Your browser does not support JavaScript!
http://iet.metastore.ingenta.com
1887

access icon free A robust non-linear feedback control strategy for a class of bioprocesses

This study proposes a multiple-input/multiple-output robust approach to the control of bioprocesses based on a cascaded-loop strategy. The internal loop is a classical input-to-output feedback linearising controller which is obtained from the nominal dynamics of the bioprocess. Then, the outer loop is designed based on the internal model principle to obtain zero steady-state tracking error (and disturbance rejection) for constant signals while ensuring the robust stability of the overall closed-loop system. In addition, a robust Luenberger-like observer is proposed to estimate unmeasured state variables for the feedback linearising control law. The approach is applied to the simultaneous control of biomass and substrate concentrations in a perfusion/chemostat bioreactor, where the simulation results demonstrate the effectiveness of the proposed control strategy.

References

    1. 1)
      • 19. Khalil, H.K.: ‘Nonlinear systems’ (Prentice–Hall, 1996).
    2. 2)
      • 23. Deschenes, J.-S., Desbiens, A., Perrier, M., Kamen, A.: ‘Use of cell bleed in a high cell density perfusion culture and multivariable control of biomass and metabolite concentrations’, Asia-Pacific J. Chem. Eng., 2006, 1, (1–2), pp. 8291 (doi: 10.1002/apj.10).
    3. 3)
      • 7. Boyd, S., El-Ghaoui, L., Feron, E., Balakrishnan, V.: ‘Linear matrix inequalities in system and control theory’ (SIAM, 1994).
    4. 4)
      • 5. Guay, M., Dochain, D., Perrier, M.: ‘Adaptive extremum seeking control of continuous stirred tank bioreactors with unknown growth kinetics’, Automatica, 2004, 40, (5), pp. 881888 (doi: 10.1016/j.automatica.2004.01.002).
    5. 5)
      • 12. Francis, B.A., Wonham, W.M.: ‘The internal model principle for linear multivariable regulators’, Appl. Math. Opt., 1975, 2, (2), pp. 170194 (doi: 10.1007/BF01447855).
    6. 6)
      • 9. El Ghaoui, L., Scorletti, G.: ‘Control of rational systems using Linear-Fractional representations and linear matrix inequalities’, Automatica, 1996, 32, (9), pp. 12731284 (doi: 10.1016/0005-1098(96)00071-4).
    7. 7)
      • 4. Karafyllis, I., Jiang, Z.-P.: ‘A new small-gain theorem with an application to the stabilization of the chemostat’, Int. J. Robust Nonlinear Control, 2012, 22, (14), pp. 16021630 (doi: 10.1002/rnc.1773).
    8. 8)
      • 10. Trofino, A.: ‘Robust stability and domain of attraction of uncertain nonlinear systems’. Proc. American Control Conf., 2000, vol. 5, pp.37073711.
    9. 9)
      • 15. Coutinho, D., Fu, M., Trofino, A., Danès, P.: ‘L2-gain analysis and control of uncertain nonlinear systems with bounded disturbance inputs’, Int. J. Robust Nonlinear Control, 2008, 18, (1), pp. 88110 (doi: 10.1002/rnc.1207).
    10. 10)
      • 16. Iwasaki, T., Shibata, G.: ‘LPV systems analysis via quadratic separator for uncertain implicit systems’, IEEE Trans. Autom. Control, 2001, 46, (8), pp. 11951208 (doi: 10.1109/9.940924).
    11. 11)
      • 18. Coutinho, D., Gomes da Silva, Jr.J.M.: ‘Computing estimates of the region of attraction for rational control systems with saturating actuators’, IET Control Theory Applic., 2010, 4, (3), pp. 315325 (doi: 10.1049/iet-cta.2008.0314).
    12. 12)
      • 8. Papachristodoulou, A., Prajna, S.: ‘Analysis of non-polynomial systems using the sum of squares decomposition’, in Henrion, D., Garulli, A. (Eds): ‘Positive polynomials in control’ (Springer–Verlag, 2005) pp. 2343.
    13. 13)
      • 2. Kravaris, C., Kantor, J.C.: ‘Geometric methods for nonlinear process control. 2. Controller synthesis’, Ind. Eng. Chem. Res., 1990, 29, pp. 23102323 (doi: 10.1021/ie00108a002).
    14. 14)
      • 6. Deschenes, J.-S., Desbiens, A., Perrier, M., Kamen, A.: ‘Multivariable nonlinear control of biomass and metabolite concentrations in a high-cell-density perfusion bioreactor’, Ind. Eng. Chem. Res., 2006, 45, (26), pp. 89858997 (doi: 10.1021/ie060582e).
    15. 15)
      • 1. Bastin, G., Dochain, D.: ‘On-line estimation and adaptive control of bioreactors’ (Elsevier, 1990).
    16. 16)
      • 20. Dawson, D., Qu, Z., Carroll, J.: ‘On the state observation and output feedback problems for nonlinear uncertain dynamic systems’, Syst. Control Lett., 1992, 18, (3), pp. 217222 (doi: 10.1016/0167-6911(92)90008-G).
    17. 17)
      • 13. Bernard, O., Queinnec, I.: ‘Dynamic models of biochemical processes: properties of models’, in Dochain, D. (Ed.), ‘Automatic control of bioprocesses’ (ISTE Ltd. and John Wiley & Sons, 2008), pp. 1746.
    18. 18)
      • 21. Andrieu, V., Praly, L.: ‘A unifying point of view on output feedback designs for global asymptotic stabilization’, Automatica, 2009, 45, pp. 17891798 (doi: 10.1016/j.automatica.2009.04.015).
    19. 19)
      • 17. Dussy, S.: ‘Multiobjective robust control toolbox for linear-matrix-inequality-based control’, in El Ghaoui, L., Niculescu, S.-I. (Eds): ‘Advances in linear matrix inequality methods in control’ (SIAM, 2000), pp. 309320.
    20. 20)
      • 11. Coutinho, D., Trofino, A., Fu, M.: ‘Guaranteed cost control of uncertain nonlinear systems via polynomial Lyapunov functions’, IEEE Trans. Autom. Control, 2002, 47, (9), pp. 15751580 (doi: 10.1109/TAC.2002.802737).
    21. 21)
      • 3. Antonelli, R., Astolfi, A.: ‘Nonlinear controllers design for Robust stabilization of continuous biological reactors’. Proc. 2000 IEEE Conf. on Control and Application, Anchorage, Alaska, 2000, pp. 760765.
    22. 22)
      • 14. Coutinho, D., Bazanella, A.S., Trofino, A., Silva, A.S.: ‘Stability analysis and control of a class of differential-algebraic nonlinear systems’, Int. J. Robust Nonlinear Control, 2004, 14, (16), pp. 13011326 (doi: 10.1002/rnc.950).
    23. 23)
      • 22. Gauthier, J.P., Hammouri, H., Othman, S.: ‘A simple observer for nonlinear systems applications to bioreactors’, IEEE Trans. Autom. Control, 1992, 37, (6), pp. 875880 (doi: 10.1109/9.256352).
http://iet.metastore.ingenta.com/content/journals/10.1049/iet-cta.2012.0336
Loading

Related content

content/journals/10.1049/iet-cta.2012.0336
pub_keyword,iet_inspecKeyword,pub_concept
6
6
Loading
This is a required field
Please enter a valid email address