Adaptive identification and control algorithms for nonlinear bacterial growth systems. (English) Zbl 0544.93043

Summary: This paper suggests how nonlinear adaptive control of nonlinear bacterial growth systems could be performed. The process is desribed by a time- varying nonlinear model obtained from material balance equations. Two different control problems are considered: substrate concentration control and production rate control. For each of these cases, an adaptive minimum variance control algorithm is proposed and its effectiveness is shown by simulation experiments. A theoretical proof of convergence of the substrate control algorithm is given. A further advantage of the nonlinear approach of this paper is that the identified parameters (namely the growth rate and a yield coefficient) have a clear physical meaning and can give, in real time, a useful information on the state of the biomass.


93C40 Adaptive control/observation systems
92Cxx Physiological, cellular and medical topics
93C10 Nonlinear systems in control theory
93E10 Estimation and detection in stochastic control theory
93E12 Identification in stochastic control theory
93E25 Computational methods in stochastic control (MSC2010)
Full Text: DOI


[1] Aborhey, S.; Williamson, D., State and parameter estimation of microbial growth processes, Automatica, 14, 493-498, (1978) · Zbl 0425.93034
[2] Antunes, S.; Installé, M., The use of phase-plane analysis in the modelling and the control of a biomethanization process, (), 165-170
[3] Bastin, G.; Dochain, D.; Haest, M.; Installé, M.; Opdenacker, P., Modelling and adaptive control of a continuous anaerobic fermentation process, (), 299-306
[4] Bastin, G.; Dochain, D.; Haest, M.; Installé, M.; Opdenacker, P., Identification and adaptive control of a biomethanization process, (), 271-282
[5] Belanger, P.R., On type I systems and the Clarke-gawthrop regulator, Automatica, 19, 91-94, (1983) · Zbl 0498.93074
[6] Cheruy, A.; Panzarella, L.; Denat, J.P., Multimodel simulation and adaptive stochastic control of an activated sludge process, (), 127-183
[7] Clarke, D.W.; Gawthrop, P.J., Self-tuning control, (), 633-640 · Zbl 0507.93048
[8] D’Ans, G.; Kokotovic, P.V.; Gottlieb, D., A nonlinear regulator problem for a model of biological waste treatment, IEEE trans. aut. control, AC-16, 341-347, (1971)
[9] Goodwin, G.C.; McInnis, B.; Long, R.S., Adaptive control algorithms for waste water treatment and ph neutralization, Opt. control appl. meth., 3, 443-459, (1982) · Zbl 0502.93047
[10] Goodwin, G.C.; Sin, K.S., ()
[11] Halme, A., Modelling and control of biotechnical processes, () · Zbl 0507.93059
[12] Holmberg, A., On the accuracy of estimating in the parameters of models containing Michaelis-Menten type nonlinearities, (), 199-208
[13] Holmberg, A.; Ranta, J., Procedures for parameter and state estimation of microbial growth process models, Automatica, 13, 181-193, (1982) · Zbl 0487.93052
[14] Ko, K.Y.; McInnis, B.C.; Goodwin, G.C., Adaptive control and identification of the dissolved oxygen process, Automatica, 18, 727-730, (1982) · Zbl 0493.93036
[15] Marsili-Libelli, S., On-line estimation of bioactivities in activated sludge processes, (), 121-126
[16] Roques, H.; Yve, S.; Saipanich, S.; Capdeville, B., Is Monod’s approach adaquate for the modelisation of purification processes using biological treatment?, Water resources, 16, 839-847, (1982)
[17] Spriet, J.A., Modelling of the growth of micro-organisms: a critical appraisal, (), 451-456
[18] Stephanopoulos, G.; San, Ka-Yiu, On-line estimation of time-varying parameters: application to biochemical reactors, (), 195-199
[19] Takamatsu, T.; Shioya, S.; Kurome, H., Dynamics and control of a mixed culture in an activated sludge process, (), 103-109
[20] Vandenberg, L.; Patel, G.B.; Clark, D.S.; Lentz, C.P., Factors affecting rate of methane formation from acetic acid by enriched methanogenic cultures, Can. J. microbiol., 22, 1312-1319, (1976)
[21] Van den Heuvel, J.C.; Zoetmeyer, R.J., Stability of the methane reactor: a simple model including substrate inhibition and cell recycle, Process biochemistry, 14-19, (1982), May-June
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.