, 43:41 | Cite as

Reduced order modelling and predictive control of multivariable nonlinear process

  • Anuj Abraham
  • N Pappa
  • Daniel Honc
  • Rahul Sharma


In this paper, an efficient model-predictive control strategy that can be applied to complex multivariable process is presented. A reduced order generalized predictive algorithm is proposed for online applications with reduction in complexity and time elapsed. The complex multivariable process considered in this work is a binary distillation column. The reduced order model is developed with a recently proposed hybrid algorithm known as Clustering Dominant Pole Algorithm and is able to compute the full set of dominant poles and their cluster centre efficiently. The controller calculates the optimal control action based on the future reference signals, current state and constraints on manipulated and controlled variables for a high-order dynamic simulated model of nonlinear multivariable binary distillation column process. The predictive control algorithm uses controlled auto-regressive integrated moving average model. The performance of constraint generalized predictive control scheme is found to be superior to that of the conventional PID controller in terms of overshoot, settling time and performance indices, mainly ISE, IAE and MSE.


Predictive control distillation column reduced order model dominant pole clustering 


  1. 1.
    Honc D, Sharma R, Abraham A, Dušek F and Pappa N 2016 Teaching and practicing model predictive control. In: Proceedings of the 11th IFAC Symposium on Advances in Control Education (ACE), Bratislava-Slovakia, IFAC-PapersOnline 49(6): 34–39Google Scholar
  2. 2.
    Mahfouf M and Linkens D A 1997 Constrained multivariable generalized predictive control (GPC) for anaesthesia: the quadratic-programming approach (QP). Int. J. Contr. 67(4): 507–528MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Wilkinson D J, Morris A J and Tham M T 1994 Multivariable constrained predictive control (with application to high performance distillation). Int. J. Contr. 59: 841–862CrossRefzbMATHGoogle Scholar
  4. 4.
    Scokaert P O M and Clarke D W 1994 Stabilizing properties of constrained predictive control. Proc. Inst. Electr. Eng. 141: 295–304zbMATHGoogle Scholar
  5. 5.
    Clarke D W, Mohtadi C and Tuffs P S 1987 Generalized predictive control, part I: the basic algorithm. Automatica 23: 137–148CrossRefzbMATHGoogle Scholar
  6. 6.
    Clarke D W, Mohtadi C and Tuffs P S 1987 Generalized predictive control, part II: extensions and interpretations. Automatica 23: 149–160CrossRefzbMATHGoogle Scholar
  7. 7.
    Aguirre L A 1993 Quantitative measure of modal dominance for continuous systems. In: Proceedings of the 32nd Conference on Decision and Control, pp. 2405–2410Google Scholar
  8. 8.
    Nagar S K and Singh S K 2004 An algorithmic approach for system decomposition and balanced realized model reduction. J. Franklin Inst. 341: 615–630MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Martins N, Pinto H J C P and Lima L T G 1992 Efficient methods for finding transfer function zeros of power systems. IEEE Trans. Power Syst. 7(3): 1350–1361CrossRefGoogle Scholar
  10. 10.
    Abraham A, Pappa N, Honc D and Sharma R 2015 A hybrid method for determination of effective poles using Clustering Dominant Pole Algorithm. Int. J. Math. Comput. Nat. Phys. Eng. 7(3): 102–106Google Scholar
  11. 11.
    Martins N, Lima L T G and Pinto H J C P 1996 Computing dominant poles of power system transfer functions. IEEE Trans. Power Syst. 11(1): 162–170CrossRefGoogle Scholar
  12. 12.
    Minh V T and Pumwa J 2012 Modeling and adaptive control simulation for a distillation column. In: Proceedings of the 2012 UKSim, 14 th International Conference on Modelling and Simulation, pp. 61–65Google Scholar
  13. 13.
    Minh V T and Abdul Rani M 2009 Modelling and control of distillation column in a petroleum process. Math. Probl. Eng. 2009: 404702CrossRefzbMATHGoogle Scholar
  14. 14.
    Ogunnaike B A and Ray W H 1994 Process dynamics modeling and control. New York: Oxford University PressGoogle Scholar
  15. 15.
    Petro Vietnam Gas Company 2009 Condensate processing plant project—process description. Tech. Rep. 82036-02BM-01. Washington, USA: Petro VietnamGoogle Scholar
  16. 16.
    Mittal A K, Prasad R and Sharma S P 2004 Reduction of linear dynamic systems using an error minimization technique. J. Inst. Eng. India 84: 201–206Google Scholar
  17. 17.
    Rommes J and Martins N 2008 Computing transfer function dominant poles of large second-order dynamical systems. SIAM J. Sci. Comput. 30(4): 2137–2157MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Parmar G, Mukherjee S and Prasad R 2007 System reduction using factor division algorithm and eigen spectrum analysis. Int. J. Appl. Math. Model. 31: 2542–2552CrossRefzbMATHGoogle Scholar
  19. 19.
    Rommes J and Martins N 2006 Efficient computation of transfer function dominant poles using subspace acceleration. IEEE Trans. Power Syst. 21(3): 1218–1226CrossRefGoogle Scholar
  20. 20.
    Antoulas A C and Sorensen D C 2001 Approximation of large-scale dynamical systems: an overview. Int. J. Appl. Math. Comput. Sci. 11(5): 1093–1121MathSciNetzbMATHGoogle Scholar
  21. 21.
    Kumar V and Tiwari J P 2012 Order reducing of linear system using clustering method factor division algorithm. Int. J. Appl. Inf. Syst. 3(5): 1–4Google Scholar
  22. 22.
    Aguilera-González A, Astorga-Zaragoza C M, Adam-Medina M, Theilliol D, Reyes-Reyes J and García-Beltrán C D 2013 Singular linear parameter-varying observer for composition estimation in a binary distillation column. IET Control Theory Appl. 7(3): 411–422MathSciNetCrossRefGoogle Scholar
  23. 23.
    Mishra R K, Khalkho R and Rajesh Kumar B 2013 Effect of tuning parameters of a model predictive binary distillation column. In: Proceedings of the IEEE International Conference on Emerging Trends in Computing, pp. 660–665Google Scholar
  24. 24.
    Yang J S 2005 Optimization-based PI/PID control for a binary distillation column. In: Proceedings of the American Control Conference, pp. 3650–3655Google Scholar
  25. 25.
    Camacho E F 1993 Constrained generalized predictive control. IEEE Trans. Automat. Contr. 38(2): 327–332MathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    Ansarpanahi S, Noor S B M and Marhaban M H 2008 Stability study of model predictive control in presence of undesirable factors. J. Appl. Sci. 8(20): 3683–3689CrossRefGoogle Scholar
  27. 27.
    Holkar K S and Waghmare L M 2010 An overview of model predictive control. Int. J. Contr. Automat. 3(4): 47–63Google Scholar
  28. 28.
    Abraham A, Pappa N, Shanmugha Priya M and Hexy M 2017 Predictive control design for a MIMO multivariable process using order reduction techniques. Int. J. Model. Simul. 37(4): 199–207CrossRefGoogle Scholar
  29. 29.
    Wayne Bequette B 2012 Process control modeling, design and simulation. India: Prentice HallGoogle Scholar
  30. 30.
    Clarke D W and Scattolini R 1991 Constrained receding-horizon predictive control. Proc. Inst. Electr. Eng. 138: 347–354zbMATHGoogle Scholar
  31. 31.
    Tsang T T C and Clarke D W 1998 Generalized predictive control with input constraints. Proc. Inst. Electr. Eng. 35(6): 451–460zbMATHGoogle Scholar

Copyright information

© Indian Academy of Sciences 2018

Authors and Affiliations

  • Anuj Abraham
    • 1
  • N Pappa
    • 2
  • Daniel Honc
    • 3
  • Rahul Sharma
    • 4
  1. 1.Department of Applied Electronics & Instrumentation, Rajagiri School of Engineering & TechnologyAPJ Abdul Kalam Technological UniversityKeralaIndia
  2. 2.Department of Instrumentation Engineering, Madras Institute of Technology CampusAnna UniversityChennaiIndia
  3. 3.Department of Process Control, Faculty of Electrical Engineering and InformaticsUniversity of PardubicePardubiceCzech Republic
  4. 4.Department of Electrical and Electronics Engineering, Amrita School of EngineeringAmrita UniversityCoimbatoreIndia

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