Optimal Control Systems with Reduced Parametric Sensitivity Based on Particle Swarm Optimization and Simulated Annealing

  • Radu-Emil Precup
  • Radu-Codruţ David
  • Stefan Preitl
  • Emil M. Petriu
  • József K. Tar
Part of the Studies in Computational Intelligence book series (SCI, volume 366)


This chapter discusses theoretical and design aspects for optimal control systems with a reduced parametric sensitivity using Particle Swarm Optimization (PSO) and Simulated Annealing (SA) algorithms. Sensitivity models with respect to the parametric variations of the controlled process are derived and the optimal control problems are defined. The new objective functions in these optimization problems are integral quadratic performance indices that depend on the control error and squared output sensitivity functions. Different dynamic regimes are considered. Relatively simple PSO and SA optimization algorithms are developed for the minimization of the objective functions, which optimize the control system responses and reduce the sensitivity to parametric variations of the controlled process. Examples of optimization problems encountered in the design of optimal proportional-integral (PI) controllers for a class of second-order processes with integral component are used to validate the proposed methods.


Particle Swarm Optimization Simulated Annealing Particle Swarm Optimization Algorithm Fuzzy Controller Reference Input 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Rosenwasser, E., Yusupov, R.: Sensitivity of automatic control systems. CRC Press, Boca Raton (2000)zbMATHGoogle Scholar
  2. 2.
    Yaniv, O.: Design of low-order controllers satisfying sensitivity constraints for unstructured uncertain plants. Int. J. Robust Nonlinear Control 14, 1359–1370 (2004)MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Oded, T., Arkady, L.: Design of low order controllers satisfying sensitivity constraints for unstructured uncertain plants. In: Proceedings of 23rd IEEE Convention of Electrical and Electronics Engineers in Israel, Herzlia, Israel, pp. 33–36 (2004)Google Scholar
  4. 4.
    Shirao, J., Imai, J., Konishi, M.: Structure design with sensitivity control performance limitation for electromechanical systems. In: Proceedings of SICE-ICASE International Joint Conference SICE-ICCAS 2006, Busan, Korea, pp. 2362–2367 (2006)Google Scholar
  5. 5.
    Precup, R.E., Preitl, S., Korondi, P.: Fuzzy controllers with maximum sensitivity for servosystems. IEEE Trans. Ind. Electron 54, 1298–1310 (2007)CrossRefGoogle Scholar
  6. 6.
    Marchetti, G., Barolo, M., Jovanovic, L., Zisser, H., Seborg, D.E.: An improved PID switching control strategy for type 1 diabetes. IEEE Trans. Biomed. Eng. 55, 857–865 (2008)CrossRefGoogle Scholar
  7. 7.
    Wang, Y.G., Xu, X.M.: PID tuning for unstable processes with sensitivity specification. In: Proceedings of Chinese Control and Decision Conference CCDC 2009, Guilin, China, pp. 3460–3464 (2009)Google Scholar
  8. 8.
    Precup, R.E., Preitl, S.: Optimisation criteria in development of fuzzy controllers with dynamics. Eng. Appl. Artif. Intell. 17, 661–674 (2004)CrossRefGoogle Scholar
  9. 9.
    Köppen, M.: Light-weight evolutionary computation for complex image-processing applications. In: Proceedings of 6th International Conference on Hybrid Intelligent Systems HIS 2006, Auckland, New Zealand, pp. 3–3 (2006)Google Scholar
  10. 10.
    Zhou, H., Schaefer, G., Shi, C.: A mean shift based fuzzy c-means algorithm for image segmentation. In: Proceedings of 30th Annual International Conference of the IEEE Engineering in Medicine and Biology Society EMBC 2008, Vancouver, BC, Canada, pp. 3091–3094 (2008)Google Scholar
  11. 11.
    Schaefer, G., Nakashima, T., Zavisek, M.: Analysis of breast thermograms based on statistical image features and hybrid fuzzy classification. In: Bebis, G., Boyle, R., Parvin, B., Koracin, D., Remagnino, P., Porikli, F., Peters, J., Klosowski, J., Arns, L., Chun, Y.K., Rhyne, T.-M., Monroe, L. (eds.) ISVC 2008, Part I. LNCS, vol. 5358, pp. 753–762. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  12. 12.
    Abraham, A., Corchado, E., Corchado, J.M.: Hybrid learning machines. Neurocomputing 72, 2729–2730 (2009)CrossRefGoogle Scholar
  13. 13.
    Precup, R.E., Preitl, S.: On the stability and sensitivity analysis of fuzzy control systems for servo-systems. In: Nedjah, N., de Macedo Mourelle, L. (eds.) Fuzzy Systems Engineering, Theory and Practice, pp. 131–161. Springer, Heidelberg (2005)Google Scholar
  14. 14.
    Ekel, P.Y., Menezes, M., Schuffner Neto, F.H.: Decision making in a fuzzy environment and its application to multicriteria power engineering problems. Nonlinear Analysis: Hybrid Syst. 1, 527–536 (2007)MathSciNetzbMATHCrossRefGoogle Scholar
  15. 15.
    Xu, J., Wu, H., Wang, Y.: Unpower aerocraft augmented state feedback tracking guaranteed cost control. J. Syst. Eng. Electron 19, 125–130 (2008)zbMATHGoogle Scholar
  16. 16.
    Fmmo, C., Calado, JMF.: Approaches to human arm movement control - A review. Annu Rev Control 33, 69–77 (2009)CrossRefGoogle Scholar
  17. 17.
    Chen, J., Kong, C.K.: Performance assessment for iterative learning control of batch units. J. Process Control 19, 1043–1053 (2009)CrossRefGoogle Scholar
  18. 18.
    Kim, D.H., Abraham, A., Cho, J.H.: A hybrid genetic algorithm and bacterial foraging approach for global optimization. Inf. Sci. 177, 3918–3937 (2007)CrossRefGoogle Scholar
  19. 19.
    Nolle, L.: On a novel ACO-estimator and its application to the target motion analysis problem. Knowl-Based Syst. 21, 225–231 (2008)CrossRefGoogle Scholar
  20. 20.
    Köppen, M., Kinoshita, Y., Yoshida, K.: Auxiliary objectives for the evolutionary multi-objective principal color extraction from logo images. In: Proceedings of IEEE Congress on Evolutionary Computation CEC 2008, Hong Kong, China, pp. 3537–3544 (2008)Google Scholar
  21. 21.
    Plant, W.R., Schaefer, G., Nakashima, T.: An overview of genetic algorithms in simulation soccer. In: Proceedings of IEEE Congress on Evolutionary Computation CEC 2008, Hong Kong, China, pp. 3897–3904 (2008)Google Scholar
  22. 22.
    Kennedy, J., Eberhart, R.C.: Particle swarm optimization. In: Proceedings of IEEE International Conference on Neural Networks ICNN 1995, Perth, Australia, pp. 1942–1948 (1995)Google Scholar
  23. 23.
    Kennedy, J., Eberhart, R.C.: A new optimizer using particle swarm theory. In: Proceedings of 6th International Symposium on Micro Machine and Human Science MHS 1995, Nagoya, Japan, pp. 39–43 (1995)Google Scholar
  24. 24.
    Kirkpatrick, S., Gelatt Jr., C.D., Vecchi, M.P.: Optimization by simulated annealing. Science 20, 671–680 (1983)MathSciNetCrossRefGoogle Scholar
  25. 25.
    Geman, S., Geman, D.: Stochastic relaxation, Gibbs distribution and the Bayesian restoration in images. IEEE Trans. Pattern Anal. Mach. Intell. 6, 721–741 (1984)zbMATHCrossRefGoogle Scholar
  26. 26.
    Kalai, A.T., Vempala, S.: Simulated annealing for convex optimization. Math. Oper. Res. 31, 253–266 (2006)MathSciNetzbMATHCrossRefGoogle Scholar
  27. 27.
    Ledesma, S., Torres, M., Hernández, D., Aviña, G., García, G.: Temperature cycling on simulated annealing for neural network learning. In: Gelbukh, A., Kuri Morales, Á.F. (eds.) MICAI 2007. LNCS (LNAI), vol. 4827, pp. 161–171. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  28. 28.
    David, R.C., Rădac, M.B., Preitl, S., Tar, J.K.: Particle swarm optimization-based design of control systems with reduced sensitivity. In: Proceedings of 5th International Symposium on Applied Computational Intelligence and Informatics SACI 2009, Timisoara, Romania, pp. 491–496 (2009)Google Scholar
  29. 29.
    Kim, T.H., Maruta, I., Sugie, T.: Robust PID controller tuning based on the constrained particle swarm optimization. Automatica 44, 1104–1110 (2008)MathSciNetCrossRefGoogle Scholar
  30. 30.
    Lin, C.M., Lin, M.H., Chen, C.H., Yeung, D.S.: Robust PID control system design for chaotic systems using particle swarm optimization algorithm. In: Proceedings of 2009 International Conference on Machine Learning and Cybernetics ICMLC, Baoding, China, vol. 6, pp. 3294–3299 (2009)Google Scholar
  31. 31.
    Fang, H., Chen, L.: Application of an enhanced PSO algorithm to optimal tuning of PID gains. In: Proceedings of Chinese Control and Decision Conference CCDC 2009, Guilin, China, pp. 35–39 (2009)Google Scholar
  32. 32.
    Su, C., Wu, Y.: Adaptive neural network predictive control based on PSO algorithm. In: Proceedings of Chinese Control and Decision Conference CCDC 2009, Guilin, China, pp. 5829–5833 (2009)Google Scholar
  33. 33.
    Mukherjee, V., Ghoshal, S.P.: Intelligent particle swarm optimized fuzzy PID controller for AVR system. Electr. Power Syst. Res. 77, 1689–1698 (2007)CrossRefGoogle Scholar
  34. 34.
    Mohan Rao, A.R., Sivasubramanian, K.: Multi-objective optimal design of fuzzy logic controller using a self configurable swarm intelligence algorithm. Comput. Struct. 86, 2141–2154 (2008)CrossRefGoogle Scholar
  35. 35.
    Tang, H.Y., Ding, B., Qi, W.G.: Research on traffic mode of elevator applied fuzzy C-mean clustering algorithm based on PSO. In: Proceedings of International Conference on Measuring Technology and Mechatronics Automation ICMTMA 2009, Zhangjiajie, China, vol. 2, pp. 582–585 (2009)Google Scholar
  36. 36.
    Veenhuis, C., Köppen, M., Vicente-Garcia, R.: Evolutionary multi-objective optimization of particle swarm optimizers. In: Proceedings of IEEE Congress on Evolutionary Computation CEC 2007, Singapore, pp. 2273–2280 (2007)Google Scholar
  37. 37.
    Das, S., Abraham, A., Konar, A.: Automatic kernel clustering with a multi-elitist particle swarm optimization algorithm. Pattern Recognit. Lett. 29, 688–699 (2008)CrossRefGoogle Scholar
  38. 38.
    Shayeghi, H., Shayanfar, H.A., Jalili, A.: Load frequency control strategies: a state-of-the-art survey for the researcher. Energy Convers Manag. 50, 344–353 (2009)CrossRefGoogle Scholar
  39. 39.
    Sabat, S.L., dos Santos Coelho, L., Abraham, A.: MESFET DC model parameter extraction using quantum particle swarm optimization. Microelectron Reliab. 49, 660–666 (2009)CrossRefGoogle Scholar
  40. 40.
    Liang, X.R., Fan, Y.K., Jiang, T.: Application of PSO algorithm to coordinated ramp control. In: Proceedings of 2009 International Conference on Machine Learning and Cybernetics ICMLC, Baoding, China, vol. 3, pp. 1712–1716 (2009)Google Scholar
  41. 41.
    Zhang, Y., Hu, Y.: On PID controllers based on simulated annealing algorithm. In: Proceedings of 27th Chinese Control Conference CCC 2008, Kunming, China, pp. 225–228 (2008)Google Scholar
  42. 42.
    Cao, X.R.: Stochastic learning and optimization - A sensitivity-based approach. Annu. Rev. Control 33, 11–24 (2009)CrossRefGoogle Scholar
  43. 43.
    Qiu, X.Z., Xu, Z.G., Zhang, L.M., Zhou, J.X., Si, F.Q.: Nonlinear predictive control on the load system of a thermal power unit based on AOSVR and SAPSO. In: Proceedings of Asia-Pacific Power and Energy Engineering Conference APPEEC 2009, Wuhan, China, p. 4 (2009)Google Scholar
  44. 44.
    Wu, M., Xu, C.H., She, J.H., Yokoyama, R.: Intelligent integrated optimization and control system for lead-zinc sintering process. Control Eng. Pract. 17, 280–290 (2009)CrossRefGoogle Scholar
  45. 45.
    Haber, R.E., Haber-Haber, R., Jiménez, A., Galán, R.: An optimal fuzzy control system in a network environment based on simulated annealing. An application to a drilling process, Appl. Soft Comput. 9, 889–895 (2009)Google Scholar
  46. 46.
    Buyamin, S., Finch, J.W.: Comparative study on optimising the EKF for speed estimation of an induction motor using simulated annealing and genetic algorithm. In: Proceedings of IEEE International Electric Machines & Drives Conference IEMDC 2007, Antalya, Turkey, vol. 2, pp. 1689–1694 (2007)Google Scholar
  47. 47.
    Sayol, J., Nolle, L., Schaefer, G., Nakashima, T.: Comparison of simulated annealing and SASS for parameter estimation of biochemical networks. In: Proceedings of IEEE Congress on Evolutionary Computation CEC 2008, Hong Kong, China, pp. 3568–3571 (2008)Google Scholar
  48. 48.
    Qin, X.S., Huang, G.H., He, L.: Simulation and optimization technologies for petroleum waste management and remediation process control. J. Environ. Manag. 90, 54–76 (2009)CrossRefGoogle Scholar
  49. 49.
    Åström, K.J., Hägglund, T.: PID controllers theory: design and tuning. Instrument Society of America, Research Triangle Park, NC (1995)Google Scholar
  50. 50.
    Preitl, S., Precup, R.E.: An extension of tuning relations after symmetrical optimum method for PI and PID controllers. Automatica 35, 1731–1736 (1999)zbMATHCrossRefGoogle Scholar
  51. 51.
    Abonyi, J.: Fuzzy model identification for control. Birkhäuser, Boston (2003)zbMATHGoogle Scholar
  52. 52.
    Itagaki, N., Nishimura, H., Takagi, K.: Two-degree-of-freedom control system design in consideration of actuator saturation. IEEE/ASME Trans. Mechatronics 13, 470–475 (2008)CrossRefGoogle Scholar
  53. 53.
    Precup, R.E., Preitl, S.: PI and PID controllers tuning for integral-type servo systems to ensure robust stability and controller robustness. Electrical Eng (Archiv für Elektrotechnik) 88, 149–156 (2006)CrossRefGoogle Scholar
  54. 54.
    del Valle, Y., Venayagamoorthy, G.K., Mohagheghi, S., Hernandez, J.C., Harley, R.G.: Particle swarm optimization: Basic concepts, variants and applications in power systems. IEEE Trans. Evol. Comput. 12, 171–195 (2008)CrossRefGoogle Scholar
  55. 55.
    Khanesar, M.A., Tavakoli, H., Teshnehlab, M., Shoorehdeli, M.A.: A novel binary particle swarm optimization. In: Proceedings of Mediterranean Conference on Control & Automation MED 2007, Athens, Greece, p. 6 (2007)Google Scholar
  56. 56.
    Kessler, C.: Das symmetrische Optimum. Teil I. Regelungstechnik 6, 395–400 (1955)Google Scholar
  57. 57.
    Kessler, C.: Das symmetrische Optimum. Teil II. Regelungstechnik 6, 432–436 (1955)Google Scholar
  58. 58.
    Horváth, L., Rudas, I.J.: Modeling and problem solving methods for engineers. Academic Press, Elsevier, Burlington, MA (2004)Google Scholar
  59. 59.
    Johanyák, Z.C., Kovács, S.: Sparse fuzzy system generation by rule base extension. In: Proceedings of 11th International Conference on Intelligent Engineering Systems INES 2007, Budapest, Hungary, pp. 99–104 (2007)Google Scholar
  60. 60.
    Vaščák, J.: Fuzzy cognitive maps in path planning. Acta Tech. Jaurinensis Ser. Intell. Comput. 1, 467–479 (2008)Google Scholar
  61. 61.
    Klančar, G., Matko, D., Blažič, S.: Wheeled mobile robots control in a linear platoon. J. Intell. Robotic Syst. 54, 709–731 (2009)CrossRefGoogle Scholar
  62. 62.
    Chiou, J.S., Liu, M.T.: Numerical simulation for fuzzy-PID controllers and helping EP reproduction with PSO hybrid algorithm. Simul Modell Pract. Theory 17, 1555–1565 (2009)CrossRefGoogle Scholar
  63. 63.
    Liu, K., Tan, Y., He, X.: An adaptive staged PSO based on particles’ search capabilities. In: Tan, Y., Shi, Y., Tan, K.C. (eds.) ICSI 2010. LNCS, vol. 6145, pp. 52–59. Springer, Heidelberg (2010)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Radu-Emil Precup
    • 1
  • Radu-Codruţ David
    • 1
  • Stefan Preitl
    • 1
  • Emil M. Petriu
    • 2
  • József K. Tar
    • 3
  1. 1.Department of Automation and Applied Informatics“Politehnica” University of TimisoaraTimisoaraRomania
  2. 2.School of Information Technology and EngineeringUniversity of OttawaOttawaCanada
  3. 3.Institute of Intelligent Engineering SystemsÓbuda UniversityBudapestHungary

Personalised recommendations