Simple nonlinear observers for on-line estimation of kinetic rates in bioreactors

Farza, M.; Busawon, Krishna; Hammouri, Hassan

doi:10.1016/s0005-1098(97)00166-0

Cited by 137 publications

(87 citation statements)

References 4 publications

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“…(1) adaptive systems attempts to estimate the influent disturbances [26], the parameters [7,12], the state variables [9,10] and/or kinetics [11,14,15] on-line. With the information estimated, a PID like, or more sophisticated control strategies can be readily applied; (2) robust and optimal control [13,28], on the other hand, is based only on simplified linear models used to develop a feedback law to treat nonlinearities, parameter variations and load disturbances, while (3) feedback linearization or similar [4,24,29] is employed to compensate the known nonlinear kinetics through certain implied information contained in (on-line) measurable parameters such as the off gases; and (4) intelligent control system [17,18,30] utilises the experiences gained from the reactor operation.…”

Section: Introductionmentioning

confidence: 99%

Bifurcation and stability analysis of an anaerobic digestion model

et al. 2006

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This paper presents the dynamic behaviour of the anaerobic digestion process, based on a simplified model. The hydraulic, biological and physicochemical processes such as those which underpin anaerobic digestion have more than one stable stationary solution and they compete with each other. Further, the attractive domains of the stable solutions vary with the key parameters. Thus, some initial transient process moving toward one stable solution could suddenly move towards another solution, at which a so-call catastrophe takes places (e.g. washout). The paper systematically analyses the stationary solutions with their associated stability, which provides insight and guidance for anaerobic digestion reactor design, operation and control.

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Section: Introductionmentioning

confidence: 99%

Bifurcation and stability analysis of an anaerobic digestion model

et al. 2006

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“…Moreover we take k 4 =0 and we have a kind of high gain observer with a bounded error on the penultimate unmeasured variable (x 3 ) and an asymptotic observer for the last state (z); we can prove using the results of Farza et al [4] that the hybrid observer converges towards an error as small as we want with a fixed convergence rate (because of the asymptotic observer).…”

Section: Resultsmentioning

confidence: 99%

“…One can notice that the final error bound 14 depend on h, that is to say if h is large this bound goes to zero, and we go as near as we want: it is the idea of ''practical observer'' [4]. Remark 35 All proofs and simulations have been done for fixed d and s in .…”

Section: Third Step (Conclusion)mentioning

confidence: 94%

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Hybrid bounded error observers for uncertain bioreactor models

Lemesle

Gouzé

2005

Bioprocess Biosyst Eng

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In this paper, we build bounded error observers for a common class of partially known bioreactor models. The main idea is to construct hybrid bounded observers "between" high gain observer, which has an adjustable convergence rate but requires perfect knowledge of the model, and asymptotic observer which is very robust towards uncertainty but has a fixed convergence rate. An hybrid bounded error observer which reconstructs the two state variables is constructed considering two steps: first step is similar to a high gain observer meaning that fast convergence rate but error depending on the knowledge of the model are obtained; second step is a switch to an observer similar to the asymptotic one meaning that fixed convergence rate towards an error as small as desired is obtained. Thus, a better convergence rate of estimated variables than the classical asymptotic observer is obtained.

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“…The latter is a dynamical system that combines a nominal model of the process with online measurements of the input and the output of the process to estimate states and/or parameters. In bioprocess engineering, many algorithms have been developed in the literature [2,3,4,5,6,7].…”

Section: Observer Designmentioning

confidence: 99%

Observer design for differential-algebraic model of an aerobic culture of a recombinant yeast

Assoudi¹,

Yaagoubi²,

Hammouri

2003

Bioprocess and Biosystems Engineering

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The mathematical model of an aerobic culture of recombinant yeast presented in work by Zhang et al. (1997) is given by a differential-algebraic system. The classical nonlinear observer algorithms are generally based on ordinary differential equations. In this paper, first we extend the nonlinear observer synthesis to differential-algebraic dynamical systems. Next, we apply this observer theory to the mathematical model proposed in Zhang et al. (1997). More precisely, based on the total cell concentration and the recombinant protein concentration, the observer gives the online estimation of the glucose, the ethanol, the plasmid-bearing cell concentration and a parameter that represents the probability of plasmid loss of plasmid-bearing cells. Numerical simulations are given to show the good performances of the designed observer.

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Simple nonlinear observers for on-line estimation of kinetic rates in bioreactors

Cited by 137 publications

References 4 publications

Bifurcation and stability analysis of an anaerobic digestion model

Bifurcation and stability analysis of an anaerobic digestion model

Hybrid bounded error observers for uncertain bioreactor models

Observer design for differential-algebraic model of an aerobic culture of a recombinant yeast

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