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PROEFSCHRIFT
ter verkrrjging van de graad van in de technische wetenschappen aan de Technische Universiteit Delft, op gezag van de Rector Magnificus, prof. dr. J.M. Dirken, in het openbaar
te verdedigen ten overstaan van het College van Dekanen op 9 October 1986 te 16.00 uur door
JRR
uRfi
BREUCEL
geboren te Dordrecht5.D.Ü.
TR diss ^
1501
Dit proefschrift is goedgekeurd door de promotor Dr.ir. N.W.F. Kossen en de co-promotor Prof.ir. G. Honderd.
Contents
Summary. i
Samenvatting. v
Introduction. ix
Chapter 1.
Computer control of the dissolved oxygen concentration during
a gluconic acid batch fermentation. 1
Chapter 2.
Computer control of an aerobic batch process in a two reactor
system. 21
Chapter 3.
Design and testing of a controller suitable for an industrial
scale process showing gradients. 38
Chapter 4.
State reconstruction using element balancing methods or an
observer: a comparison applied to an ethanol production process. 63
Chapter 5.
On-line discrimination applied to an ethanol producing process
with Zymomonas mobilis in an up-flow reactor. 94
Chapter 6.
In-line optimization of an ethanol production process with
Zymomonas mobilis in an up-flow reactor. 122
Chapter 7.
Monitoring a bench scale UASB reactor using a state observer. 147
General conclusions. 176
Index to programs 178
Stellingen behorende bi.i het proefschrift van Jan van Breugel
1. Ben aantal auteurs gaat er ten onrechte van uit, dat de biomassa
concentratie een on-line meetbare toestandsvariabele is, waardoor
de publicaties noodgedwongen slechts gesimuleerde 'experimenten'
behandelen. .
D. Dochain en G. Bastin; Proceedings of the 1 IFAC/IEEE Sympo
sium on modelling and control of biotechnological processes
(Johnson ed.); Pergamon Press (1985)
J.A. Gallegos en J.A. Gallegos; Biotechnol. & Bioeng., 26 (1984)
M.J. Rolf en H.C. Li»; Chem. Eng. Comm., 29 (1984)
2. Doordat micro-organismen een groot aantal 'interne' regulatie
mechanismen bevatten doen zij zich meestal niet complexer voor dan
'gewone' chemische processen. Er is dan ook geen reden, mathemati
sche modellen niet in te zetten bij het regelen en optimaliseren
van deze processen.
J.R. Wilson; Proceedings Analytical Methods and Problems in
Biotechnology, Noordwijkerhout, The Netherlands (1984)
F.IJ. Dijkstra; Proefschrift TH Delft (1976)
Dit Proefschrift
3. Indien men aanneemt, dat het transport van korrelvornig
bacterie-materiaal in een 'up-flow anaerobic sludge blanket reactor' uit
sluitend plaatsvindt door meesleuring in het zog van opstijgende
gasbellen,.leidt dit tot onrealistische aannamen betreffende het
hydrodynamisch gedrag van zo'n reactor.
R.R. van der Meer en P.M. Heertjes, Biotechnol. & Bioeng., 15
(1983)
W.L. B o l l e , J . van Breugel, G.Ch. van Eybergen, N.W.F. Rossen en
W. van G i l s ; accepted for p u b l i c a t i o n i n B i o t e c h n o l . & Bioeng.
(1986)
4. De 'time delay kernel' methode om biologische processen te model
leren, bevat een groot aantal parameters van onbekende waarde en
gebruik ervan, in plaats van een mechanistisch model gebaseerd op
massabalansen, is daarom af te keuren.
N.S. Wang en G. Stephanopoulos; Biotechnol. & Bioeng., H (1984)
5. Menging d.m.v. impulstransport wordt wel genoemd als het belang
rijkste probleem bij schaalvergroting van (bio)reactoren. Een ver
beterde influentdistributie kan eraan bijdragen dit probleem op te
lossen.
N.W.F. Hossen, 7 International Symposium on Biotechnology, New
Delhi, India (1984)
6. Het 'parallel processing' model voor de beschrijving van cognitie
ve processen kan hoogstens betrekking hebben op onderbewuste
denk-mechnanismen.
7. Parametergevoeligheidsanalyse is de sleutel tot goede parameter-en toestandsschattingparameter-en.
Dit proefschrift; hoofdstukken 3, 5, 6 en 7
8. Door de concurrentie met de industrie, moeten promovendi in de technische wetenschappen steeds vaker aangetrokken worden uit een vakgebied dat nauwelijks aansluit bij dat waarop het promotie onderzoek gericht is. Rekening houdend met arbeidsduurverkorting, inwerkperiode, onderwijsbelasting en verslaggeving, blijven er iets minder dan 500 dagen over om het feitelijke onderzoek uit te voeren.
9. Gezien de, soms Messiaanse, verwachtingen die men koestert t.o.v. de Biotechnologie, verdient het wellicht aanbeveling de naam te veranderen in 'Biotheologie'.
ZO. Een nieuw computersysteem geeft men eerst aan zijn ergste vijan den, vervolgens aan zijn beste viend en daarna gaat men er zelf mee aan de slag.
11. Gezien de vergankelijkheid van een proefschrift (zeker in de auto-matiseringshoek), is het weinig complimenteus het aan iemand op te dragen.
Summary
The application of systems theoretical and control engineering techniques to biotechnical processes is the central theme of this thesis. The use of mechanistic mathematical models plays an important role in this appliation. These models can be used, amongst others, to design controllers, to calculate process variables for which no sensors are available yet and to optimize processes with the aid of e.g. an economic criterion.
In the first part of this dissertation, chapters 2,3 and 4, the design and development of controllers is emphasized. Eventually, these controllers' have to be applicable to industrial scale aerobic processes showing gradients in the oxygen concentration. This constraint limits the part of laboratory 'data that can be used. The production of gluconic acid by the bacterium Gluconobacter oxydans has been selected as a model proces. In a batch type fermenter a number of control strategies are compared, e.g. control with the stirrer speed and gas phase oxygen enrichment. Using a batch process, leads to strongly varying characteristic times. This problem can be solved either using adaptive controllers or a combination of a model -and a rather simple feedback controller. From experiments, the use of the latter proves to be preferable.
The oxygen gradients, that occur in industrial fermenters, can be simulated on a laboratory scale by connecting an aerated and an unaerated reactor using a pump. Both reactors are well mixed. The oxygen level in the unaerated reactor has to be controlled by mixing oxygen and nitrogen in the gas flow bubbling through the aerated reactor. Due to the limitation mentioned above, only measurements in the aerated reactor may be used. Therefore, a mathematical model of the process has been applied to estimate non measurable or (non measured) parameters and state variables. A
sensitivity analysis shows the ratio of aerated and unaerated volume and the volumetric mass transfer coefficient to be parameters, that can be
adequately estimated using measurements in the aerated reactor. However, the circulation flow, which is responsible for the entire transport of
measurements. Assuming a pseudo steady state for the oxygen balance in the unaerated reactor, solves this problem and yields sufficiently reliable estimates for this parameter.
The oxygen concentration in the unaerated reactor and the biomass concentration are the two most important state variables, that have to be reconstructed from the measurements. In the model, the biomass
concentration is present only in combination with a number of kinetic parameters. Together they form the oxygen consumption rate. Therefore, the oxygen consumption rate has been regarded as a state variable instead of the biomass concentration. As an additional advantage, the control system becomes independent of the micro-organism used.
The parameters can be estimated with a standard deviation of 10 % maximum with respect to the averaged value. The estimates agree very well with the design or literature values. The oxygen concentration in the unaerated reactor can be controlled satisfactorily well at the desired setpoint using the control system described in this thesis.
In the second part, chapters 5,6 and 7, a number of different subjects are treated. In chapter 5, two methods for state reconstruction, are compared. Chapter 6 applies on-line model discrimination to a number of models and in chapter 7 it is shown that a model can be used to achieve in-line process optimization. The process, to which these methods are applied, is the continuous production of ethanol from glucose with a flocculating strain of the bacterium Zymomonas mobilis in an up-flow reactor.
When element and reduction equivalent balances are being compared to state observers, the latter prove to have a number of significant advantages. The observer calculates correct estimates for the biomass and glucose
concentration from ethanol concentration and carbon dioxide production measurements. This holds for stationairy as well as transient states. The balancing methods only yield realistic results after a gross simplification and only, according with their definition, during steady states. Extension of these balancing methods to dynamic equations seems promising.
A priori parameter sensitivity analysis proves to be an important tool to select which parameters should be estimated on-line when model
discrimination is concerned. With a multi dimensional analysis, parameters showing a strong interdependency can be traced. Such parameters can cause problems during estimation. A model including simple kinetics proves to be most adequate to describe the process. A model incorporating more complex
kinetic equations also gives a good description in most cases. However, a model incorporating a structured hydrodynamic submodel, is almost never selected to be the best. The discrimination procedure is especially succesful, when the process is being disturbed by changes in the input variables.
In process optimization, a mechanistic mathematical model can be used to achieve a rapid approximation of the desired setpoints or trajectories of setpoints for the. real process. The criterion applied to the optimization often is economic in nature and can also take into account e.g. downstream processing costs. ..The present state of the process serves as a base for the optimization. To-determine this state, the same model is being used in a state observer. Moreover, the built-in settler plays an important role in the overall performance of the up-flow reactor. The efficiency of biomass retainment has a direct impact on the optimum setpoints of the process inputs. Numerous mechanisms and disturbances influence the settler behaviour and for this reason the settler efficiency is estimated on-line. From experiments it can be concluded that especially the' influent flow is adjusted immediately by the optimization algorithm when the settler efficiency changes.
The methods, as described in the above, have been applied to an independent process in chapter 8: the anaerobic purification of wastewater. This process is highly sensitive to overloading and toxic compounds. Therefore, it is important to monitor this process carefully. The amount of biomass and the substrate concentration are two important variables that can not be measured on-line. For this reason, much attention is paid to the
construction of a state observer and the required mathematical model. Experiments using an inert tracer, prove a one ideal mixer model including a dead volume and a plug flow region to give an adequate description of the hydrodynamic behaviour of the laboratory scale fermenter. An inhibition model is used to describe the conversion of substrate into products. The parameters determined during the experiments, agree well with literature data.
Hydrodynamic and kinetic submodel are integrated into an observer.
Stationairy as well as transient states can be tracked satisfactorily with this observer. It should be noticed that only the offgas (mainly methane) is available to the observer. The observer detects changes in the inputs of
present in the biogas flow measurements, is removed by the observer. Overload experiments show that the use of an inert tracer not always leads to an adequate hydrodynamic model. Gradients in the pH over the reactor, cause the observer to generate incorrect estimates.
The last chapter in this dissertation gives an evaluation of the
applicability of system theoretical and control engineering techniques to biotechnical processes. Especially state estimation, parameter sensitivity analysis, parameter estimation and hillclimbing are very useful tools when optimization and control of these processes are concerned. It should be noted that the quality of the models has an extreme influence on the results obtained with the techniques mentioned above.
Samenvatting
De toepassing van systeem- en regeltechnische methoden op biotechnische processen is het centrale thema van dit proefschrift. Daarbij speelt het gebruik van mechanistische mathematische modellen een belangrijke rol. Deze modellen kunnen o.a. gebruikt worden voor het ontwerpen van regelaars, voor het berekenen van procesvariabelen waar nog geen on-line sensoren voor zijn en voor het optimaliseren van processen aan de hand van bijv. een economisch criterium.
In het eerste deel van het proefschrift, de hoofdstukken 2,3 en 4, wordt de nadruk gelegd op het ontwikkelen van regelaars. Deze regelaars moeten uiteindelijk toepasbaar zijn op beluchte processen, die op industrieële schaal zuurstofgradiënten vertonen. Als modelproces is de
gluconzuurbereiding met het microörganisme Gluconobacter oxydans gekozen. In een batch reactor zijn verschillende regelstrategieën vergeleken, zoals toerentalaanpassing en het verrijken van de gasfase met zuurstof. Doordat het een batchproces betreft, verandert een aantal karakteristieke tijden van-het systeem sterk van waarde gedurende een experiment. Dit probleem kan zowel met een adapterende regelaar als met een model gecombineerd met een eenvoudige terugkoppeling opgelost worden. Uit experimenten blijkt dat het model hierbij de voorkeur verdient.
De zuurstofgradiënten, die in productiereactoren optreden, kunnen op laboratoriumschaal nagebootst worden door een beluchte en een onbeluchte reactor via een rondpomplus met elkaar te verbinden. Beide reactoren worden goed geroerd. Het is de bedoeling het zuurstofniveau in de onbeluchte reactor op een bepaalde waarde te regelen. Hierbij is gekozen voor een regeling gebaseerd op het mengen van zuurstof en stikstof in de toegevoerde gasstroom. Alleen metingen, die op industrieële schaal ook beschikbaar zijn, mogen bij deze regeling gebruikt worden. Daarom is een mathematisch model van het proces gebruikt om niet-meetbare (of niet-gemeten) parameters en toestanden te schatten, uit een parametergevoeligheidsanalyse blijkt, dat de volumeverdeling tussen het beluchte en onbeluchte compartiment en de zuurstofoverdrachtscoëfficiënt van gas naar vloeistof goed geschat kunnen
verantwoordelijk is voor het gehele zuurstoftransport naar de onbeluchte reactor, kan echter niet direct uit de beschikbare metingen bepaald worden. Via een pseudo steady state aanname voor de zuurstofbalans in het onbeluchte ■ compartiment kan toch een goede schatting voor het rondpompdebiet gemaakt
worden.
De zuurstofconcentratie in de niet-beluchte reactor en de
biomassaconcentratie zijn de twee belangrijkste toestandsvariabelen, die uit de metingen gereconstrueerd moeten worden. De biomassaconcentratie komt in het model alleen in combinatie met een aantal kinetiekparameters voor en vormt daarmee de zuurstofconsumptiesnelheid. In plaats van de
biomassaconcentratie apart te schatten, wordt deze
zuurstofconsumptiesnelheid als toestandsvariabele berekend. Dit heeft als bijkomend voordeel, dat het regelsysteem vrijwel onafhankelijk van het gebruikte microörganisme is geworden.
Uit experimenten blijkt dat de on-line geschatte parameters een standaard afwijking van maximaal 10 % vertonen ten opzichte van het gemiddelde en goed overeenkomen met literatuur- of ontwerpwaarden. De zuurstofconcentratie in de onbeluchte reactor kan met het ontworpen regelsysteem goed op het gewenste niveau gehouden worden.
In het tweede deel van het proefschrift, de hoofdstukken 5,6 en 7, worden een aantal onderwerpen behandeld. In hoofdstuk 5 worden twee methoden voor toestandsreconstructie met elkaar vergeleken, in hoofdstuk 6 wordt on-line discriminatie toegepast op een aantal modellen en in hoofdstuk 7 wordt getoond dat met een procesmodel een on-line optimalisatie verwezenlijkt kan worden. Het proces, waarmee deze methoden op bruikbaarheid getest zijn, is de continue productie van ethanol uit glucose met een flocculerende stam van de bacterie Zymomonas mobilis in een up-flow reactor.
Wanneer elementen- en reductie equivalenten balansen vergeleken wordt met toestandswaarnemers, blijkt, voor het onderzochte proces, de observer een aantal significante voordelen te hebben. De uit de ethanolconcentratie- en kooldioxideproductie-metingen te schatten waarden voor de biomassa- en glucose concentratie, worden door de waarnemer, zowel voor stationaire als overgangstoestanden, correct berekend. De balansmethoden geven slechts na een verregaande vereenvoudiging realistische resultaten, maar, geheel volgens hun definitie, alleen voor stationaire toestanden. Een uitbreiding van de balansmethoden naar dynamische vergelijkingen is een veelbelovende aanvulling van deze techniek.
Bij het onderzoek naar modeldiscriminatie bleek een a priori
gevoeligheidanalyse van het model van belang om te bepalen welke parameters het beste on-line geschat kunnen worden. Met een multi-dimensionale gevoeligheidsanalyse kunnen daarbij parameters die een sterke onderlinge afhankelijkheid vertonen, opgespoord worden. Dit type parameters veroorzaakt problemen bij het schatten. Een model met een simpele
reactiekinetiek bleek het beste in staat het proces te beschrijven. Ook een model met complexe kinetiekvergelijkingen gaf in veel gevallen een goede beschrijving, maar een model met een gestructureerd stromingsmodel werd vrijwel nooit als beste gekozen. De discriminatieprocedure is vooral succesvol, wanneer het proces verstoord werd door stappen in de ingangsvariabelen.
Bij het optimaliseren van een proces, kan een mechanistisch mathematisch model'gebruikt worden om sneller tot een benadering van de gewenste procesvoering te komen. Plet criterium, dat daarbij gebruikt wordt, is vaak economisch van aard en kan ook kosten van bijvoorbeeld een opwerkingsstap in rekening brengen. De optimalisatie vindt plaats vanuit de momentane toestand van het proces. Ten einde deze toestand te bepalen, wordt hetzelfde model gebruikt in een toestandswaarnemer. Bij de up-flow reactor speelt de ingebouwde bezinker een belangrijke rol. Het rendement waarmee deze bezinker uitspoeling van de biomassa voorkomt, heeft een directe
invloed op het werkpunt van de reactor. Daar het bezinkerrendement door tal van processen en verstoringen beïnvloed wordt, moet deze parameter
voortdurend geschat worden. Uit experimenten blijkt, dat met name de vloeistofstroom door de reactor direct door de optirnalisatiealgorithme bijgesteld wordt, indien het rendement van de bezinker verandert.
De methoden, zoals die voor de hierboven beschreven processen zijn ontwikkeld en getest, zijn in hoofdstuk 8 toegepast op een onafhankelijk systeem: de anaerobe zuivering van afvalwater. Dit proces is gevoelig voor overbelasting en toxische stoffen. Een goede bewaking van de reactor is dan ook noodzakelijk. Een probleem hierbij is dat een aantal variabelen, zoals de hoeveelheid biomassa en de substraatconcentratie in de reactor, niet on-line gemeten kunnen worden. Veel aandacht is daarom geschonken aan het ontwikkelen van een toestandswaarnemer en het mathematisch model dat daarvoor nodig is. Uit experimenten met een inerte tracer blijkt een één menger model met een dood volume en een propstroom bezinkergedeelte, een goede hydrodynamische beschrijving van de reactor te geven. Met kinetiek
experimenten en modeldiscriminatie is aangetoond, dat een inhibitiemodel de omzetting van substraat naar producten adequaat weergeeft. De parameters, die hierbij bepaald zijn, vertonen waarden, die overeenkomen met
literatuurgegevens.
De observer, waarin bovenstaand hydrodynamisch en kinetiek model
geïntegreerd zijn, is in staat zowel stationaire als overgangstoestanden goed te volgen. Om de toestandsvariabelen te reconstrueren heeft de observer alleen de beschikking over metingen van de biogasstroom, die de reactor verlaat. Uit experimenten blijkt, dat de waarnemer binnen een kwart van de hydraulische verblijftijd reageert op veranderingen aan de ingang van het proces. De ruis, die aanwezig' is in de biogasstroommetingen, wordt door de observer weggefilterd.
Dat metingen met een inerte tracer niet' in gevallen tot een goed
stromingsmodel van een reactor leidt, blijkt uit experimenten, waarbij de reactor overbelast wordt. Met name de gradiënten in de pH over de reactor, zijn er de oorzaak van, dat de waarnemer verkeerde schattingen voor de toestandsvariabelen berekent.
Het laatste hoofdstuk van dit proefschrift geeft een evaluatie van de toepasbaarheid van systeemtheoretische methoden op biotechnische systemen voor zover ze tijdens dit onderzoek toegepast en getest zijn. Het blijkt dat met- name toestandsschatten, parametergevoeligheidsanalyse,
parameterschatten en heuvelklimmethoden, belangrijke hulpmiddelen kunnen zijn bij het optimaliseren en regelen van processen. Hierbij dient opgemerkt te worden, dat vooral de kwaliteit van de modellen direct van invloed is op de resultaten die met de bovenstaande technieken behaald worden.
-Introduction
Aim and scope
The aim of this study is to investigate and to propagate the application of control engineering techniques in bioengineering.
The fermentation industry holds a backward position compared with
conventional chemical industries in respect of the application of in-line control and optimization methods. Some plausible reasons are:
- a shortness of adequate dynamic process-models suitable for control purposes especially when scale effects are involved.
- the lack of on-line sensors for substrates, biomass and products; a severe problem mentioned by almost all authors publishing about this subject.
- the major part of the processes in the biotechnical industries is carried out in batch or fed-batch reactors, causing characteristic times to vary.
- the knowledge about various stages of the design of a process is very segregated: the people working on a bench scale are not the persons designing the reactor equipment and the control engineers lack specific knowledge concerning the properties and constraints of both the biochemical processes and the production reactors.
These communication problems can be solved when biochemists,
microbiologists, (bio-)chemical engineers and control -engineers have a common language. A mechanistic mathematical description of the parts of a process can serve this purpose. At the moment, control engineers, for example, build there own dynamic models for control purposes. These models often are black boxes, viz. not based on the knowledge of mechanisms. Microbiologists and (bio-)chemists on the other hand, describe the bench scale reaction kinetics with static models.
Models with a mechanistic background assure the optimal use of the knowledge of all scientists involved . Mechanistic models do have a major drawback:
engineer has to simplify these models by means of a feedback to the people that postulated them. Vice versa, the process engineers must carefully translate the process constraints into specifications for the control systems. So, information interchange plays a very important role.
The sensoring problem often results in poor possibilities to control the process. Temperature, pH and oxygen concentration in the liquid and oxygen and carbon dioxide in the vent gas in the case of an aerobic process are the only process parameters usually measurable on a full scale. A lot of . research is carried out to develop new sensors, however the specifications for industrial use (e.g. sterilizability, stability, reproducability, mechanical strength) are hard to meet.
An other possibility is to introduce mathematical models to calculate missing process variables. Models used for this purpose are called
2
observers. For linear systems, the Luenberger observer is well known. A dynamic description of the relevant processes is of vital importance for control purposes. In some cases an internal structure of the reactor and/or the biomass has to be accounted for. This leads towards the construction of a dynamic mechanistic mathematical model.
In practice, all measurable signals contain noise to a certain degree. Very noisy signals can make the use of special filters necessary. Sometimes the filtering and reconstructional functions are combined: e.g. the Kalman filter . The Kalman filter as such, however, is only applicable to linear processes. Furthermore, the spectral composition of the noise has to be known. Biotechnical processes tend to be highly non-linear and
linearization introduces unacceptable errors. The main advantage of the Luenberger-type observer is the possibility to use non-linear models in the observer. Moreover, the signals acquisited on-line contain little noise. Based upon these considerations, the Luenberger-type observer is used throughout this thesis to estimate non measurable state variables. Often, the model contains parameters with an unknown value. The values of these parameters vary from one fermentation to the other. Since models can never describe long term processes without getting very complicated, the •model parameters even can vary during one and the same process. Before the
nón-measurable process variables (the missing states, in the system dynamic terminology) can be calculated from the model, the unknown parameter values have to be estimated. Here, an additional advantage of the mechanistic model shows up: the parameters in the model represent physical or
physiological properties and therefore should get realistic values. These values can be compared to data found in the literature or determined from separate experiments.
To make things even more complicated, the choise of the structure of the model as a whole can be uncertain. In other words, more than one model can be formulated to describe a process. It has to be decided, in the course of a fermentation, which model is valid or, more correct, which one is most adequate. (In fact switching of models can be necessary because specific knowledge about relevant mechanisms is still lacking or cannot be quantitatively modelled yet.) Once a model is selected by a model
discrimination procedure and all its parameter values are known, it can be used for reconstruction purposes and to design controllers (which can be readily constructed from a good model description).
Another application of mathematical models is the optimization of processes. The biotechnical industries in particular, use a rather conventional approach for this purpose: succesful fermentations are duplicated by using a recipe. Optimization takes place by slightly varying the recipe and afterwards it is determined whether the results have improved or not (using a certain criterion). Since most fermentations take hours and sometimes days or weeks, this is very time consuming. Moreover, the whole procedure has to be repeated with every change in micro-organism (cell or -subsystem), substrate or reactor set-up.
As an alternative, a model of the process can be used to optimize the same criterion. Obviously, the model has to be quite adequate to be sure, that the calculated optimum is close to the optimum of the real process.
The relations between parameter estimation, state reconstruction,
modeldiscrimination, optimization and process control are sketched in fig. 1. In this figure a set-up for two, parallel, models is presented; of course this scheme can be extended to n models, n being determined by the capacity of the computer system used and the complexity of the models. It is a matter of design whether complex, multiparameter models are used (allowing the parameters to vary strongly when a process switches from one regime to.another), or multiple simple models, each with its own working area. Subsets of figure 1 are treated in various parts of this thesis. Their merits will be outlined by applying them to more or less different
active optimization passive optimization Controller
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Organization of this thesis
The work described in this thesis was carried out within the laboratory of bioengineering of the Delft University of Technology. Financial support was obtained from the Innovation Oriented Programme on Biotechnology of the Netherlands Dept. of Economical Affairs.
After the description in the previous paragraph of the objectives of this study and the problems encountered, the chapters to come can be roughly divided into two, parallel readable, sets: the first set (chapters 2,3 and 4) concerning the aerobic conversion of glucose into gluconic acid by Gluconobacter oxydans with the emphasis on the control of the process, the second set (chapters 5,6 and 7) deals with an anaerobic ethanol producing process using a flocculating strain of Zymomonas mobilis; on-line model discrimination and in-line optimization of the process are the main items in this part. These two sets are followed by a chapter applying the methods and software tools to an independent process: the ananerobic purification of waterwater, where state estimation is used to monitor this rather delicate process. In a final chapter, the merits of the methods, which are common use in the system dynamics discipline, will be discussed, when they are applied to biotechnical processes. Contents of the chapters are briefly outlined in the following:
In chapter 2 classical control theory is applied to a gluconic acid batch fermentation in a well-mixed tank reactor. The design of the controllers is based upon a mechanistic mathematical model. Control of the dissolved oxygen concentration using either the stirrer speed or the oxygen/nitrogen ratio in the gas supply is compared.
Chapter 3 extents the experimental set-up to the same conversion in a two reactor system which is a realistic bench scale representation of an
4
industrial scale process showing oxygen gradients . The key problem is to control the non-measurable oxygen level in one reactor by adapting the composition of the gas mixture in the other reactor. This state estimation problem can be solved by means of a Luenberger observer. During the in-line estimates the oxygen level was maintained at a constant level with a
Chapter 4 combines in-line parameter- and state estimation. The controller contains essential time constants for the process, e.g. the residence time in both the reactors. On a production scale neither the ratio of the volumes of the aerated and badly aerated zones nor the circulation flow in the reactor is known. So, these parameters have to be estimated in-line and substituted in the controller and observer equations. Eventually, the controller bases its action upon an estimate of the oxygen concentration in the non-aerated reactor. This completes the development of a controller suitable for an industrial process showing gradients.
Chapter 5 compares two methods for state reconstruction: element balances and a state observer. The process involved is the anaerobic, continuous production of ethanol in an up-flow type reactor with a flocculent strain of the bacterium Zymomonas mobilis. The data-acquisition software is described since it plays a key role throughout the chapters concerning this process. The same data-acquisition programs are used for the elemental balancing software and for the observer. Some stationairy and dynamic situations are investigated.
In chapter 6, model discrimination is applied to the ethanol production process. Three rivaling models are postulated and it is decided on-line which model is most adequate> to describe the process presently. Since both the models contain one or more parameters and non-measurable states, estimation of parameters and states is necessary.
In chapter 7, the process model describing the ethanol production is extended with a submodel of a (stationary) destination unit. With this extension it is possible to define a criterion function according to which the process can be optimized economically. Two inputs are available to influence the process: the influent flow and substrate concentration in this flow. A hillclimber, containing the total model, calculates the optimal settings for both the inputs. It is left to the dynamics of the process to adapt to the new input values. This is defined as passive optimization since no action is taken to force the process to its new optimal state.
In chapter 8, in order to test the methodology developed in the previous chapters, the techniques are applied to an 'independent* process: the
anaerobic purification of lower fatty acid containing wastewater. This process shows many analogies with the ethanol production process. The processes are both continuous; the reactor is of the up-flow type. The gas production can be used to estimate parameters and states. To construct the model, necessary in the observer, hillclirnber and parameter estimator, fluid flow and kinetical experiments have to be carried out. State estimation as a first step to monitoring and optimization of the process is studied in this chapter.
In chapter 9 the conclusions of chapters 2-8 are listed and some general conclusions are stated concerning the potentials of established control engineering techniques, e.g. state estimation, optimization, controller design, if applied to biotechnical processes.
References
1. G.Ch. van Eybergen, personal communication. Delft University of Technology, Delft (1985)
2. D.G. Luenberger, IEEE Trans. Autom. Control, AC-11, 2_,
pp 190-197 (1968)
3. A.H. Jazwinski, Stochastic Processes and Filtering Theory, Academic, New York (1970)
4. N.M.G. Oosterhuis, PhD Thesis, Delft University of Technology, Delft (1984)
COMPUTER CONTROL OF THE DISSOLVED OXYGEN CONCENTRATION DURING A GLUCONIC ACID BATCH FERMENTATION
1 1 2 3
J. van Breugel , G.Ch. van Eybergen , G. Honderd and A.J. Overwater
Computer group. Lab. of Biochemical engineering. Dept. of Chem. S Chem. Technology, Delft University of Technology, Julianalaan 67, 2628 BC Delft, The Netherlands (correspondence address)
2
Lab. of Controlengineering, Dept. of Electrical Engineering, Delft Univ.
of Technology, The Netherlands
Gist-brocades nv. Delft, The Netherlands
Introduction
In this study, results are presented of research concerning the control of the dissolved oxygen concentration during a gluconic acid batch
fermentation. This process is applied to produce gluconic acid from glucose by the bacterium Gluconobacter oxydans. If the dissolved oxygen
concentration becomes too low, the growth of the bacteria and the production rate of gluconic acid are limited. On the other hand, a high concentration of oxygen is useless and control at such a level will only result in high costs, either for power input for the stirrer or for expensive pure oxygen. In this batch process the characteristic times e.g. oxygen consumption time and oxygen transfer time, will not remain constant. A process model can be used to account for these variations. Obviously, when a model is included in the controller structure, the use of an on-line computer is inevitable. However, in the fermentation industry, computers are not as commonly used as
1,2
m the conventional process industry . Besides the varying characteristic times, some other reasons possibly are:
- The processes are complex and highly non-linear which makes controller design more difficult.
- Reliable sensors for a lot of important process variables are lacking, especially on an industrial scale.
- In very large industrial scale reactors often gradients occur. This makes it impossible to determine the spot where a variable to be controlled should be measured.
As a result, more process knowledge and more advanced control engineering techniques are necessary to achieve control of biotechnical processes.
Theory
A model describing the process
It has been shown , that the dissolved oxygen concentration should at least have a value of 20% of the value of air saturation, to guarantee an optimal progress of the process.
In figure 1, the dissolved oxygen concentration and the response of the control
C|(t = o)
m i n . 0 2' t r a n s f e r C( ( s e f p o i n t ) 0 0 ±i* + 8 ±.11 » - t i m e (h)Fig. 1 The profiles of controlled input variable and manipulated variable for a typical expe'riment
variable (e.g. stirrer speed, oxygen concentration in the gas phase) are MAX.02 -TRANSFER
■controlled input variable(N, Cg) Ü2" concentration (Cj)
sketched as a function of time for a typical experiment. At the start of the experiment a minimum stirrer speed is maintained to assure some mixing of the liquid and to prevent exhaustion of the medium surrounding the oxygen electrode. The minimum oxygen concentration in the inlet gasflow is fixed at the concentration in air (21 % vol.). The oxygen uptake rate (OUR) is small and the dissolved oxygen concentration is higher than the setpoint. The OUR increases in time due to growth of the amount of biomass and because of this the dissolved oxygen concentration decreases. When the setpoint is reached, the oxygen transfer rate (OTR) increases in time to compensate the increasing OUR. The oxygen concentration is controlled at the chosen setpoint. When the maximum possible oxygen transfer is reached, the
dissolved oxygen concentration will decrease to a low value and it will stay there until the glucose is completely utilized.
Equation 1 and 2 give the oxygen balance in the liquid. It is assumed that the volume of the liquid is constant (in practice, there is a slight increase in the volume due to the addition of a NaOH solution for pH control).
OTR = k ^ . (^ - C±) (1)
d Cl
— - OTR - r ^ (2)
It is clear that the OTR can be influenced by the k a and the..concentration of oxygen in the gas. The k^a depends on the stirrer speed and the gasflow. This can be described by the following equation:
b c
k a = a'.N .v (3)
The stirrer speed has a greater influence on the k a than the superficial gas velocity has. For this reason, the k a is varied only by changing the stirrer speed. The gas flow will have a constant value. Equation 3 can be rewritten as:
b
k1a = a.N (4)
-The parameter b normally has a value between 1.2 and 2.1 (ref. 4 ) . -The value of b can temporarily lie well outside this range after the addition of an anti-foam agent. From equation 1 it follows that the OTR may be
increased by either increasing the k a i.e. the stirrer speed or the gas phase oxygen concentration C .
The dynamic behaviour of the electrode (fig. 2) can be described by the following equation: dC e dt .(C - C ) 1 e (5)
k has a value of about 0.1 1/s.
first order approximation^
■ electrode response
i r
5 10
- » - time (s)
Fig. 2 Measured and calculated oxygen electrode response
In the model it is assumed that the gas phase is ideally mixed. The dynamics of the gas phase are neglected because the residence time of the gas is small compared with the other time constants (1/k and 1/k a ) . Table
Table 1 Some relevant characteristic times (s)
bacterial growth 7000 mass transfer 10 - 100 sensor response 10 residence time gas 3 sampling period < 10
Design of feedback controllers
The controllers are designed in the Laplace domain. Thus, it is assumed that the controllers are continuous. In practice, this is not the case. However, the results of the design can be applied in discrete controllers provided that the sampling period is significantly lower than the smallest time constant of the process.
Design of controllers using the stirrer speed
Combining eq. 2 and 4, the oxygen balance in this case becomes:
dC ,
d T
= a-
N-
(c" - V -
ro
2 (6)In this case, air is used to aerate the liquid,, so, C is assumed to be 9
constant and C /H is substituted by C". 9
Equation 6 is non-linear in the stirrer speed. Therefore, the equation is linearized around a certain working point and written in perturbation variables, after which Lapace transformation is possible. The following equation results:
s.C^s) = a.b.N*(b 1 ,.(C" - C1).N(s) - k1a*.C1(s) - rQ (s) (7)
N , C and k a respectively are the stirrer speed, the dissolved oxygen concentration and the oxygen transfer coefficient at the point where linearization has taken place.
a.b.N ( '.(C" - C ).N(s) r (s)
C . ( s ) = ■ ; 2 (8)
(s + k a ) (s + k a )
The equation for the sensor in the Laplace domain is:
s.C (s) = k .(C,(s)- C (s)) (9)
e e l e
C (s) = ^ , . C.(s) (10) e s + k 1
In figure 3, the equations of the process and the sensor are given in a block diagram. CON(s) stands for the transfer function of the controller. Setp(s) is the setpoint and E(s) is equal to Setp(s) minus Ce(s). The oxygen uptake by the bacteria is included into the block diagram as a disturbance of the system output.
A very simple controller consists of a pure integration:
f
1Time domain: N(t) = N(0) + K.E(t) dt (11)
0'
Laplace domain: N(s) = K. (12)
In all controllers, it is necessary to have at least one integration to compensate for the exponentially increasing OUR.
SETP (s) ,x-x E (s)
RO g(5) ,
N(s) .b.N?(c*-cf I
7-*è
Cl (s)Fig. 3 Block d i a g r a m for c o n t r o l w i t h the s t i r r e r speed
T h e t r a n s f e r f u n c t i o n of the c o n t r o l l e r is in t h i s c a s e e q u a l t o K / s . T h e transfer function of the c l o s e d s y s t e m , g i v e n b y C . ( s ) / S e t p ( s ) , can be c a l c u l a t e d : S e t p ( s ) *(b-l) a.b.N .(C11- C )
*
(s + k a ) *(b-l) a.b.N ' . ( e - C, ) k 1 e (13) (s + k a ) (s + k )The characteristic equation of the closed system is in this case equal to:
,*(b-l)
a.b.N AC"- C, ) k
1 . e = 0 (14)
(s + k,a ) (s + k )
1 e
The position of the poles (viz. the solutions of the characteristic equation for s) and thus the dynamic behaviour of the system can be chosen with the parameter K.
the pole of the process, given by s = - k a, increases as a result from about 0.01 1/s to 0.10 1/s.
A pure integration is from a control technical point of view not desirable because of the negative effect on the stability of the system. For this-reason, the following (PI-) controller can be chosen to compensate for the pole of the process:
„, . K.(s + k*a) K.k'a
k~a is an estimation of the real value of the k a. k a is calculated from measurements of the gas phase according to equation 16:
4> .(C . - C )
k > = g q'l n q (16)
1 C
v.(
f - c ^
In fact, the k.a refers to the total volume of the broth, that is, the volume of the liquid plus the volume of the gas hold-up. In most cases, however, the volume of the gas hold-up is small (5 % vol. or less) compared with the volume of the liquid.
If it is assumed that the k.a-pole is compensated ideally, the following characteristic equation results:
1 + -.a.b.N*( b'1 ).(C"- C , ) . ke = 0 (17)
1
mr
Again, it is possible to choose the position of the poles with the gain of the controller K. From the gas phase measurements the controller gain can be updated in the course of the process.
Design of controllers using the gas phase oxygen concentration
The dissolved oxygen concentration is now controlled by the concentration of oxygen in the gas phase. The stirrer speed, has a constant value. In this case the oxygen balance is linear. In the Laplace domain the oxygen balance
s.C (s) = k a.(Cq( s )- CA s ) ) ~ r (s)
H 2
(18)
The block diagram is given in figure 4.
SETPIsl^o, Ed Ce(s) RO ?ls) Cg(s)
T*&
Cl(s) ..Fig. 4 Block d i a g r a m - f o r c o n t r o l w i t h t h e g a s p h a s e o x y g e n c o n c e n t r a t i o n , W h e n an i n t e g r a t i n g c o n t r o l l e r is u s e d , t h e c h a r a c t e r i s t i c e q u a t i o n is e q u a l t o :i
+*. v
e = 0 (19) H.(s + kna (s + k ) 1 eWhen a controller with an integration and a compensation of the k a is used, the characteristic equation is:
1 + K .kla. ke = 0 s H (s + k )
(20)
Again, the poles of the closed system can be chosen by the gain of the controllers. The k.a is kept
process are constant as well.
The use of a model in the controllers
As already stated, the OUR is a disturbance of the system. This disturbance is well known and it is evident to use this knowledge in the control of the process.
The aim of the control of the process was to assure an optimal growth and product formation. Therefore, if we can keep the oxygen concentration at its setpoint, it can be assumed that the growth rate is constant. The oxygen uptake by the bacteria can be derived as follows:
dC
(21) dt
U.C • (22)
Combining equation 21 and 22 and integrating the differential equation:
C (t) = C (O).exp(u.t) (23)
Assuming the oxygen consumption directly coupled to growth:
U-C 0„ Y Y 2 ox ox (24) Rewriting equation 24: Y .r (t) ox O C (t) = " (25)
Equation 25 can be substituted in eq. 23 for t = t and t = 0 s.:
r0 ( t ) = r0 (°'-exP(M-t) (26)
During the control, C (t) is in the ideal case equal to the value of the setpoint and dC,/dt is equal to zero.
a.Nb(t).(C"-setp) = r (O).exp(U.t) (27) 2
According to this equation, the increase in the stirrer speed from t = 0 is equal to:
b
= exp( .t) or N(t) = N(0).exp(U.t/b) (28)
In the same way, it is possible to show that the following equation is valid when the oxygen concentration in the gas phase is used to control the process:
C (t) = H.setp + (C (0) - H.setp).exp(U.t) (29) g g
Theoretically, it should be possible to control the process with the
equations 28 and 29. In practice, it always is necessary to use feedback to some extent, because a model never is perfect and model parameters can vary. However, the importance of the feedback part can be reduced when a model is applied.
Materials and methods
The bacterium Gluconobacter oxydans ATCC 621H is maintained by regular transfers on solid media, consisting of 1% wt. yeast extract, 2% wt. glucose, 2% wt. calcium carbonate and 2.5% wt. agar. Preceeding each experiment a small amount of this biomass is brought into a flask containing
100 ml of a liquid medium. This exists of 0.2% wt. yeast extract, 11% wt. glucose and 1% wt. calcium carbonate. After 12 hours of growth at 30 °C, this 100 ml. inoculum is transferred to a flask, containing 1000 ml of liquid medium. After another growth cycle (12 h., 30 °C) this inoculum was transferred to the fermenter (15 1.; Applikon bv, Schiedam, The
Netherlands). The medium of the fermenter consists of 0.4% wt. yeast extract and 10% wt. glucose. The total volume of-liquid in the fermenter is about 11 litres. The fermenter is equipped with sensors for the
measurement of the stirrer speed, the temperature, the pressure, the pH, the dissolved oxygen concentration (Biolafitte oxygen electrode) and the presence of foam (figure 5 ) . The oxygen concentration in the off-gas is
-measured using a paramagnetic analyzer (Taylor/Servomex OA 540). The pH and temperature are controlled with dedicated analog closed loop controllers at 5 and 30 °C resp. The gasflow in most cases is 10 1/min and the stirrer speed is adjustable between 0 and 900 rpm.
The desired values of the stirrer speed, the gasflow and the oxygen concentration in the gas can be adjusted by the computer. For the
adjustment of the oxygen concentration in the gas, two mass-flow controllers are present; one for oxygen and one for nitrogen gas (Brooks 5850). All computer hardware was manufactured by Hewlett Packard (for a detailed description see ref. 5 ) . Data acquisition and control programs are running on the HP 1000/A 600 micro computer. On-line parameter estimation software is available on the faster HP 1000/A 900 mini computer.
Conductivity sensor Ifoamltontroll
. . .
N pH \0
0 O C o o1—1
1—1
0
o° °
\ o o °' H—
o o o o o o o c 0 o oD
o°
a'
0 o V offgas analysis Cg / - -c" - 7 "h
O
Results and discussion
The results of experiments with several controllers are presented in this paragraph. In these experiments, the controller gain is generally set to a value causing a theoretial overshoot of 5% after a step in the setpoint.
In figure 6, the result of an experiment with an integrating controller based upon the stirrer speed is plotted. In this figure, the dissolved oxygen concentration-and the stirrer speed are shown. The controller is in discrete form equal to:
N(nT) = N((n-1)T) + K.T.E(nT) (30)
K is the gain of the controller, which was calculated with equation 13 and increased by a factor 20 during the experiment. The sampling period, T, was 10 s.
In figure 7, the result of another experiment with an integrating controller is given. Here, the dissolved oxygen concentration was controlled by the - oxygen concentration in the gas. The stirrer speed was 300 rpm and the k a
was about 0.01 1/s. For this case, the discrete controller can be given by:
C (nT) = C ((n-l)T) + K.T.E(nT) (31) 9 9
The sampling period was 10 s. In the beginning, the gain of the controller had the value for an overshoot of 5%. The gain increased during the experiment by a factor 5 to avoid large deviations of the dissolved oxygen concentration from the setpoint.
As can be seen in figure 7, the oxygen concentration in the gas increased from about 20% to 100%. The dissolved oxygen concentration showed large variations at the end of the experiment, because large gradients occurred in the liquid.
The discrete implementation of the controller with an integration and a compensation is given below:
-1.0-1
TO•o
ai M B i_o
c
0.0
- O 2 - C O N C . [ 0 - 1 0 0 % ]
(100%= air saturation)
s t i r r e r speed[0-1000rpm]
/
setpoint
0.0
1 r
-i 1 1 1 rtime (h) ►
7.0
Fig. 6 Integral control action based upon the stirrer speed.
10-1
° 2 CONC. [ 0 - 1 0 0 % ] (100%= air saturation)
0 2 GAS (0-100%)
TO>
O0.0
7^wv=^^7^7=*g>tr
setpoint
0.0
l I I I I I I
time (h) ^ ~ i».1
Fig. 7 Integral control action based upon the gas phase oxygen concentration.
°2 CONC.IO-100%1 (100%= air saturation)
10-1
- - 0 2 GAS (0-100%
T3 OJ Oc —
0.0
,,;J '1 1 r
0.0
- 1 r—
time (h)
i r
setpoint
3.5
Fig. 8 Results of a controller with an integration and a compensation of k^a Control with C
1.0
J3 ro-Ë
u
o —
0.0
O 2 - C 0 N U 0 - 1 V ] s t i r r e r speed [0-1000rprn]
v~—
0.0
1 1 1 r
time (h) —
X
setpoint
1 r
5.5
Fig. 9 Results of a controller combining a feedforward and a feedback control action with the stirrer speed. Sampling period: 10 s.
-C (nT) = -C ((n-l)T) + K.(E(nT) - E((n-1)T) + K.T.k,a.E(nT) (32)
9 9 1
In figure 8, the result of an experiment with this controller is given. The stirrer speed was 300 rpm and the k a about 0.01 l/s. The sampling period was 5 s. The gain of the controller could be much higher than the gain of the integrating controller. This resulted in a smaller deviation from the setpoint.
In figure 9, again the result of control with the stirrer speed is shown. This time, however, the controller consisted of the model equation, given by equation 21, and an integrating feedback controller. The sampling period was 10 s. The gain of the feedback controller was 10 times lower than the value, which was used during the experiment plotted in figure 6.
Nevertheless the oxygen concentration is kept well at its setpoint.
In figure 10, another result of an experiment using the model has been is presented. In this case, the dissolved oxygen concentration sampling period was extended to 5 minutes. The measurements were used to adapt the
parameters of the model i.e. U/b. Although fluctuations occured, the oxygen concentration never shows severe deviations from the setpoint. An overview of the experimental results can be found in table II. In this table the results can also be found of the controllers of which no figures have been presented.
1.0-1
J 3 (O
f5 * - I
0.0
°2-CONC [ 0 - 1 V ] st-irrer speed [0 -1000 r p m ]
V
- s ^ " ^ *,~ » ^
setpoint
0.0
1
I I
time (h)
.5,5
Fig. 10 Results of the same controller as in figure 9.
Adaptation of a model parameter. Sampling period: 300 s.
Table II Overview of experimental results
(mod=model; f.b.=feedback; n.a.=not applicable)
control control fig sample variable action time (s)
steady state error (% of setpoint) theoretical experimental N N C g
c
g N N C gc
i PI i PI mod+f mod+f mod+f mod+f b. b. b b. 6 -7 8 9 10 -10 10 10 5 10 300 -5 7 4 8 3 n.a. n.a.Conclusions
From the results discussed above, it can be concluded that control of the ** dissolved oxygen concentration with the stirrer speed as well as control
using the oxygen concentration in the gas, are equally satisfactory. Both methods can be used on an industrial scale. Control using the gas phase oxygen concentration is less preferable since expensive pure oxygen is involved.
It can be concluded that the feedback controllers all performed well. The controllers with a compensation of the k a and an integration gave better results than controllers with an integration only. It can be concluded that the mechanistic model as proposed is a convenient and satisfactory way for the design of feedback controllers.
The use of feedforward control to compensate the well know oxygen uptake in combination with a normal feedback controller, theoretically is preferable over a pure feedback controller. It could be shown that this was also true in practice.
Another advantage of the use of a model is that the design of the feedback part of the controller may be less optimal.
This can be of importance for processes on a large scale. Here it is impossible to speak of one, homogeneous, oxygen concentration in the liquid. Hence, a conventional feedback controller e.g. using measurements in the neighbourhood of the stirrer will give bad results. Oosterhuis has shown that the process on a large scale can be simulated in a two compartment set-up on a laboratory scale. In one compartment, the oxygen transfer is high and in the other compartment, the oxygen transfer is very low. There is a circulation flow between the two compartments. These compartments represent the area near the stirrers and the bulk of the liquid respectivily. This model set-up is presently in use for the design of controllers applicable to the process on a large scale.
Nomenclature
a, a', b and c are constants
C = sensor reading oxygen cone. (mol/m )
6 3
C = oxygen cone, in gas phase (moi/m ')■
g 3
C . = oxygen cone, inlet qas flow (mol/m )
g,in * 3
C, = dissolved oxygen concentration (mol/m ) 3 C = biomass concentration (C-eq/m ) CON ~ controller transfer function
C" = oxygen cone, for air saturated water (mol/m ) E = error signal
H = Henry coefficient (mol/mol) k = velocity constant of the sensor (1/s)
((1/k ) is the time constant of the sensor) e
k a = specific vol. mass transfer coefficient (1/s) K = controller gain
N = stirrer speed (s) OTR = oxygen transfer rate (mol/(m .s))
r = oxygen uptake rate (OUR) (mol/(m..s))
2 3 r = growth rate of bacteria (C-eq/(m .s))
T = sampling period (s) superficial gas velocity (m/s)
3 V = total volume of the broth ■ (m )
Y = yield of biomass on oxygen (C-eq/mol) U = specific growth rate, (1/s) (J) = volumetric gas flow (m /s)
References
1) Proceedings of the First IFAC Workshop (Modelling and Control of Biotechnical.Processes), Editor A. Halme, Helsinki, August 17-19, 1982 2) Computer Applications in Fermentation Technology (Proceedings of the
third international conference on computer applications in s
fermentation technology, Manchester, August 31 - September 3 1981), London, Society of Chemical Industry, 1982.
3) Oosterhuis, N.M.G., Scale-up of Bioreactors (a scale down approach), Thesis, University of Technology Delft (1984).
4) Riet, K van 't, Ind. Eng. Chem. Process. Des. Dev., 18 (1979), 367-375. 5) Breugel, J. van, P.R. van Driest, G.Ch. van Eybergen, R.J. van Heese and
B.P.J.M. Ramakers, in Innovations in Biotechnology, 331-351, 1984, Elsevier Science Publishers bv Amsterdam, E.H. Houwink and R.R. v.d. Meer editors.
COMPUTER CONTROL OF AN AEROBIC BATCH PROCESS IN A TWO REACTOR SYSTEM
J. van Breugel * G.Ch. van Eybergen , G. Honderd , A.J. Overwater and 2
H.B. Verbruggen
Computer group. Lab. of Biochem. Eng., Dept. of Chem. and Chemical Technol., Delft univ. of Technol., Julianalaan 67, 2628 BC Delft, The Netherlands (mailing address).
2
Lab. of Control Eng., Dept. of Electrical Eng., Delft Univ. of Technol.,
Delft, The Netherlands
Gist-brocades nv. Delft, The Netherlands
Introduction
One of the main research items in the laboratory of biochemical engineering is the mathematical modelling of biotechnical processes. In describing these processes, empirical or mechanistic models can be used. Empirical models lack a physical foundation and are not suitable for extrapolation purposes. It is our intention to develop control algorithms applicable to bench scale as well as industrial scale reactors, therefore attention is focused on mechanistic modelling. It should be emphasized that only those mechanisms relevant to the control of the process have to be included in the model. Otherwise, a highly descriptive model, that cannot be verified and is too complex to use in a control structure, results. Secondly, all models and the controllers containing them, should be tested in practical
situations with real processes. At the moment, the majority of the publications dealing with the modelling and control of biotechnical
processes describe controllers containing a model, which are used to control another, often more complex, model of the same process.
-An adequate process model has several applications:
- the estimation of unknown parameters, e.g. kinetic, mass transport, hydrodynamic parameters.
- the estimation of non-observable state variables. It is a well known fact, that there is a tremendous lack of suitable sensors. - the optimization of a certain performance index defined in the
model, that represents a desirable state of sequence of states (trajectory).
At the moment three processes are being studied:
- the production of gluconic acid from glucose in an aerobic batch process
- the production of ethanol from glucose in an anaerobic continuous process
- the purification of wastewater in an up-flow anaerobic sludge blanket reactor
In this paper the.gluconic acid production process will be highlighted. During this process gluconic acid is produced from glucose by the bacterium Gluconobacter oxydans. If the dissolved oxygen concentration becomes too* low, the growth rate of the bacteria and the production rate of gluconic acid are limited. On the other hand a high concentration of oxygen is useless and control at such a level will only result in high costs, either for power input for the stirrer or for expensive pure oxygen. The practical importance of this research is in the field of optimal production with respect to minimal costs for oxygen transfer.
Theory
Process description
was used. In this reactor several strategies were tested: P# PI and PID controllers both applied to the stirrer speed and the composition of the inlet gas flow. A simple model describing the dynamics of the process
2 combined with a simple feedback controller proved to be well satisfying . On an industrial scale the stirrer speed cannot simply be changed, so oxygen enrichment of the inlet air flow is used to supply the bacteria with enough oxygen. Moreover, gradients in the oxygen concentration occur in a full scale reactor, A maximum productivity however, only is reached when a sufficient oxygen level is realized in the entire reactor volume. On a bench scale this can be simulated in a two reactor system (fig. 1 ) . One reactor is being stirred and aerated, in the other reactor only stirring takes place. The two reactors are interconnected by a pump simulating the circulation flow induced by the impellers on a large scale.
electrode X off gas oxygen
cp
D-electrode 1ie») rfz
I • - ~ l ^
-®-
J~~-oxygen analyser off gas ( c9 ' C, V, C,
C J
: E O
: E O
-oxygen nitrogenFig. 1 The experimental s e t - u p .
-Development of a model
Based upon mass balances for the two reactor system the following model equations can be derived for the process:
The biomass:
■ST * U c ( 1 )
dt max x
For the aerated volume:
d Cl «"c
St " v*
(V V
+ 0TR"
ri
(2)For the non-aerated reactor:
dc «j,
-^ - ^ ( Cr C2) - r2 (3)
The oxygen transfer rate in the aerated reactor:
OTR = k a (-T? - C, ) (4) 1 M 1
The d i s s o l v e d oxygen i s assumed t o be a t a l e v e l t h a t permits the b a c t e r i a
t o grow a t a maximum r a t e . As a l r e a d y s t a t e d there i s a d i r e c t r e l a t i o n
between growth and oxygen consumption:
M
cm a X X - r ( 0 ) e x p ( u ( t - t _ ) ) ( 5 ) 1 2 max Y max 0
The sensors used are an oxygen electrode and a gasphase oxygen analyser. Assuming the gasphase in both the reactors to be mixed ideally, the following mass balance holds:
dC
__a
.
d t*
= a (c .
-V g , i n g- c )
gv
- OTR — V g (6)On the analogy of the full-scale reactor, where the dissolved oxygen
concentration is measured near the stirrer, an oxygen electrode is placed in the aerated reactor. Its response is described using a first order
approximation:
d Ce
IT
= ke
(C1
' V
(7)The values of some relevant hydrodynamic and kinetic parameters are listed in table I.
Table I Values of relevant parameters
H k e kla V, 1
v.,
2 V g Y ox*
c<t>
g V max Tl T2 S e t p=
=
==
=
=
=
=
=
=
=
=
=
3 3 . 0 . 1 0 . 0 5 6 - 3 2 . 5 10 - 3 8 . 0 10 - 3 22 10 0 . 2 5 2 . 7 10 3 . 3 10 - 4 1.4 10 10 30 - 40 0 . 0 5 - 1 s - 1 s m3 m3 m3 C - e q . / m o l e m / s 3 m / s - 1 s s s m o l e / m3Materials and methods
The bacterium Gluconobacter oxydans ATCC 621H is used in all experiments. A Biolafitte/Applikon bv 15 S fermenter is used as the larger reactor, with a liquid volume of 10 1. The volume of the smaller reactor is 2.5 1. The medium in the fermenters consists of 0.4% w/w yeast extract and 10% w/w glucose. The experimental set-up is shown in Fig. 1.
The pump, simulating the circulation flow, has a capacity of 0-20 1/min. The exact amount of liquid that circulates during an experiment is
determined with acid pulse-pH response measurements, using special software, that allows large numbers of pH response curves to be fitted with fluid flow models.
Temperature and pH are controlled with dedicated analog closed loop controllers at values of 30 °C and 5 respectivily. The flows of oxygen and nitrogen can be adjusted separately, using mass-flow controllers (Brooks 5850). The total gasflow is kept to a value of 2 1/min. The oxygen concentration in the liquid is determined with a Schott and a Biolafitte electrode. The oxygen concentration in the off-gas is measured using a paramagnetic analyzer (Taylor/Servomex OA 540).
Computer hardware of Hewlett Packard is used . Data acquisition and control programs are running on the HP1000/A600 microcomputer. On-line
parameter estimation and state observer software are available on the faster HP1000/A900 minicomputer. The two computers are interconnected using DS1000/IV networking software. All applications software is self-designed and written in FORTRAN 77.
Design of the controllers
full-scale reactor. Since it is our final goal to design a controller suitable for application to an industrial scale, part of our knowledge of the bench scale system should not be used to develope a controller. The distribution of the reactor volume over an aerated and a non-aerated part and the size of the circulation flow are process parameters that are known in a two reactor set-up, but cannot be determined in a large scale reactor. The same holds for the oxygen concentration in the non-aerated volume.
Some intermediate steps will be necessary before such a (pseudo-) large scale controller can be realized.
Control based upon the oxygen electrode in the non-aerated reactor
Equations 1 and 2 are Laplace transformed ' :
C (s) + T, k.a C <s)/H - T r « ,„, _ _£ 1 1 g 1 max C1( S ) - sT l + T ^ a ♦ 1 (8)
C(s) - T
r ^ , . 1 2 max c2
<s)= — ^ m —
(9)T and T are the mean residence time in V and V respectively. The two last terms in eq. 8 and 9 are assumed to be a disturbance of the process and are omitted. C (s) has to be cc
function results from eq, 8 and 9:
C2(s) T1 k^/H
and are omitted. C (s) has to be controlled by C (s), this transfer
V
S ) Tl
T2
S2 + S ( T1
T2
kl
a + Tl
+V
+ Tl
kl
a(10)
To calculate the poles of the process, T , T and k a have to be known. In the experimental configuration used, T = 10 s, T = 40 s and k a = 0.05 s So, the poles of the process are P = - 0.0075 s and P = - 0.17 s. The small pole makes it difficult to control the process. It is logical to design a controller compensating this pole. Furthermore, an integration is included:
