© The Institution of Engineering and Technology
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)
-
19. Khalil, H.K.: ‘Nonlinear systems’ (Prentice–Hall, 1996).
-
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. 82–91 (doi: 10.1002/apj.10).
-
3)
-
7. Boyd, S., El-Ghaoui, L., Feron, E., Balakrishnan, V.: ‘Linear matrix inequalities in system and control theory’ (SIAM, 1994).
-
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. 881–888 (doi: 10.1016/j.automatica.2004.01.002).
-
5)
-
12. Francis, B.A., Wonham, W.M.: ‘The internal model principle for linear multivariable regulators’, Appl. Math. Opt., 1975, 2, (2), pp. 170–194 (doi: 10.1007/BF01447855).
-
6)
-
9. El Ghaoui, L., Scorletti, G.: ‘Control of rational systems using Linear-Fractional representations and linear matrix inequalities’, Automatica, 1996, 32, (9), pp. 1273–1284 (doi: 10.1016/0005-1098(96)00071-4).
-
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. 1602–1630 (doi: 10.1002/rnc.1773).
-
8)
-
10. Trofino, A.: ‘Robust stability and domain of attraction of uncertain nonlinear systems’. Proc. American Control Conf., 2000, vol. 5, pp.3707–3711.
-
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. 88–110 (doi: 10.1002/rnc.1207).
-
10)
-
16. Iwasaki, T., Shibata, G.: ‘LPV systems analysis via quadratic separator for uncertain implicit systems’, IEEE Trans. Autom. Control, 2001, 46, (8), pp. 1195–1208 (doi: 10.1109/9.940924).
-
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. 315–325 (doi: 10.1049/iet-cta.2008.0314).
-
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. 23–43.
-
13)
-
2. Kravaris, C., Kantor, J.C.: ‘Geometric methods for nonlinear process control. 2. Controller synthesis’, Ind. Eng. Chem. Res., 1990, 29, pp. 2310–2323 (doi: 10.1021/ie00108a002).
-
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. 8985–8997 (doi: 10.1021/ie060582e).
-
15)
-
1. Bastin, G., Dochain, D.: ‘On-line estimation and adaptive control of bioreactors’ (Elsevier, 1990).
-
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. 217–222 (doi: 10.1016/0167-6911(92)90008-G).
-
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. 17–46.
-
18)
-
21. Andrieu, V., Praly, L.: ‘A unifying point of view on output feedback designs for global asymptotic stabilization’, Automatica, 2009, 45, pp. 1789–1798 (doi: 10.1016/j.automatica.2009.04.015).
-
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. 309–320.
-
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. 1575–1580 (doi: 10.1109/TAC.2002.802737).
-
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. 760–765.
-
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. 1301–1326 (doi: 10.1002/rnc.950).
-
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. 875–880 (doi: 10.1109/9.256352).
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