Model-based Control

  • Fabrizio Caccavale
  • Mario Iamarino
  • Francesco Pierri
  • Vincenzo Tufano
Part of the Advances in Industrial Control book series (AIC)


This chapter is focused on the temperature control of chemical batch reactors. First, a general overview on control of chemical processes is provided. Then, a model-based control scheme, based on a combination of an adaptive nonlinear observer and an adaptive cascade control, is presented, and its stability properties are rigorously analyzed. Also, model-free variants of the controller–observer scheme are discussed. Finally, a case study, based on the phenol–formaldehyde reaction introduced in the Chap.  2, is developed in order to test the adaptive model-based approach and compare its performance with those obtained by adopting model-free approaches and classical linear PID controllers.


Tracking Error Extend Kalman Filter Model Predictive Control Positive Gain Adaptive Observer 
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.

List of Principal Symbols


phenol (reduced model)


vector defined in (5.18)


matrix defined in (5.16)


scalar quantity defined in (5.22) [K s−1]


matrix defined in (5.28)


matrix defined in (5.17)


matrix defined in (5.18)


vector defined in (5.19)


vector defined in (5.19)


mass heat capacity [J kg−1 K−1]


concentration [mol]


matrix defined in (5.21)


error vector between desired and measured output [K]

f, g, h

functions defining the nonlinear state space model (5.5)


controller gain


molar enthalpy change of reaction [J mol−1]


reaction intermediate (reduced model)


m×n identity matrix


rate constant


scalar gains of the observers


matrix gains of the observers


positive definite matrix defined in (5.43)


number of compounds involved in the reaction


number of time steps


number of radial basis functions


m×n null matrix


desired product (reduced model)


positive definite matrix defined in (5.42)


heat transfer area [m2]


time [s]


temperature [K]


temperature of the fluid entering the jacket [K]


sampling time [s]


control input variable


overall heat transfer coefficient [J m−2 K−1 s−1]


vector of control input variables


transformed input in (5.6)


volume [m3]


vector of state variables


measured output variable


vector of measured output variables


Euclidean norm

Greek Symbols


parameters defined in (5.20)


parameter defined in (5.19)


gain setting the parameter estimate update rate


error vector defined in (5.41)


parameter US


vector of unknown parameters defined in (5.32)


centroid of an RBF


eigenvalue of a matrix


vector defined in (5.28)


density [kg m−3]


interpolation error of the RBFI


stoichiometric coefficient

φx, φv

nonlinear functions in (5.6)


vector radial basis functions defined in (5.32)


vector defined in (5.41)


vector defined in (5.20)


vector defined in (5.48)


width of an RBF

Subscripts and Superscripts




derivative term (PID)




energy balance




integral term (PID)




mass balance


maximum value


minimum value




proportional term (PID)






initial conditions

\(\;\widehat{\ }\)


\(\;\widetilde{\ }\)

estimation error


  1. 1.
    P.S. Agachi, Z.K. Nagy, M.V. Cristea, and A. Imre-Lucaci. Model Based Control. Case Studies in Process Engineering. Wiley-VCH, Weinheim, 2006. CrossRefGoogle Scholar
  2. 2.
    M. Agarwal. Combining neural and conventional paradigms for modeling, prediction and control. International Journal of Systems Science, 28:65–81, 1997. CrossRefMATHGoogle Scholar
  3. 3.
    A. Altınten, F. Ketevanlioğlu, S. Erdoğan, H. Hapoğlu, and M. Alpbaz. Self-tuning PID control of jacketed batch polystyrene reactor using genetic algorithm. Chemical Engineering Journal, 138:490–497, 2008. CrossRefGoogle Scholar
  4. 4.
    J. Alvarez-Ramirez and J. Alvarez. Robust temperature control for batch chemical reactors. Chemical Engineering Science, 60:7108–7120, 2005. CrossRefGoogle Scholar
  5. 5.
    K.J. Aström and B. Wittenmark. Adaptive Control, 2nd Edition. Addison-Wesley, Reading, 1995. MATHGoogle Scholar
  6. 6.
    N. Aziz, M.A. Hussain, and I.M. Mujtaba. Performance of different types of controllers in tracking optimal temperature profiles in batch reactors. Computers and Chemical Engineering, 24:1069–1075, 2000. CrossRefGoogle Scholar
  7. 7.
    J.B. Balchen, B. Lie, and I. Solberg. Internal decoupling in nonlinear process control. Modeling Identification and Control, 9:137–148, 1988. MathSciNetCrossRefGoogle Scholar
  8. 8.
    R.D. Bartusiak, C. Georgakis, and M.J. Reilly. Nonlinear feedforward/feedback control structures designed by reference synthesis. Chemical Engineering Science, 44:1837–1851, 1989. CrossRefGoogle Scholar
  9. 9.
    V.M. Becerra, P.D. Roberts, and G.W. Griffiths. Applying the extended Kalman filter to systems described by nonlinear differential-algebraic equations. Control Engineering Practice, 9:267–281, 2001. CrossRefGoogle Scholar
  10. 10.
    M.A. Beyer, W. Grote, and G. Reinig. Adaptive exact linearization control of batch polymerization reactors using a Sigma-Point Kalman filter. Journal of Process Control, 18:663–675, 2008. CrossRefGoogle Scholar
  11. 11.
    N.V. Bhat and T.J. McAvoy. Use of neural nets for dynamic modelling and control of chemical process systems. Computers and Chemical Engineering, 14:583–599, 1990. CrossRefGoogle Scholar
  12. 12.
    S.P. Bhattacharyya, A. Datta, and L.H. Keel. Linear Control Theory. CRC Press, Boca Raton, 2009. Google Scholar
  13. 13.
    D. Bonvin, P. de Valliére, and D.W.T. Rippin. Application of estimation techniques to batch reactors. I. Modelling thermal effects. Computers and Chemical Engineering, 13:1–9, 1989. CrossRefGoogle Scholar
  14. 14.
    M.W. Brown, P.L. Lee, G.R. Sullivan, and W. Zhou. A constrained nonlinear multivariable control algorithm. Transactions IChemE, 68:464–476, 1990. Google Scholar
  15. 15.
    F. Caccavale, M. Iamarino, F. Pierri, and V. Tufano. An adaptive controller-observer scheme for temperature control of non-chain reactions in batch reactors. International Journal of Adaptive Control and Signal Processing, 22:627–651, 2008. MathSciNetCrossRefMATHGoogle Scholar
  16. 16.
    F. Caccavale, F. Pierri, and L. Villani. An adaptive observer for fault diagnosis in nonlinear discrete-time systems. ASME Journal of Dynamic Systems, Measurement and Control, 130:1–9, 2008. CrossRefGoogle Scholar
  17. 17.
    F. Cameron and D.E. Seborg. A self-tuning controller with a PID structure. International Journal of Control, 38:401, 1983. CrossRefMATHGoogle Scholar
  18. 18.
    T. Clark-Pringle and J.F. MacGregor. Nonlinear adaptive temperature of multi-product semi-batch polimerization reactors. Computers and Chemical Engineering, 21:1395–1405, 1997. CrossRefGoogle Scholar
  19. 19.
    D.W. Clarke and C. Mohtadi. Properties of generalized predictive control. Automatica, 25:859–875, 1989. MathSciNetCrossRefMATHGoogle Scholar
  20. 20.
    D.W. Clarke, C. Mohtadi, and P.S. Tuffs. Generalized predictive control—Part I. The basic algorithm. Automatica, 23:137–148, 1987. CrossRefMATHGoogle Scholar
  21. 21.
    D.W. Clarke, C. Mohtadi, and P.S. Tuffs. Generalized predictive control—Part II. Extensions and interpretations. Automatica, 23:149–160, 1987. CrossRefMATHGoogle Scholar
  22. 22.
    B.J. Cott and S. Macchietto. Temperature control of exothermic batch reactors using generic model control (GMC). Industrial & Engineering Chemistry Research, 28:1177–1184, 1989. CrossRefGoogle Scholar
  23. 23.
    J.R. Cutler and B.L. Ramaker. Dynamic matrix control—a computer control algorithm. In Proceedings of the Joint Automatic Control Conference, 1980. Google Scholar
  24. 24.
    M. Farza, K. Busawon, and H. Hammouri. Simple nonlinear observers for on-line estimation of kinetic rates in bioreactors. Automatica, 34:301–318, 1998. MathSciNetCrossRefMATHGoogle Scholar
  25. 25.
    C. Filippi, J.L. Greffe, J. Bordet, J. Villermaux, J.L. Barnay, B. Ponte, and C. Georgakis. Tendency modeling of semi-batch reactors for optimization and control. Chemical Engineering Science, 41:913–920, 1986. CrossRefGoogle Scholar
  26. 26.
    K. Funahashi. On the approximate realization of continuous mappings by neural networks. Neural Networks, 2:183–192, 1989. CrossRefGoogle Scholar
  27. 27.
    B. Guo, A. Jiang, X. Hua, and A. Jutan. Nonlinear adaptive control for multivariable chemical processes. Chemical Engineering Science, 56:6781–6791, 2001. CrossRefGoogle Scholar
  28. 28.
    S. Haykin. Neural Networks: A Comprehensive Foundation. Prentice Hall, Upper Saddle River, 1998. Google Scholar
  29. 29.
    M.A. Henson and D.E. Seborg. An internal model control strategy for nonlinear systems. AIChE Journal, 37:1065–1081, 1991. MathSciNetCrossRefGoogle Scholar
  30. 30.
    M.A. Henson and D.E. Seborg. Adaptive nonlinear control of ph neutralization process. IEEE Transactions on Control Systems Technology, 2:169–179, 1994. CrossRefGoogle Scholar
  31. 31.
    M.A. Henson and D.E. Seborg. Nonlinear Process Control. Prentice Hall, Upper Saddle River, 1997. Google Scholar
  32. 32.
    G. Karer, I. Škrjanc, and B. Zupančič. Self-adaptive predictive functional control of the temperature in an exothermic batch reactor. Chemical Engineering & Processing: Process Intensification, 47:2379–2385, 2008. CrossRefGoogle Scholar
  33. 33.
    E. Katende and A. Jutan. A new constrained self-tuning PID controller. The Canadian Journal of Chemical Engineering, 71:625–633, 1993. CrossRefGoogle Scholar
  34. 34.
    E. Katende and A. Jutan. Nonlinear predictive control of complex processes. Industrial and Engineering Chemistry, 35:2721–2728, 1996. Google Scholar
  35. 35.
    H.K. Khalil. Nonlinear Systems, 2nd Edition. Prentice Hall, Upper Saddle River, 1996. Google Scholar
  36. 36.
    K. Konakom, P. Kittisupakorn, and I.M. Mujtaba. Batch control improvement by model predictive control based on multiple reduced-models. Chemical Engineering Journal, 145:129–134, 2008. CrossRefGoogle Scholar
  37. 37.
    C. Kravaris and C.B. Chung. Nonlinear state feedback synthesis by global input–output linearization. AIChE Journal, 33:592–603, 1987. MathSciNetCrossRefGoogle Scholar
  38. 38.
    J.H. Lee, M. Morari, and C.E. Garcia. State-space interpretation of model predictive control. Automatica, 30:707–717, 1994. MathSciNetCrossRefMATHGoogle Scholar
  39. 39.
    K.S. Lee and J.H. Lee. Model predictive control for non linear batch processes with asymptotically perfect tracking. Computers and Chemical Engineering, 21:873–879, 1997. Google Scholar
  40. 40.
    P.L. Lee and R.B. Newell. Generic model control—a case study. Canadian Journal of Chemical Engineering, 67:478–483, 1989. CrossRefGoogle Scholar
  41. 41.
    P.L. Lee and G.R. Sullivan. Generic model control. Computers and Chemical Engineering, 12:573–580, 1988. CrossRefGoogle Scholar
  42. 42.
    P.L. Lee and W. Zhou. A new multivariable deadtime control algorithm. Chemical Engineering Communications, 91(1):49–63, 1990. MathSciNetCrossRefGoogle Scholar
  43. 43.
    S. Li, K.J. Lim, and D.G. Fisher. A state-space formulation of model predictive control. AlChE Journal, 35:241–249, 1989. CrossRefGoogle Scholar
  44. 44.
    L. Ljung, J. Sjoberg, and H. Hjalmarsson. On neural networks model structures in system identification. In S. Bittanti and G. Picci, editors, Identification, Adaptation, Learning, pages 366–393. Springer, Berlin, 1996. CrossRefGoogle Scholar
  45. 45.
    R. Luus and O.N. Okongwu. Towards practical optimal control of batch reactors. Chemical Engineering Journal, 75:1–9, 1999. CrossRefGoogle Scholar
  46. 46.
    L. Magni, D.M. Raimondo, and F. Allgöwer, editors, Nonlinear Model Predictive Control. Springer, Berlin, 2009. MATHGoogle Scholar
  47. 47.
    I.M. Mujtaba, N. Aziz, and M.A. Hussain. Neural network based modelling and control in batch reactor. Chemical Engineering Research and Design, 84:635–644, 2006. CrossRefGoogle Scholar
  48. 48.
    Z.K. Nagy and R.D. Braatz. Robust nonlinear model predictive control of batch processes. AIChE Journal, 49:1776–1786, 2003. CrossRefGoogle Scholar
  49. 49.
    A.A. Patwardhan, J.B. Rawlings, and T.F. Edgar. Nonlinear model predictive control. Chemical Engineering Communications, 87:1–23, 1990. CrossRefGoogle Scholar
  50. 50.
    I. Pektas. High-temperature degradation of reinforced phenolic insulator. Journal of Applied Polymer Science, 67:1877–1883, 1998. CrossRefGoogle Scholar
  51. 51.
    F. Pierri, G. Paviglianiti, F. Caccavale, and M. Mattei. Observer-based sensor fault detection and isolationfor chemical batch reactors. Engineering Applications of Artificial Intelligence, 21:1204–1216, 2008. CrossRefGoogle Scholar
  52. 52.
    M.M. Polycarpou and A.J. Helmicki. Automated fault detection and accommodation: a learning systems approach. IEEE Transactions on Systems, Man, and Cybernetics, 25:1447–1458, 1995. CrossRefGoogle Scholar
  53. 53.
    J. Richalet, A. Rault, J.L. Testud, and J. Papon. Model predictive heuristic control: application to industrial processes. Automatica, 14:413–428, 1978. CrossRefGoogle Scholar
  54. 54.
    H. Schuler and C.U. Schmidt. Calorimetric state estimators for chemical reactor diagnosis and control: reviews of methods and application. Chemical Engineering Science, 47(4):899–915, 1992. CrossRefGoogle Scholar
  55. 55.
    H. Seki, M. Ogawa, S. Ooyama, K. Akamatsu, M. Ohshima, and W. Yang. Industrial application of a nonlinear model predictive control to polymerization reactors. Control Engineering Practice, 9:819–828, 2001. CrossRefGoogle Scholar
  56. 56.
    P.D. Signal and P.L. Lee. Generic model adaptive control. Chemical Engineering Communications, 115(1):35–52, 1992. CrossRefGoogle Scholar
  57. 57.
    P. Tatjewski. Advanced Control of Industrial Processes. Springer, London, 2007. MATHGoogle Scholar
  58. 58.
    O. Ubricha, B. Srinivasanb, P. Lerenac, D. Bonvin, and B. Stoessel. The use of calorimetry for on-line optimisation of isothermal semi-batch reactors. Chemical Engineering Science, 56:5147–5156, 2001. CrossRefGoogle Scholar
  59. 59.
    P. Vega, P. Prada, and V. Aleixandre. Self-tuning predictive PID controller. In Proceeding of Inst. Electrical Engineering, pages 303–308, 1991. Google Scholar
  60. 60.
    D. Wang, D.H. Zhou, Y.H. Jin, and S.J. Qin. A strong tracking predictor for nonlinear processes with input time delay. Computers and Chemical Engineering, 28:2523–2540, 2004. CrossRefGoogle Scholar
  61. 61.
    D.I. Wilson, M. Agarwal, and D.V.T. Rippin. Experiences implementing the extended Kalman filter on an industrial batch reactor. Combustion and Flame, 22:1653–1672, 1998. Google Scholar
  62. 62.
    X.Q. Xie, D.H. Zhou, and Y.H. Jin. Strong tracking filter based adaptive generic model control. Journal of Process Control, 9:337–350, 1999. CrossRefGoogle Scholar
  63. 63.
    K. Yamuna Rani and S.C. Patwardhan. Data-driven model based control of a multi-product semi-batch polymerization reactor. Chemical Engineering Research and Design, 85:1397–1406, 2007. CrossRefGoogle Scholar
  64. 64.
    X. Zhang, M.M. Polycarpou, and T. Parisini. A robust detection and isolation scheme for abrupt and incipient faults in nonlinear systems. IEEE Transactions on Automatic Control, 47:576–593, 2002. MathSciNetCrossRefMATHGoogle Scholar
  65. 65.
    W. Zhou and P.L. Lee. Robust stability analysis of generic model control. Chemical Engineering Communications, 117(1):41–72, 1992. CrossRefGoogle Scholar

Copyright information

© Springer-Verlag London Limited 2011

Authors and Affiliations

  • Fabrizio Caccavale
    • 1
  • Mario Iamarino
    • 2
  • Francesco Pierri
    • 3
  • Vincenzo Tufano
    • 4
  1. 1.Dipartimento di Ingegneria e Fisica dell’AmbienteUniversità degli Studi della BasilicataPotenzaItaly
  2. 2.Dipartimento di Ingegneria e Fisica dell’AmbienteUniversità degli Studi della BasilicataPotenzaItaly
  3. 3.Dipartimento di Ingegneria e Fisica dell’AmbienteUniversità degli Studi della BasilicataPotenzaItaly
  4. 4.Dipartimento di Ingegneria e Fisica dell’AmbienteUniversità degli Studi della BasilicataPotenzaItaly

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