International Journal of Fuzzy Systems

, Volume 20, Issue 3, pp 803–816 | Cite as

Application of Single- and Multi-Objective Evolutionary Algorithms for Optimal Nonlinear Controller Design in Boiler–Turbine System

  • T. PiraisoodiEmail author
  • M. Willjuice Iruthayarajan
  • K. Mohaideen Abdul Kadhar


This paper presents an application of evolutionary algorithm techniques for optimal nonlinear controller design in drum-type boiler–turbine system. Designing of controller for third-order boiler–turbine system is always a complicated task due to the presence of highly interactive nonlinearities. The present work is the first one which attempts to design and implement recently developed finite time convergent controller in third-order boiler–turbine dynamics, and it is described as multi-input–multi-output (MIMO) nonlinear system. The present work explores the possibility of application of single-objective and multi-objective evolutionary algorithm techniques toward optimal tuning of finite time convergent controller to achieve the desired performance for third-order boiler–turbine system. The single-objective evolutionary algorithm techniques such as real-coded genetic algorithm (RGA), modified particle swarm optimization (MPSO), differential evolution (DE), and self-adaptive differential evolution (SADE) are implemented with the minimization of integral square error (ISE) as an objective to obtain optimal tuning parameters. Also, the present paper explores the possibility of simultaneous minimization of conflicting objectives such as ISE and computational cost of the proposed controller using multi-objective evolutionary algorithms such as non-dominated sorting genetic algorithm (NSGA) and modified non-dominated sorting genetic algorithm-II (MNSGA-II). The performance of the proposed optimal finite time convergent controller is validated by simulating different kinds of set point changes, and the obtained results are presented as various case studies. The adaptability of the proposed controller during parameter variations is also examined. The performance of the single-objective and multi-objective evolutionary algorithms has been statistically analyzed, and the results are reported. The results reveal that among the four single-objective EA techniques, SADE offers better performance due to its inherit self-adaptive capability. Also, during multi-objective optimization, MNSGA-II has provided better solution due the presence of dynamic crowding distance (DCD) and control elitism (CE) strategies.


Boiler–turbine system Finite time convergent controller Single-objective and multi-objective evolutionary algorithms Optimal tuning 


  1. 1.
    Wu, X., Shen, J., Li, Y., Lee, K.Y.: Hierarchical optimization of boiler–turbine unit using fuzzy stable model predictive control. Control Eng. Pract. 30, 112–123 (2014)CrossRefGoogle Scholar
  2. 2.
    Wu, J., Nguang, S.K., Shen, J., Liu, G., Li, Y.G.: Robust H tracking control of boiler–turbine sytems. ISA Trans. 49, 369–375 (2010)CrossRefGoogle Scholar
  3. 3.
    Sayed, M., Gharghory, S.M., Kamal, H.A.: Gain tuning PI controllers for boiler-turbine unit using a new hybrid jump PSO. J. Electr. Syst. Inf. Technol. 2, 99–110 (2015)Google Scholar
  4. 4.
    Chen, P.C.: Gain-scheduled l 1 optimal control for boiler–turbine dynamics with actuator saturation. J. Process Control 14, 263–277 (2004)CrossRefGoogle Scholar
  5. 5.
    Chen, P.C.: Multi-objective control of nonlinear boiler–turbine dynamics with actuator magnitude and rate constraints. ISA Trans. 52, 115–128 (2013)CrossRefGoogle Scholar
  6. 6.
    Ghabraei, S., Moradi, H., Vossoughi, G.: Multivariable robust adaptive sliding mode control of an industrial boiler–turbine in the presence of modeling imprecisions and external disturbances; A comparison with type-I servo controller. ISA Trans. 58, 398–408 (2015)CrossRefGoogle Scholar
  7. 7.
    Tan, W., Marquez, H.J., Chen, T., Liu, J.: Analysis and control of a nonlinear boiler–turbine unit. J. Process Control 15, 883–891 (2005)CrossRefGoogle Scholar
  8. 8.
    Moon, U.C., Lee, K.Y.: An adaptive dynamic matrix control with fuzzy-interpolated step-response model for a drum-type boiler–turbine system. IEEE Trans. Energy Convers. 26(2), 393–401 (2011)CrossRefGoogle Scholar
  9. 9.
    Wu, X., Shen, J., Li, Y., Lee, K.Y.: Data driven modeling and predictive control for boiler–turbine unit. IEEE Trans. Energy Convers. 28(3), 470–481 (2013)CrossRefGoogle Scholar
  10. 10.
    Jalali, A.A., Golmohammad, H.: An optimal multiple-model strategy to design a controller for nonlinear processes; A boiler–turbine unit. Comput. Chem. Eng. 46, 48–58 (2012)CrossRefGoogle Scholar
  11. 11.
    Wu, X., Shen, J., Li, Y., Lee, K.Y.: Fuzzy modeling and stable model predictive tracking control of large-scale power plants. J. Process Control 24, 1600–1626 (2014)Google Scholar
  12. 12.
    Yang, S., Qian, C.: Adaptive controller design for a nonlinear drum boiler–turbine system. IEEE International Conference on Control Applications, pp. 335–340 (2008)Google Scholar
  13. 13.
    Tanaka, M., Yamaguchi, K., Ogura, D., Chen, Y., Tanaka, K.: Nonlinear control of F16 air craft via multiple nonlinear model generation for any trimmed equilibriums. Int. J. Fuzzy Syst. 16, 140–152 (2014)Google Scholar
  14. 14.
    Lee, C.H., Hsueh, H.Y.: Observer based adaptive control for a class of nonlinear non-affine systems using recurrent type fuzzy logic systems. Int. J. Fuzzy Syst. 15, 55–65 (2013)MathSciNetGoogle Scholar
  15. 15.
    Li, Y., Tong, S.: Fuzzy adaptive backstepping decentralized control of switched nonlinear large scale systems with switching jumps. Int. J. Fuzzy Syst. 17, 12–21 (2015)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Qjan, C., Lin, W.: A continuous feedback approach to global strong stabilization of nonlinear systems. IEEE Trans. Autom. Control 46, 1061–1079 (2001)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Bhat, S.P., Bernstein, D.S.: Continuous finite-time stabilization of the translational and rotational double integrators. IEEE Trans. Autom. Control 43(5), 678–682 (1998)MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Hong, Y., Huang, J., Xu, Y.: On an output feedback finite-time stabilization problem. IEEE Trans. Autom. Control 46(2), 305–309 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Yang, S., Qian, C., Du, H.: A genuine nonlinear approach for controller design of a boiler–turbine system. ISA Trans. 51, 446–453 (2012)CrossRefGoogle Scholar
  20. 20.
    Moon, U.C., Lee, K.Y.: A boiler–turbine system control using a fuzzy auto-regressive moving average (FARMA) model. IEEE Trans. Energy Convers. 18(1), 142–148 (2003)CrossRefGoogle Scholar
  21. 21.
    Dimeo, R., Lee, K.Y.: Boiler–turbine control system design using a genetic algorithm. IEEE Trans. Energy Convers. 10(4), 752–759 (1995)CrossRefGoogle Scholar
  22. 22.
    Li, Y., Shen, J., Lee, K.Y., Liu, X.: Offset-free fuzzy model predictive control of a boiler–turbine system based on genetic algorithm. Sim. Model. Pract. Theory 26, 77–95 (2012)CrossRefGoogle Scholar
  23. 23.
    Moon, U.C., Lee, K.Y.: Step-response model development for dynamic matrix control of a drum-type boiler–turbine system. IEEE Trans. Energy Convers. 24(2), 423–430 (2009)CrossRefGoogle Scholar
  24. 24.
    Iruthayarajan, M.W., Baskar, S.: Evolutionary algorithms based design of multivariable PID controller. Expert Syst. Appl. 36, 9159–9167 (2009)CrossRefGoogle Scholar
  25. 25.
    Chuang, Y.C., Chen, C.T., Hwang, C.: A real coded genetic algorithm with a direction based cross over operator. Inf. Sci. 305, 320–348 (2015)CrossRefGoogle Scholar
  26. 26.
    Manikandan, S., Ramar, K., Iruthayarajan, M.W., Srinivasagan, K.G.: Multilevel thresholding for segmentation of medical brain images using real coded genetic algorithm. Measurement 47, 558–568 (2014)CrossRefGoogle Scholar
  27. 27.
    Gaing, Z.L.: A particle swarm optimization approach for optimum design of PID controller in AVR system. IEEE Trans. Energy Convers. 19(20), 384–391 (2004)CrossRefGoogle Scholar
  28. 28.
    Ghoshal, S.P.: Optimizations of PID gains by particle swarm optimizations in fuzzy based automatic generation control. Electr. Power Syst. Res. 72, 203–212 (2004)CrossRefGoogle Scholar
  29. 29.
    Mukherjee, V., Ghoshal, S.P.: Intelligent particle swarm optimized fuzzy PID controller for AVR system. Electr. Pow. Syst. Res. 77(12), 1689–1698 (2007)CrossRefGoogle Scholar
  30. 30.
    Tang, L., Zhao, Y., Liu, J.: An improved differential algorithm for practical dynamic scheduling in steel making-continuous casting production. IEEE Trans. Evol. Comput. 18, 209–225 (2014)CrossRefGoogle Scholar
  31. 31.
    Mohanty, B., Panda, S., Hota, P.K.: Controller parameters tuning of differential evolutionary algorithm and its application to load frequency control of multi-source power system. Int. J. Electr. Power Energy Syst. 54, 77–85 (2014)CrossRefGoogle Scholar
  32. 32.
    Qin, A.K., Suganthan, P.N.: Self-adaptive differential evolution algorithm for numerical optimization. IEEE Cong. Evol. Comput. 2, 1785–1791 (2005)Google Scholar
  33. 33.
    Elsayed, S., Sarker, R.A., Essam, D.L.: An improved self adaptive differential evolutionary algorithm for optimization problems. IEEE Trans. Industr. Inf. 9, 89–99 (2013)CrossRefGoogle Scholar
  34. 34.
    Fan, Q., Yan, X.: Self adaptive differential evolution with discrete mutation control parameters. Expert Syst. Appl. 42, 15551–15572 (2015)Google Scholar
  35. 35.
    Murugan, P., Kannan, S., Baskar, S.: NSGA-II algorithm for multi-objective generation expansion planning problem. Electr. Power Syst. Res. 79, 622–628 (2009)CrossRefGoogle Scholar
  36. 36.
    Murugan, P., Kannan, S., Baskar, S.: Application of NSGA-II algorithm to single-objective transmission constrained generation expansion planning. IEEE Trans. Power Syst. 24, 1790–1797 (2009)CrossRefGoogle Scholar
  37. 37.
    Dhanalakshmi, S., Kannan, S., Mahadevan, K., Baskar, S.: Applicaton of modified NSGA-II algorithm to combined economic and emission dispatch problem. Int. J. Electr. Power Energy Syst. 33, 992–1002 (2011)CrossRefGoogle Scholar
  38. 38.
    Ramesh, S., Kannan, S., Baskar, S.: Application of modified NSGA-II algorithm to multiobjective reactive power planning. Appl. Soft Comput. 12, 741–753 (2012)CrossRefGoogle Scholar
  39. 39.
    Jeyadevi, S., Baskar, S., Babulal, C.K., Iruthayarajan, M.W.: Solving multiobjective optimal reactive power dispatch using modified NSGA-II. Int. J. Electr. Power Energy Syst. 33, 219–228 (2011)CrossRefGoogle Scholar
  40. 40.
    Astrom, K.B., Bell, R.D.: Drum-boiler dynamics. Automatica 36, 363–378 (2000)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Taiwan Fuzzy Systems Association and Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  • T. Piraisoodi
    • 1
    Email author
  • M. Willjuice Iruthayarajan
    • 1
  • K. Mohaideen Abdul Kadhar
    • 1
  1. 1.National Engineering CollegeKovilpattiIndia

Personalised recommendations