A Passivity Approach to the Stabilization of Free-Radical Polymerization Reactor


Nguyen T. Sang(1), Hoang N. Ha(2*), M.A. Hussain(3)

(1) Department of Chemical Engineering, Faculty of Engineering, University Malaya, Kuala Lumpur, Malaysia
(2) Institute of Research and Development, Duy Tan university, Da Nang, Viet Nam
(3) Department of Chemical Engineering, Faculty of Engineering, University Malaya, Kuala Lumpur, Malaysia
(*) Corresponding Author


This work proposes a tracking error passivity-based multivariable control via
feedback passivation for a class of free-radical polymerization systems in a continuously
stirred tank reactor (CSTR). Firstly, this system dynamics with high nonlinearity is
passivized by input coordinate transformations, the resulting passive system is then rewritten into a canonical form strongly related to the so-called Port Control Hamiltonian
structure. Actually, this representation allows to show the physical meanings of system
dynamics such as dissipative, non-dissipative terms and supply rate. From this, a feedback
controller based on tracking error is designed for the globally exponential stabilization at
an arbitrarily chosen reference trajectory passing the desired equilibrium point. The
theoretical developments are then illustrated for polystyrene polymerization system in
the CSTR. The numerical simulations show that the trajectories of styrene polymerization
system considered as an illustrative example of FRP system converges globally
exponentially to the imposed trajectories.


Free-radical polymerization, polystyrene, passivity-based control, feedback passivation, tracking error, multivariable system

Full Text:



  1. Antonelli, R., & Astolfi, A. (2003). Continuous stirred tank reactors: easy to stabilise? Automatica, 39(10), 1817-1827.
  2. Assala, N., Viel, F., & Gauthier, J. P. (1997). Stabilization of polymerization CSTR under input constraints. Computers & Chemical Engineering, 21(5), 501-509.
  3. Bao, J., & Lee, P. L. (2007). Process Control -The Passive Systems Approach (1st ed.): Springer-Verlag London.
  4. Biswas, P., & Samanta, A. N. (2013, 23- 26 June 2013). Backstepping control of polymerization reactor. Paper presented at the Control Conference (ASCC), 2013 9th Asian.
  5. Blanchini, F. (1999). Set invariance in control. Automatica, 35(11), 1747-1767.
  6. Chen, H., Kremling, A., & Allgöwer, F. (1995). Nonlinear predictive control of a benchmark CSTR. Paper presented at the Proceeding of 3rd European control conference (ECC), Rome, Italy.
  7. Chou, Y.-S., & Wu, C.-H. (2007). Passivity-based control of the phthalic anhydride fixed-bed reactor. Chemical Engineering Science, 62(5), 1282-1297.
  8. Engell, S., & Klatt, K. U. (1993, 2-4 June 1993). Nonlinear Control of a NonMinimum-Phase CSTR. Paper presented at the 1993 American Control  Conference.
  9. Favache, A., & Dochain, D. (2009). Thermodynamics and chemical systems stability: The CSTR case study revisited. Journal of Process Control, 19(3), 371- 379.
  10. Fossas, E., Ros, R. M., & Sira-Ramírez, H. (2004). Passivity-Based Control of a Bioreactor System. Journal of Mathematical Chemistry, 36(4), 347- 360. doi:10.1023/B:JOMC.0000044522.3674 2.4b
  11. Freitas Filho, I. P., Biscaia, E. C., & Pinto, J. C. (1994). Steady-state multiplicity in continuous bulk polymerization reactors—a general approach. Chemical Engineering Science, 49(22), 3745-3755.
  12. Ghasem, N. M., Sata, S. A., & Hussain, M. A. (2007). Temperature control of a bench-scale batch polymerization reactor for polystyrene production. Chemical Engineering & Technology, 30(9), 1193-1202.
  13. Hidalgo, P. M., & Brosilow, C. B. (1990). Nonlinear model predictive control of styrene polymerization at unstable operating points. Computers & Chemical Engineering, 14(4), 481-494.
  14. Hoang, H., Couenne, F., Jallut, C., & Le Gorrec, Y. (2011). The port Hamiltonian approach to modeling and control of continuous stirred tank reactors. Journal of Process Control, 21(10), 1449- 1458.
  15. Hoang, H., Couenne, F., Jallut, C., & Le Gorrec, Y. (2012). Lyapunov-based control of non isothermal continuous stirred tank reactors using irreversible thermodynamics. Journal of Process Control, 22(2), 412-422.
  16. Hoang, H., Couenne, F., Jallut, C., & Le Gorrec, Y. (2013). Thermodynamics based stability analysis and its use for nonlinear stabilization of the CSTR. Computers & Chemical Engineering, 58, 156-177.
  17. Hoang, H., Couenne, F., Le Gorrec, Y., Chen, C. L., & Ydstie, B. E. (2013). Passivity-based nonlinear control of CSTR via asymptotic observers. Annual Reviews in Control, 37(2), 278-288.
  18. Hoang, H., & Dochain, D. (2013). On an evolution criterion of homogeneous multi-component mixtures with chemical transformation. Systems & Control Letters, 62(2), 170-177.
  19. Hosen, M. A., Hussain, M. A., & Mjalli, F. S. (2011). Control of polystyrene batch reactors using neural network based model predictive control (NNMPC): an experimental investigation. Control Engineering Practice, 19(5), 454-467.
  20. Hosen, M. A., Hussain, M. A., Mjalli, F. S., Khosravi, A., Creighton, D., & Nahavandi, S. (2014). Performance analysis of three advanced controllers for polymerization batch reactor: an experimental investigation. Chemical Engineering Research and Design, 92(5), 903-916.
  21. Jaisinghani, R., & Ray, W. H. (1977). On the dynamic behaviour of a class of homogeneous continuous stirred tank polymerization reactors. Chemical Engineering Science, 32(8), 811-825.
  22. Khalil, H. K. (2002). Nonlinear systems (Third ed.): Prentice Hall.
  23. Kuhlmann, A., & Bogle, D. (1997). Study on nonminimum phase behaviour and optimal operation. Computers & Chemical Engineering, 21, S397-S402.
  24. Lederle, F., & Hübner, E. G. (2017). Radical polymerization of styrene in presence of poly(2,2,6,6- tetramethylpiperidine-N-oxyl-4-yl methacrylate) - formation of polymer brushes. Polymer, 111, 258-264.
  25. Matyjaszewski, K., & Davis, T. P. (2002). Handbook of Radical Polymerization. Willey.
  26. Melo, P. A., Biscaia Jr, E. C., & Pinto, J. C. (2003). The bifurcation behavior of continuous free-radical solution loop polymerization reactors. Chemical Engineering Science, 58(13), 2805-2821.
  27. Meyer, T., & Keurentjes, J. (2005). Handbook of polymer reaction engineering: WILEY-VCH.
  28. Nguyen, S., Hoang, H., & Hussain, M. A. (2017a). Feedback passivation plus tracking-error-based multivariable control for a class of free-radical polymerization reactors. Submitted to "International Journal of Control".
  29. Niemiec, M., & Kravaris, C. (2003). Nonlinear model-state feedback control for nonminimum-phase processes. Automatica, 39(7), 1295- 1302.
  30. Ortega, R., Van der Schaft, A., Mareels, I., & Maschke, B. (2001). Putting energy back in control. IEEE Control Systems, 21(2), 18-33.
  31. Ortega, R., Van der Schaft, A., Maschke, B., & Escobar, G. (2002). Interconnection and damping assignment passivity-based control of port-controlled Hamiltonian systems. Automatica, 38(4), 585-596.
  32. Petrovic, V., Ortega, R., & Stankovic, A. M. (2001). Interconnection and damping assignment approach to control of PM synchronous motors. IEEE Transactions on Control Systems Technology, 9(6), 811-820.
  33. Ramírez, H., Sbarbaro, D., & Ortega, R. (2009). On the control of non-linear processes: an IDA–PBC approach. Journal of Process Control, 19(3), 405- 414.
  34. Riverol, C. (2001). Passivity-based control for a non-isothermal tank used in the production of pineapple syrup. Food Control, 12(6), 373-378.
  35. Russo, L. P., & Bequette, B. W. (1998). Operability of chemical reactors: multiplicity behavior of a jacketed styrene polymerization reactor. Chemical Engineering Science, 53(1), 27-45.
  36. Sira-RamÍrez, H. (1998). A general canonical form for feedback passivity of nonlinear systems. International Journal of Control, 71(5), 891-905.
  37. Sira-RamÍrez, H., & AnguloNunez, I. (1997). Passivity-based control of nonlinear chemical processes. International Journal of Control, 68(5), 971-996.
  38. Sira-Ramírez, H., Perez-Moreno, R. A., Ortega, R., & Garcia-Esteban, M. (1997). Passivity-based controllers for the stabilization of Dc-to-Dc power converters. Automatica, 33(4), 499-513.
  39. Szederkényi, G., Kristensen, N. R., Hangos, K. M., & Bay Jørgensen, S. (2002). Nonlinear analysis and control of a continuous fermentation process. Computers & Chemical Engineering, 26(4–5), 659-670.
  40. Viel, F., Busvelle, E., & Gauthier, J. P. (1995). Stability of polymerization reactors using I/O linearization and a high-gain observer. Automatica, 31(7), 971-984.
  41. Viel, F., Jadot, F., & Bastin, G. (1997). Global stabilization of exothermic chemical reactors under input constraints. Automatica, 33(8), 1437- 1448.
  42. Willems, J. C. (1972). Dissipative dynamical systems part I: General theory. Archive for Rational Mechanics and Analysis, 45(5), 321-351. doi:10.1007/bf00276493
  43. Ydstie, B. E. (2002). Passivity based control via the second law. Computers & Chemical Engineering, 26(7–8), 1037- 1048.
  44. Ydstie, B. E., & Alonso, A. A. (1997). Process systems and passivity via the Clausius-Planck inequality. Systems & Control Letters, 30(5), 253-264.

DOI: https://doi.org/10.22146/ajche.49558

Article Metrics

Abstract views : 58 | views : 24


  • There are currently no refbacks.