department,
College of computers and Information Technology, Taif University,
Taif, Saudi Arabia.
Nidhal.Benhassen@enit.rnu.tn,karim.saadaoui@isa2m.rnu.tn, mohamed.benrejeb@enit.rnu.tn

ABSTRACT: In this article, the set of all stabilizing lead-lag controllers applied to a class of linear time delay systems is obtained. The original problem is divided into two sub-problems with the help of Kharitonov’s Lemma. This essential step allows the application of the D-decomposition method and the determination of the complete set of stability regions. In the second part of this paper, stability regions are used as search space for Genetic Algorithms (GA) to minimize several performance indices of the closed loop system. An example is given to show the effectiveness of the proposed controller design.

KEYWORDS: Time delay systems; Second order phase lead-lag controller; Stability; D-decomposition; Genetic Algorithms.

>>FULL TEXT: PDF

CITE THIS PAPER AS:
Nidhal BEN HASSEN, Karim SAADAOUI, Mohamed BENREJEB,
Lead-lag Controller Design for Time Delay Systems Using Genetic Algorithms, Studies in Informatics and Control, ISSN 1220-1766, vol. 26(1), pp. 87-94, 2017. https://doi.org/10.24846/v26i1y201710

REFERENCES

  1. Alikhani H. & Madady A. (2013). First-order controller design for second order integrating systems with time delay. in Proceedings of IEEE Conference on Control Applications, Hyderabad.
  2. Amri I., Soudani D. & Benrejeb M. (2010). Delay dependent robust expo-nential stability criterion for perturbed and uncertain neutral systems with time varying delays. Studies in Informatics and Control, 19 (2), 135-144.
  3. Bellman R.E. & Cooke K.L. (1963). Differential-difference equations. Academic Press, New York.
  4. Ben Hassen N., Saadaoui K. & Benrejeb M. (2015). Stabilizing time delay systems with prespecified gain and phase margins by lead-lag controllers. Journal of Systems Applications Engineering & Development, 9, 47-53.
  5. Borne P., Dauphin-Tanguy G., Richard J.P., Rotella F. & Zambettakis I. (1993). Analyse et régulation des processus industriels. Tome I: Régulation continue. Editions Technip, Paris.
  6. Chen C. K., Kuo H. H., Yan J. J. & Liao T. L. (2009). GA-based PID active queue management control design for a class of TCP communication networks. Expert Systems with Application on Science Direct, 36 (2), 1903-1913.
  7. Chen H. C. & Chang S. H. (2006). Genetic Algorithms based optimization design of a PID controller for an active magnetic bearing. Journal of Computer Science and Network Security, 6, 95-99.
  8. Dang Q. V., Dequidt A., Vermei-Ren L. & DAMBRINE M. (2014). Design and control of force feedback haptic systems with time delay. Springer Int. Publishing, 373-387.
  9. Elmadssia S., Saadaoui K. & M., Benrejeb (2012). PI controller design for time delay systems using an extension of the Hermit-Biehler theorem. Journal of Industrial Engineering, vol. 2013.
  10. Elmadssia S., Saadaoui K. & Benrejeb M. (2016). New stability conditions for nonlinear time varying delay systems. Journal of Systems Science, 47, 2009-2021.
  11. Efimov D., Polyakov A., Perru-Quetti W. & Richard J. P. (2016). Weighted homogeneity for time delay systems: Finite time and independent of delay stability. IEEE Trans. on Automat. Cont., 61, 210-215.
  1. Gryazina E. N. & Polyak B. T. (2006). Stability regions in the parameter space: D-decomposition revisited. Automatica, 42, 13-26.
  2. Guerra R.G.V., Rubio J.F.M., Cuéllar B.M. & Sánchez G.I.D. (2016). Dynamic delayed controllers for unstable recycling systems with time delays. Studies in Informatics and Control, 25 (2), 195-206.
  3. Hetel L., Fiter C., Omran H., Seuret A., Fridman E., Richard J. P. & Niculescu S. I. (2017). Recent developments on the stability of systems with aperiodic sampling: an overview. Automatica, 76, 309-335.
  4. Hohenbicher N. & Ackermann, J. (2003). Computing stable regions in parameter spaces for a class of quasi-polynomials. in Proceedings of 4th IFAC Workshop on Time Delay Systems, TDS’ 03, Rocquencourt.
  5. Kharitonov V. L., Niculescu S., Moreno J. & Michiels W. (2005). Static out-put stabilization: Necessary conditions for multiple delay controllers. IEEE Trans. on Automat. Cont., 50,  82-86.
  6. Marra M. A. & Walcott B. L. (1996). Stability and optimality in genetic algo-rithm controllers. in Proceedings of IEEE International Symposium on Intelligent Control, Dearborn.
  7. Masum A. K. M., Shahjalal M., Faruque M. F. & Sarker M. I. H. (2011). Solving the vehicle routing problem using genetic algorithm. Journal of Advanced Computer Science and Applications (IJACSA), 2 (7), 126-131.
  8. Ohri J., Kumar N. & Chinda M. (2014). An improved genetic algorithm for PID parameter tuning. Recent Advances in Electrical and Computer Engineering, Venice (pp. 191-198).
  9. Osusky J. & Vesely V. (2010). Modification of Neimark D-partition method for desired phase margin. In Proceedings of the International Conference on Cybernetics and Informatics, Vyšná Boca.
  10. Pandey I. K. & Dewan L. (2014). Stabilizing sets of PID controllers for mini-mum phase integrating processes with dead time. In Proceedings of the 13th Intl. Conference on Circuits, Systems, Electronics, Control & Signal Processing, CSECS, Lisbon.
  11. Pekar L. & R. Prokop (2010). Non-delay parameter depending stability of a time delay system. Proceedings of 14th WSEAS Int. Conf. on Systems, Corfu.
  12. Pillai R. P., Jadhav S. P. & Patil M. D. (2013). Tuning of PID controllers using advanced genetic algorithm. Journal of Advanced Computer Science and Applications (IJACSA), Special issue of selected paper, 1-6.
  13. Rico J. E. N. & Camacho E. F. (2007). Control of dead time processes. Springer, London.
  14. Saadaoui K. (2003). Fixed order controller design via parametric methods. PhD Thesis, Bilkent University.
  15. Saadaoui K. & Ozguler A.B. (2009). Stabilizing first-order controllers with desired stability region. Control and Intelligent Systems, 37, 31-38.
  16. Saadaoui K., Moussa A. & Benrejeb M. (2009). PID controller design for time delay systems using genetic algorithms. The Mediterranean Journal of Measurement and Control, 5, 31-36.
  17. Saadaoui K., Testouri S. & Benrejeb M. (2010). Robust stabilizing first order controllers for a class of time delay systems. ISA Transactions, 49, 277-282.
  18. Saadaoui K., Ben Hassen N. & Benrejeb M. (2015). Stabilizing time delay systems by PID controllers. 2nd Int. Conference on Automation, Control, Engineering and Computer Science, Proceedings of Engineering & Technology, ACECS, Sousse.
  19. Serban C. & Carp D. (2016). Optimization of container stowage in a yard block using a genetic algorithm. Studies in Informatics and Control, 25 (1), 123-130.
  20. Tan N., Kaya I., Yeroglu C. & Atherton D. P. (2006). Computation of stabilizing PI and PID controllers using the stabilizing boundary locus. Energy Conver-sion & Management, 47, 3045-3058.
  21. Wang H., Vasseur C., Koncar V., Chamroo A. & Christov N. (2010). Sampled tracking for delayed systems using two-time-scale sampled data cont-rollers. Studies in Informatics and Control, 19 (4), 339-346.
  22. Zhong, Q. C. (2006). Robust control of time delay systems.  Springer, London.