Robust Model Predictive Control and Fault-Handling of Batch Processes

  • Prashant MhaskarEmail author
  • Abhinav Garg
  • Brandon Corbett
Part of the Advances in Industrial Control book series (AIC)


This Chapter considers the control of batch processes subject to input constraints and model uncertainty with the objective of achieving a desired product quality. First, a computationally efficient non-linear robust MPC is designed. The robust MPC scheme uses robust reverse-time reachability regions (RTRRs) which we define as the set of process states that can be driven to a desired neighborhood of the target end-point subject to input constraints and model uncertainty. A multi-level optimization based algorithm to generate robust RTRRs for specified uncertainty bounds is presented. We then consider the problem of uncertain batch processes subject to finite duration faults in the control actuators. Using the robust RTRR based MPC as the main tool, a robust safe-steering framework is developed to address the problem of how to operate the functioning inputs during the fault repair period to ensure that the desired end-point neighborhood can be reached upon recovery of the full control effort. The applicability of the proposed robust RTRR based controller and safe-steering framework subject to limited availability of measurements and sensor noise are illustrated using a fed-batch reactor system.


  1. 1.
    Cruickshank, S.M., Daugulis, A.J., McLellan, P.J.: Dynamic modeling and optimal fed-batch feeding strategies for a two-phase partitioning bioreactor. Biotech. Bioeng. 67, 224–233 (2000)CrossRefGoogle Scholar
  2. 2.
    Dadebo, S.A., McAuley, K.B.: Dynamic optimization of constrained chemical engineering problems using dynamic programming. Comput. Chem. Eng. 19, 513–525 (1995)CrossRefGoogle Scholar
  3. 3.
    Zhang, G.P., Rohani, S.: On-line optimal control of a seeded batch cooling crystallizer. Chem. Eng. Sci. 58, 1887–1896 (2003)CrossRefGoogle Scholar
  4. 4.
    Soroush, M., Kravaris, C.: Optimal-design and operation of batch reactors. 1. Theoretical framework. Ind. Eng. Chem. Res. 32, 866–881 (1993)CrossRefGoogle Scholar
  5. 5.
    Soroush, M., Kravaris, C.: Optimal-design and operation of batch reactors. 2. A case-study. Ind. Eng. Chem. Res. 32, 882–893 (1993)CrossRefGoogle Scholar
  6. 6.
    Flores-Cerrillo, J., MacGregor, J.F.: Latent variable MPC for trajectory tracking in batch processes. J. Process Control 15, 651–663 (2005)CrossRefGoogle Scholar
  7. 7.
    Valappil, J., Georgakis, C.: State estimation and nonlinear model predictive control of end-use properties in batch reactors. In: Proceedings of the 2001 American Control Conference, vol. 2, pp. 999–1004 (2001) (Arlington, VA)Google Scholar
  8. 8.
    Alamir, M., Balloul, I.: Robust constrained control algorithm for general batch processes. Int. J. Control 72, 1271–1287 (1999)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Mayne, D.Q.: Non-linear model predictive control: challenges and opportunities. In: Allgower, F., Zheng, A. (eds.) Non-Linear Model Predictive Control, pp. 23–44 (2000)CrossRefGoogle Scholar
  10. 10.
    Crowley, T., Choi, K.Y.: Experimental studies on optimal molecular weight distribution control in a batch-free radical polymerization processes. Chem. Eng. Sci. 53, 2769–2790 (1998)CrossRefGoogle Scholar
  11. 11.
    Dimitratos, J., Georgakis, C., El-Aasser, M.S., Klein, A.: Dynamic modeling and state estimation for an emulsion copolymerization reactor. Comput. Chem. Eng. 13, 21–33 (1989)CrossRefGoogle Scholar
  12. 12.
    Kozub, D., Macgregor, J.F.: Feedback control of polymer quality in semi-batch copolymerization reactors. Chem. Eng. Sci. 47(4), 929–942 (1992)CrossRefGoogle Scholar
  13. 13.
    De Valliere, P., Bonvin, D.: Application of estimation techniques to batch reactors. II. Experimental studies in state and parameter estimation. Comput. Chem. Eng. 13, 11–20 (1989)Google Scholar
  14. 14.
    Hua, X.M., Rohani, S., Jutan, A.: Cascade closed-loop optimization and control of batch reactors. Chem. Eng. Sci. 59, 5695–5708 (2004)CrossRefGoogle Scholar
  15. 15.
    Shi, D., Mhaskar, P., El-Farra, N.H., Christofides, P.D.: Predictive control of crystal size distribution in protein crystallization. Nanotechnology 16(7), 562–574 (2005)CrossRefGoogle Scholar
  16. 16.
    Shi, D., El-Farra, N.H., Li, M., Mhaskar, P., Christofides, P.D.: Predictive control of particle size distribution in particulate processes. Chem. Eng. Sci. 61, 268–281 (2005)CrossRefGoogle Scholar
  17. 17.
    Sheikhzadeh, M., Trifkovic, M., Rohani, S.: Real-time optimal control of an anti-solvent isothermal semi-batch crystallization process. Chem. Eng. Sci. 63, 829–839 (2008)CrossRefGoogle Scholar
  18. 18.
    Palanki, S., Vemuri, J.: Optimal operation of semi-batch processes with a single reaction. Int. J. Chem. React. Eng. 3 (2005)Google Scholar
  19. 19.
    Pistikopoulos, E.N., Dua, V., Bozinis, N.A., Bemporad, A., Morari, M.: On-line optimization via off-line parametric optimization tools. Comput. Chem. Eng. 26, 175–185 (2002)CrossRefGoogle Scholar
  20. 20.
    Huynh, N., Kazantzis, N.: Parametric optimization of digitally controlled nonlinear reactor dynamics using Zubov-like functional equations. J. Math. Chem. 38, 499–519 (2005)MathSciNetCrossRefGoogle Scholar
  21. 21.
    Mhaskar, P., El-Farra, N.H., Christofides, P.D.: Predictive control of switched nonlinear systems with scheduled mode transitions. IEEE Trans. Autom. Control 50, 1670–1680 (2005)MathSciNetCrossRefGoogle Scholar
  22. 22.
    Mhaskar, P.: Robust model predictive control design for fault-tolerant control of process systems. Ind. Eng. Chem. Res. 45, 8565–8574 (2006)CrossRefGoogle Scholar
  23. 23.
    Mahmood, M., Gandhi, R., Mhaskar, P.: Safe-parking of nonlinear process systems: handling uncertainty and unavailability of measurements. Chem. Eng. Sci. 63, 5434–5446 (2008)CrossRefGoogle Scholar
  24. 24.
    Aumi, S., Mhaskar, P.: Safe-steering of batch processes. AIChE J. 55, 2861–2872 (2009)CrossRefGoogle Scholar
  25. 25.
    Nomikos, P., Macgregor, J.F.: Monitoring batch processes using multiway principal component analysis. AIChE J. 40, 1361–1375 (1994)CrossRefGoogle Scholar
  26. 26.
    Cinar, A., Parulekar, S.J., Undey, C., Birol, G.: Batch Fermentation: Modeling: Monitoring, and Control. CRC Press, New York (2003)Google Scholar
  27. 27.
    Undey, C., Tatara, E., Williams, B.A., Birol, G., Cinar, A.: A hybrid supervisory knowledge-based system for monitoring penicillin fermentation. In: Proceedings of American Control Conference, Chicago, Illinois, vol. 6, pp. 3944–3948 (2000)Google Scholar
  28. 28.
    Undey, C., Tatara, E., Williams, B.A., Birol, G., Cinar, A.: On-line real-time monitoring of penicillin fermentation. In: International Symposium on Advanced Control of Chemical Processes, Pisa, Italy, vol. 6, pp. 243–248 (2000)CrossRefGoogle Scholar
  29. 29.
    Undey, C., Cinar, A.: Statistical monitoring of multiphase, multistage batch processes. IEEE Control Syst. Mag. 22, 40–52 (2002)CrossRefGoogle Scholar
  30. 30.
    Mhaskar, P., McFall, C., Gani, A., Christofides, P.D., Davis, J.F.: Isolation and handling of actuator faults in nonlinear systems. Automatica 44, 53–62 (2008)MathSciNetCrossRefGoogle Scholar
  31. 31.
    Gandhi, R., Mhaskar, P.: Safe-parking of nonlinear process systems. Comput. Chem. Eng. 32, 2113–2122 (2008)CrossRefGoogle Scholar
  32. 32.
    Terwiesch, P., Agarwal, M., Rippin, D.W.T.: Batch unit optimization with imperfect modelling: a survey. J. Process Control 4, 238–258 (1994)CrossRefGoogle Scholar
  33. 33.
    Khalil, H.K.: Nonlinear Systems, 3rd edn. Prentice Hall, New York (2002)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Prashant Mhaskar
    • 1
    Email author
  • Abhinav Garg
    • 1
  • Brandon Corbett
    • 1
  1. 1.Department of Chemical EngineeringMcMaster UniversityHamiltonCanada

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