www.elsevier.com/locate/jprocont

Journal of Process Control 17 (2007) 595–606

Oxygen control for an industrial pilot-scale fed-batchfilamentous fungal fermentation

L. Bodizs a, M. Titica b,1, N. Faria c, B. Srinivasan a,2, D. Dochain b, D. Bonvin a,*

a Ecole Polytechnique Federale de Lausanne, Lausanne, Switzerlandb CESAME, Universite Catholique de Louvain, Louvain-la-Neuve, Belgium

c Novozymes A/S, Bagsvaerd, Denmark

Received 6 February 2006; received in revised form 25 January 2007; accepted 28 January 2007

Abstract

Industrial filamentous fungal fermentations are typically operated in fed-batch mode. Oxygen control represents an important oper-ational challenge due to the varying biomass concentration. In this study, oxygen control is implemented by manipulating the substratefeed rate, i.e. the rate of oxygen consumption. It turns out that the setpoint for dissolved oxygen represents a trade-off since a low dis-solved oxygen value favors productivity but can also induce oxygen limitation. This paper addresses the regulation of dissolved oxygenusing a cascade control scheme that incorporates auxiliary measurements to improve the control performance. The computation of anappropriate setpoint profile for dissolved oxygen is solved via process optimization. For that purpose, an existing morphologically struc-tured model is extended to include the effects of both low levels of oxygen on growth and medium rheological properties on oxygen trans-fer. Experimental results obtained at the industrial pilot-scale level confirm the efficiency of the proposed control strategy but alsoillustrate the shortcomings of the process model at hand for optimizing the dissolved oxygen setpoints.� 2007 Elsevier Ltd. All rights reserved.

Keywords: Bioprocesses; Filamentous fungal fermentation; Rheological properties; Oxygen control; Dissolved oxygen setpoint; Cascade control

1. Introduction

Filamentous fungi are among the most frequently usedcell factories in the fermentation industry. Their successis due to the relatively well-established fermentation tech-nology and the versatility of strains available, thus allowingthe production of a wide variety of products: primarymetabolites, antibiotics, enzymes, and proteins [1].

Traditionally, filamentous fungal fermentations areoperated in fed-batch mode, with the feed rates beingmanipulated manually. As a result of the filamentous struc-

0959-1524/$ - see front matter � 2007 Elsevier Ltd. All rights reserved.

doi:10.1016/j.jprocont.2007.01.019

* Corresponding author. Tel.: +41 21 693 38 43; fax: +41 21 693 25 74.E-mail address: dominique.bonvin@epfl.ch (D. Bonvin).

1 M. Titica is currently with Universite de Nantes, CRTT, BP 406, 44602Saint-Nazaire, Cedex, France.

2 B. Srinivasan is currently with Ecole Polytechnique de Montreal,Montreal, Canada.

ture of the biomass, its concentration is considerablyhigher than in other biological processes. High biomassconcentration induces high viscosity, which makes oxygentransfer difficult [2]. In addition, other factors such as theinitial properties of the biomass (inoculum) can lead to sit-uations with insufficient oxygen and lower performance ofthe microorganisms. The goal of this work is to propose anoxygen control strategy that ensures high productivity andlimits the risk of running into oxygen limitation.

Usually, the level of dissolved oxygen (DO) is controlledby manipulating the airflow or the stirrer speed. However,when applied to large-scale industrial reactors, which is theultimate goal of this work, this strategy often leads to unac-ceptable power consumption. Additionally, this culture israther shear sensitive because of the filamentous structureof the microorganisms. Hence, in these cases, the dissolvedoxygen concentration can be controlled by limiting itsconsumption [3–5]. This is achieved by manipulating the

596 L. Bodizs et al. / Journal of Process Control 17 (2007) 595–606

substrate feed rate, i.e. the feed of the substance being oxi-dized. Both manual and PID control have been used forregulating the dissolved oxygen concentration, but therange in which this concentration could be confined isfairly wide. One way to cope with this difficulty is to oper-ate with a sufficiently high setpoint for oxygen concentra-tion so that, despite these large variations, oxygenlimitation does not occur. However, this policy corre-sponds to feeding less substrate, which reduces productionand is economically unacceptable. Hence, the objective isto control oxygen concentration tightly at a reasonablylow setpoint so that oxygen limitation can be avoided with-out sacrificing production. Consequently, the objective ofthis project is twofold: (i) optimization to determine a set-point profile that maximizes production, and (ii) control tofollow this setpoint while avoiding oxygen limitation.

The first objective is addressed by solving a model-basedoptimization problem. A first-principles model of the fila-mentous fungal (a-amylase producing strain of Aspergillus

oryzae) fermentation process is proposed in [6], while adata-driven model is described in [7]. Here, the former isutilized. This first-principles model is morphologicallystructured and provides a description of biomass, glucoseand enzyme concentrations of submerged cultures of fila-mentous fungi without oxygen limitation. However, sinceoxygen dynamics are crucial in the operation of fed-batchcultivations, the influence of dissolved oxygen limitationon the biomass and enzyme production needs to be incor-porated. These effects are included in the model, which isfitted and validated on experimental data from fed-batchfermentations provided by Novozymes, Denmark.

The control objective is met by a cascade-type control-ler. The poor performance of standard PID control canbe attributed to the fact that it only uses information onthe controlled variable, though much more information isavailable via auxiliary measurements such as the oxygenuptake rate (OUR) and carbon dioxide evolution rate(CER). Hence, the idea to incorporate some of these mea-surements in the control algorithm. By analyzing the struc-ture of the process model, a simple cascade control schemeis proposed, whereby the outer-loop oxygen controller pro-vides the setpoint for the OUR/CER signal that is con-trolled in the inner loop.

Experimental results show that the setpoint chosen bymodel-based optimization is not appropriate for the realprocess. Though the model was fitted and validated onexperimental data, its extrapolative power remains poordue to plant-model mismatch. However, the cascade con-troller is quite effective in keeping the dissolved oxygen ina tight range.

The paper is organized as follows. Section 2 describesthe process under consideration and its operation in indus-try. Section 3 details a first-principles model of filamentousfungal fermentation and develops oxygen transfer relation-ships. Oxygen control is considered in Section 4, with opti-mization to determine the DO setpoint and cascade controlfor its regulatation. Section 5 presents experimental results

carried out in a pilot plant at Novozymes. Finally, conclu-sions are provided in Section 6.

2. Process description and industrial practice

2.1. Fungal fermentation

The process studied in this paper is the a-amylase pro-duction by Aspergillus oryzae. The same substrate is con-sumed for both biomass growth and enzyme production.The main difficulty with this process is oxygen limitationin the liquid phase. This depletion is usually caused by highbiomass concentration, which, due to its filamentous struc-ture, increases the viscosity and makes oxygen transferdifficult.

2.2. Current operation

The fermentation at Novozymes Pilot Plant, (Bagsv-aerd, Denmark) is carried out in a 2500 L stirred vessel.pH is controlled through dosing ammonia (g) and phos-phoric acid. The fermenter is aerated at the constant rateof 1 vvm and agitation speed of 275 rpm. Temperatureand pressure are kept at a constant level by the processcontrol system DeltaV, from Fisher Rosemount.

The typical way of operating the fermentation process ispresented in Fig. 1. For the sake of confidentiality, theexperimental results have been normalized and thus nomeasurement units are presented. The substrate feedingpolicy takes into account the problem of oxygen limitationand consists of:

(1) a batch or growth phase, during which the substrateconcentration is reduced from a high initial value toits operational range,

(2) a linearly-increasing feed rate whose role is to avoidoxygen limitation in the early phase of the fed-batch,and

(3) a ‘constant’ feed rate that is chosen in order to exactlyfill the reactor in the remaining operation time andkeep the dissolved oxygen around the desired valueDOdesired = 25.

As can be seen in Fig. 1, the range of dissolved oxygen isfairly wide (20–40%). Also, towards the end of the batch,increasing the feed rate causes oxygen limitation. A largerfeed rate means more biomass, higher viscosity and thusreduced oxygen transfer. This phenomenon has beenencountered and analyzed by the biologists in Novozymes.It can be explained as follows. Once under oxygen limita-tion, the biomass changes morphology, whereby the viscos-ity of the medium increases significantly. However, thisincrease in viscosity reduces oxygen transfer even more.This positive feedback effect leads to lower and lower oxy-gen levels and eventually to the death of the microorgan-isms. Hence, if tight oxygen control is not ensured, therisk of running into oxygen limitation is very high.

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

OU

R

Time

0 0.2 0.4 0.6 0.8 1

0

20

40

60

80

100

Time

DO

0 0.2 0.4 0.6 0.8 1

0

0.2

0.4

0.6

0.8

1

Time

Feed flo

w r

ate

0 0.2 0.4 0.6 0.8 15

6

7

8

Time

pH

Batchphase

Constantfeed

DOdesired

= 25

Linearfeed

Fig. 1. Experiment I – Current operation in manual mode with threephases (batch operation, linearly-increasing feed, constant feed).

L. Bodizs et al. / Journal of Process Control 17 (2007) 595–606 597

2.3. Measurements

The measurements available are the volume V, the vis-cosity g, the dissolved oxygen pressure DO, the aerationrate Qg, the amount of oxygen consumed D[O2], and theamount of carbon dioxide produced D[CO2].

The volume is calculated from weight measurements,assuming constant density throughout the fermentation.The viscosity is determined by a viscosimeter Hydramo-tion, York England. DO is determined by an electrodeIngold, from Mettler Toledo. The oxygen and carbon diox-ide concentrations in the exhaust gases are determined by amass spectrometer VG Prima dB, from Thermo.

The oxygen uptake rate OUR and the carbon dioxideevolution rate CER are determined from gas analysis.The inlet flow rate is measured, as are the mass fractionsof oxygen and carbon dioxide in the inlet and the outletflows. By using these quantities and a nitrogen (inert) bal-ance, the volumetric output gas flow rate Gout can be deter-mined as follows:

GoutyN2;out ¼ GinyN2;inð1Þ

Gout ¼ Gin

1� yO2;in� yCO2;in

1� yO2;out � yCO2;out � yW;out

ð2Þ

where

Gout volumetric output gas flow rate (nL/h)yN2;out output mass fraction of nitrogenGin volumetric input gas flow rate (nL/h)yN2;in input mass fraction of nitrogenyO2;in input mass fraction of oxygenyO2;out output mass fraction of oxygenyCO2;out output mass fraction of carbon dioxideyW,out output mass fraction of water

The output water mass fraction can be calculated from thedilution of oxygen measurement, by purging the reactorwithout reaction [8]:

yW;out ¼ yO2;in� yO2;out ð3Þ

Once the output gas flow rate has been computed, OURand CER can be determined from balance equations with-out accumulation terms:

OUR ¼GinyO2;in

� GoutyO2;out

Vq

MO2

ð4Þ

CER ¼GoutyCO2;out � GinyCO2;in

Vq

MCO2

ð5Þ

where q is the average density of the gas flow, while MO2

and MCO2are the molecular weights for oxygen and carbon

dioxide, respectively.Note that, in general, an acceptable approximation is to

simply consider OUR � OTR, since the solubility of oxy-gen is very low [9]. Typically, the same does not hold forCER and CTR since the solubility of carbon dioxidedepends on the physical and chemical properties of themedium, such as temperature and pH. However, since herethe fermentor is operated at constant temperature, pressureand pH in the fed-batch phase (Fig. 1), it can be assumedthat the rate at which CO2 is formed by microbial metabo-lism corresponds to the carbon dioxide transfer rate andthus CER � CTR.

3. Filamentous fungal fermentation model

In this section, the influence of dissolved oxygen is incor-porated within the kinetic equations using Monod expres-sions, and an additional state – for dissolved oxygen – isintroduced in the model.

598 L. Bodizs et al. / Journal of Process Control 17 (2007) 595–606

3.1. Morphology and rate expressions

Growth kinetics. The morphologically structured modelproposed by [6] is based on the division of the biomass intothree different compartments:

• Active region (Xa) – responsible for the uptake of sub-strate and growth of the hyphal elements. It is assumedthat only the active region is responsible for enzymeproduction.

• Extension region (Xe) – responsible for new cell wall gen-eration and extension.

• Hyphal region (Xh) – the degenerated part of the hyphalelements that is inactive.

The macroscopic reactions for growth and production canbe expressed as:

S þO2!xa X e ð6Þ

S þO2!xe X a ð7Þ

X a ! X h ð8ÞS þO2!

xa P ð9Þ

where S stands for the substrate (glucose), O2 for the dis-solved oxygen and P for the product (a-amylase).

The corresponding kinetic expressions read:Branching (Eq. (6)):

q1 ¼ xaDO

DOþ KDO

k1satðsþ Ks1Þ

ð10Þ

Growth of the active region (Eq. (7)):

q2 ¼ atxe

DO

DOþ KDO

k2s

sþ Ks2

ð11Þ

Differentiation (Eq. (8)):

q3 ¼ k3xa ð12ÞThe specific growth rate of total biomass is:

l ¼ q2

xt

ð13Þ

where xt = xe + xa + xh represents the total biomass con-centration, xe, xa and xh are the concentrations of theextension, active and hyphal zones, respectively, s andDO are the substrate and dissolved oxygen concentrations,at represents the number of tips per unit mass of the exten-sion zones. The parameter at is described as a function of l(see [6,10] for details concerning the morphological model).The kinetic expressions and the model parameters are pre-sented in Appendix A.

Specific rate of enzyme production. Enzyme productionin filamentous fungi is a classical example of growth-asso-ciated product formation. The enzyme production is sub-ject to glucose (substrate) inhibition and oxygen limitation:

rps ¼l0s

Ks þ sþ s2

KI

þ kc

ssþ Kcor

!DO

DOþ KDO

ð14Þ

The expression used in [6] describes the substrate inhibitionby an exponential decrease in the specific production rateof the enzyme when the substrate concentration exceeds acertain threshold value. In this study, the expression ofthe specific rate of enzyme production is modified by usinga Haldane expression to describe the substrate inhibition.This modification has been motivated by the applicationof an extremum-seeking controller to this process [11].The parameter kc quantifies the constitutive level of enzymeproduction at high glucose concentrations (during thebatch phase).

The specific rate of dissolved oxygen consumption isexpressed as:

rDO ¼ Y XO

q2

xt

þ Y POrps

xa

xt

þ mo

DO

DOþ KDO

ð15Þ

where YXO and YPO are the yields of dissolved oxygen con-sumption for growth and enzyme production, respectively,and mo is the maintenance coefficient that represents theoxygen consumption of biomass.

The specific rate of substrate consumption is expressed as:

rs ¼ Y XS

q2

xt

þ Y PSrps

xa

xt

þ ms

DO

DOþ KDO

ð16Þ

where YXS and YPS are the yields of substrate consumptionfor growth and enzyme production, respectively, and ms isthe maintenance coefficient (based on the total amount ofbiomass).

3.2. Mass balance equations

The model proposed in [6] consists of a set of five bal-ance equations for the three regions of biomass, the sub-strate and the product concentrations, as given in Eqs.(17) – (19). An additional mass balance is included hereto describe the dissolved oxygen concentration in the biore-actor (20). Furthermore, Eq. (21) describes the bioreactorvolume that varies with time and determines the end ofthe fermentation process.

Morphological states xe, xa and xh

_xe ¼ q1 �FV

xe; xeð0Þ ¼ xe0

_xa ¼ q2 � q1 � q3 �FV

xa; xað0Þ ¼ xa0

_xh ¼ q3 �FV

xh; xhð0Þ ¼ xh0

ð17Þ

Glucose s

_s ¼ �rsxt þFVðsf � sÞ; sð0Þ ¼ s0 ð18Þ

Enzyme p

_p ¼ rpsxa �FV

p; pð0Þ ¼ p0 ð19Þ

0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 10.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Viscosity

kL

A

Fig. 2. Relationship between kLa and viscosity during a fed-batchfermentation process. As expected, kLa decreases with increasing viscosity.

L. Bodizs et al. / Journal of Process Control 17 (2007) 595–606 599

Dissolved oxygen DO

_DO¼�rDOxtþ kLaðDO� �DOÞ� FV

DO; DOð0Þ ¼DO0

ð20ÞVolume V

_V ¼ F � F evap; V ð0Þ ¼ V 0 ð21ÞIn these equations, F represents the substrate feeding rate,sf is the substrate concentration in the feed, Fevap is theevaporation rate, kLa the specific gas-liquid mass transfercoefficient for oxygen, and DO* the oxygen saturationconcentration.

The model parameters and their numerical values aregiven in Appendix A. The parameters related to the micro-scopic morphology (10) and (11) are taken from [6]. Thekinetic parameters for the Haldane expression (14) areidentified by fitting the model to simulated data generatedby the model in [6]. The yield coefficients YXS, YPS, YXO,YPO are identified from experimental data provided byNovozymes. The data used for model fitting include bothon-line measurements (DO, viscosity, OUR, CER, andV) and off-line measurements (p and xt).

3.3. Modeling oxygen transfer

The effect of oxygen on growth and production is crucialdue to the positive feedback effect mentioned in Section2.2. Hence, it is necessary to understand and model the fac-tors that affect oxygen transfer. This will be done via anempirical model that relates kLa to the state variables xt

and DO. This link will be established through the viscosityand consists of various steps:

(1) Estimation of kLa. In stirred bioreactors, the oxygentransfer coefficient, kLa, depends on the impellercharacteristics and the rheological properties of thefermentation medium. The value of kLa can be deter-mined experimentally by the dynamic OTR method(oxygen transfer rate measurement) that gives anaverage kLa value for the bioreactor [12]. On-linemeasurements of oxygen transfer rate (OTR), viscos-ity, and DO are available, as well as off-line measure-ment of the total biomass xt. The kLa-value iscalculated as:

kLa ¼ cOTR

ðDO� �DOÞ ð22Þ

where c is a proportionality factor.(2) Calibration of kLa as a function of viscosity. An empir-

ical relationship between kLa and viscosity is deter-mined experimentally. Under maximum air flowrate and constant agitation speed, the substrate feedrate is varied in such a way that oxygen limitationoccurs. kLa is estimated as mentioned above and vis-cosity is measured. The relationship can be approxi-mated by the linear equation (Fig. 2):

kLa ¼ c0 � c1g ð23Þ

where g represents the on-line measurement of viscos-ity, and c0 and c1 are linear regression coefficients(R2 = 0.94).

(3) Calibration of viscosity as a function of xt and DO.The use of Eq. (23) in the dynamic model (17),(19)–(21) requires knowledge of viscosity. For a givenstirrer speed, the viscosity of the filamentous suspen-sion is influenced by two main factors: the biomassconcentration and the fibrous structure of the bio-mass. Due to the lack of quantification of the fibrousstructure, the viscosity is simply regressed with avail-able experimental data. A linear relationship betweenviscosity and biomass concentration is adequate torepresent experimental observations (data notshown). This is also in agreement with literature datafor fermentations of Penicillium chrysogenum andAspergillus niger [12]. Nevertheless, this relation canbe improved by introducing the effect of dissolvedoxygen to give:

g ¼ g0 þ axxt � aDODO ð24Þ

where g0, ax, and aDO are linear regression coefficients(R2 = 0.84). A negative effect of DO on the viscosityis found. This effect can be explained intuitively bythe behavior of the filamentous organisms consideredin this paper. Following a decrease in the DO level,the microorganisms react by ‘reaching out for air’,that is changing their fibrous structure so as to in-crease the zone of the reaction mass from where theycan absorb oxygen. As a consequence, viscosity in-creases (see Section 2.2). Also, when the level ofDO is high, there is enough ‘air to breathe’ withinthe immediate neighborhood, so there is no need tostretch any further, thereby keeping viscosity low.The performance of the viscosity model is shown inFig. 3.

Fig. 5. Dissolved oxygen evolution during fed-batch operation – Data Set2. Measured (- -) and predicted (–) values as a function of time.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Time

Vis

cosi

ty

Fig. 3. Evolution of viscosity during fed-batch operation. Measured value(- -) and calculated value using Eq. (24) (–).

600 L. Bodizs et al. / Journal of Process Control 17 (2007) 595–606

In summary, by combining Eqs. (23) and (24), it is possibleto model the oxygen transfer coefficient kLa in terms oftotal biomass and dissolved oxygen. The accuracy of theDO prediction using Eq. (20) to model the dynamics ofDO and Eqs. (23) and (24) to express kLa in terms ofxt and DO is presented in Figs. 4 and 5 for two differentdata sets. It is seen that the oxygen model performssatisfactorily.

The simulated behavior of the reactor is presented inFig. 6. It can be observed that the substrate concentrationis much higher at the beginning, in the batch phase, thanlater on, in the fed-batch phase. This strategy favors bio-mass growth in the batch phase and production in thefed-batch phase. It is also observed that, in the fed-batchphase, the amount of inactive biomass xh increases. As aconsequence, the viscosity of the medium increases, leading

Fig. 4. Dissolved oxygen evolution during fed-batch operation – Data Set1. Measured (- -) and predicted (–) values as a function of time.

to a decrease of the oxygen transfer rate (kLa decreases).This decrease, in turn, reduces the dissolved oxygen con-centration, which might lead to oxygen limitation.

4. Oxygen control

4.1. Setpoint computation for dissolved oxygen

The model given in the previous section can be used todetermine the dissolved oxygen profile that would maxi-mize the bioreactor performance while avoiding oxygenlimitation. This optimization problem can be formulatedmathematically as follows [13]:

minF ðtÞ;tf

tf

s:t: ð10Þ–ð21Þ; ð23Þ; ð24ÞpðtfÞV ðtfÞP ½pðtfÞV ðtfÞ�min

V ðtfÞ 6 V max

F min 6 F ðtÞ 6 F max

ð25Þ

where tf is the final time, [p(tf)V(tf)]min is the minimumamount of enzyme to be produced, Vmax is the maximumvolume, Fmin and Fmax are the minimum and maximum feedrates, respectively.

Note that this optimization can be performed oncebefore the beginning of the batch or repeated several timesduring the batch. If the optimization is repeated, the avail-able measurements can be used in the optimization via asoftware sensor that estimates the current states (Fig. 7).In this study, a software sensor based on open-loop modelprediction is used [14]. This software sensor is based on themodel used for optimization, except that the equationscorresponding to the measured states DO and V are dis-carded since the state values are known from measure-ments. Furthermore, kLa is computed as in Eq. (22).

Usually, the goal of such an optimization is to computethe control inputs directly [15]. In this study, however, not

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

Bio

ma

ss

Time

xe

xa

xh

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

Time

Su

bst

rate

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

Time

Pro

du

ct

0 0.2 0.4 0.6 0.8 10

20

40

60

80

100

Time

DO

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

Time

k LA

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

Time

η

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

Time

Fe

ed

flo

w r

ate

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

Time

Vo

lum

e

Fig. 6. Simulated states, viscosity and transfer coefficient for an arbitrary feed flow rate.

ProcessControllerDO

sp F

DO, CER, OUR, V

Open-loopsoftware sensor

Optimizationx

Fig. 7. Computation of DOsp by model-based reoptimization.

Fig. 8. Illustration of direct (1) and integral (2) effects using a second-order numerical example.

x1 = ax

2 + ux

1,sp ux

1

+ -x

2x2 = uk

Fig. 9. Output control for the second-order numerical example.

x1 = ax

2 + u

ki

x1,sp u

x1

+ - + -x

2

x2,sp

x2 = uk

o

Fig. 10. Cascade control for the second-order numerical example.

L. Bodizs et al. / Journal of Process Control 17 (2007) 595–606 601

the feed rate profile F(t) but the dissolved oxygen profileDO(t) is sought. This profile is used as reference profilefor the cascade controller to be discussed in the next sub-section. The strategy is illustrated in Fig. 7.

4.2. Cascade control

A cascade control structure is chosen since it has beenobserved experimentally at Novozymes that simple output

ProcessPPIDO

sp FDO

+ - + -r

DOx

t

(rDO

xt)

sp

Fig. 11. Cascade control of dissolved oxygen. The oxygen consumptionrDOxt is approximated as b OURþCER

V based on the measurements of OUR,CER and V.

602 L. Bodizs et al. / Journal of Process Control 17 (2007) 595–606

controllers for DO control do not perform well. Hence,additional measurements are sought to improve the controlperformance. The auxiliary measurements that are avail-able for this process are pH, pressure, viscosity, V, OURand CER. Since pH and pressure have not been incorpo-rated in the model and the viscosity sensor is not alwaysreliable, the idea is to develop a control strategy that usesthe OUR, CER and V measurements.

An interesting feature can be taken from the oxygendynamics. The feed rate has two main effects on the dis-solved oxygen concentration: (i) an immediate effectthrough dilution (the last term on the right-hand side ofEq. (20)) since increasing F decreases DO, and (ii) integraleffect through oxygen consumption (first term) sinceincreasing F increases the amount of substrate in the reac-tor and thus also its consumption, which in turn decreasesDO. Furthermore, the influence of F on the oxygen transferbetween the gaseous and the liquid phases (second term) isquite negligible compared to the other two terms.

If the DO level is controlled through dilution only (thelast term on the right-hand side of Eq. (20)), the resultingchange in the amount of substrate may itself induce achange in DO, which gives rise to oscillations and poor per-formance. This is typical of systems where the zero dynam-ics play an important role in process performance [16].

This problem can be better understood by considering asimplified linearized version of Problem (17)–(21) withboth a direct and an integral effect of u : _x1 ¼ ax2 þ uand _x2 ¼ u, where a P 0 is a coefficient that representsthe relative importance of the integral effect (Fig. 8).With the input u and the controlled output x1 the trans-fer function reads x1ðsÞ

UðsÞ ¼ sþas2 . Using the proportional con-

troller k shown in Fig. 9, the closed-loop characteristicpolynomial becomes s2 + ks + ak, which will have realroots for k P 4a. Hence, in the presence of a fast zero (alarge), one needs to use a very large controller gain toensure non-oscillatory behavior. Such a large gain maynot be admissible in practice due to model mismatchand measurement errors.An efficient way of controlling this second-order systemis to use the cascade scheme given in Fig. 10, i.e.u = ki[ko (x1,sp � x1) � x2]. Note that this cascadescheme corresponds to full-state feedback for this sec-ond-order system. The characteristic polynomial iss2 + ki(ko + 1)s + a kiko, the poles of which can beplaced anywhere independently of the value of a.

Hence, the proposed cascade scheme is one way of imple-menting state feedback for the part of the dynamics thatconcerns dissolved oxygen.

The term rDOxt can be evaluated via OUR and CERmeasurements. This can be understood from Eq. (15) thatshows that rDO is the total oxygen consumptions forgrowth, production and maintenance. This oxygen con-sumption is approximately reflected by the OUR measure-ment. Furthermore, the CER measurement is an indication

of biomass activity and its concentration in the medium.For the operating conditions used in this experiment (con-stant CO2-solubility), OUR and CER are both directlyrelated to rDOxt. Hence, rDOxt can be approximated asb OURþCER

V , where b is a proportionality factor. Note thata controller using only OUR measurements would proba-bly work as well. Unfortunately, such a controller wasnot tested as part of this work.

The idea of the cascade control is to use (rDOxt)sp as themanipulated variable to control DO, while F is used to con-trol rDOxt, xt being a function of F as shown by Eq. (17).This leads to the cascade structure of Fig. 11, in whichthe role of the inner loop is to regulate the substrate con-sumption based on OUR and CER measurements, whilethe outer loop gives the setpoint for this consumption.

4.3. Controller tuning

Since, for the system at hand, cascade control corre-sponds to state feedback, there are sufficient degrees offreedom to place the poles of the closed-loop system arbi-trarily in the complex plane. Hence, the performance ofthe closed-loop system (including its stability) is deter-mined by placing the poles appropriately in the complexplane. Ideally, the desired poles are determined from sometheoretical considerations, as explained in standard text-books [17]. For this, however, the nonlinear process modelhas to be linearized and the controller gains determined onthe basis of the linear approximation.

In this study, controller tuning was carried out directlyon the nonlinear process model by trial and error. Theadvantage of this approach is that it avoids the errorsinduced by linearization, while having the disadvantageof being empirical. Nevertheless, the controller tuningwas successful, as shown in the next section.

Furthermore, a PID controller was also tuned empiri-cally. However, due to the presence of a zero in the oxygendynamics, as pointed out in the previous section, a PID con-troller does not have sufficient degrees of freedom for arbi-trary pole placement, thereby resulting in less satisfactoryresults. Note, however, that PID control may, in some cases,provide good regulatory performance; for example, a sys-tem without zero is handled successfully by PI control in [5].

5. Experimental results

The performance of PID control to regulate the processaround a constant setpoint (DOsp = 25) is illustrated in the

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

OU

R

Time

0 0.2 0.4 0.6 0.8 1

0

20

40

60

80

100

Time

DO

0.8

1

Batchphase

Cascadecontrol

DOsp

= 20

L. Bodizs et al. / Journal of Process Control 17 (2007) 595–606 603

second phase of Experiment II (Fig. 12). The performanceis rather poor, with a large DO variability (25 ± 10). Incontrast, the cascade controller used in the third phase ofthe experiment is able to keep the DO concentration withinthe interval 25 ± 2, which is a major improvement to bothmanual operation and standard PID control.

The cascade controller is further tested in ExperimentIII (Fig. 13). The setpoint for this experiment has beenobtained by solving the optimization problem (25) off-linebefore the beginning of the batch, i.e. without the softwaresensor given in Fig. 7. Since the resulting DO-profile isnearly constant, it is approximated by a constant valuefor ease of implementation [13]. The controller works satis-factorily for most of the time. However, the oscillatorybehavior typical of oxygen limitation starts after 0.75 timeunits. Since this phenomenon of oxygen limitation is highlynonlinear, the linear cascade controller is unable to bringthe fermentation back to normal operation.

The on-line reoptimized DO setpoint given in Fig. 7 isused in the second phase of Experiment IV (Fig. 14).Unfortunately, the optimization provides setpoints thatare well below DOsp = 20%, already known from Experi-ment III to lead to oxygen limitation. Since this is consid-

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

OU

R

Time

0 0.2 0.4 0.6 0.8 1

0

20

40

60

80

100

DO

Time

0 0.2 0.4 0.6 0.8 1

0

0.2

0.4

0.6

0.8

1

Fee

d flo

w r

ate

Time

Batchphase

PIDcontrol

Cascadecontrol

DOsp

= 25

Fig. 12. Experiment II – Batch phase followed by PID control andcascade control.

0 0.2 0.4 0.6 0.8 1

0

0.2

0.4

0.6

Time

Fee

d flo

w r

ate

Fig. 13. Experiment III – Batch phase followed by cascade control. TheDO setpoint, which has been obtained to optimize the bioreactorperformance, is lower than in Experiment II.

ered unacceptable, a safe and constant setpoint is used inthe third phase of this experiment. In this third phase, sev-eral external perturbations act on the system, ranging fromsensor failure at time 0.55 to manual setpoint changes attime 0.7.

These experiments have demonstrated that, even thoughthe model has been fitted to give good one-step ahead pre-diction and fairly reasonable multi-step simulations, thesetpoints provided by solving optimization problem (25)off-line (Experiment III) or on-line (Experiment IV) arein the region of oxygen limitation. This observation canbe explained by the plant-model mismatch present in theoxygen dynamics. However, these experiments have shownthat the cascade controller is able to follow the desired DOsetpoint more accurately than traditional PID control.

Unfortunately, though the regulatory performance ofthe controller is excellent, the transients exhibit some over-shoot. This is mainly due to input saturation not beingaccounted for in the control design. Other strategies, suchas controlling OUR, could be applied since they give amore reliable indication of biomass activity than DO earlyin the batch.

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

OU

R

Time

0 0.2 0.4 0.6 0.8 1

0

20

40

60

80

100

Time

DO

0 0.2 0.4 0.6 0.8 1

0

0.2

0.4

0.6

0.8

1

Time

Fee

d flo

w r

ate

Batchphase

Cascade control -Reoptimized

setpoint

Cascade control - Constant setpoint

DOsp

= 25

Fig. 14. Experiment IV – Batch phase followed by cascade control usingfirst a reoptimized and then a constant DO setpoint. Note that the curvecorresponding to the setpoint is hidden behind the measurement curve.The perturbations in the third phase are due to sensor failure andattempted manual setpoint changes.

604 L. Bodizs et al. / Journal of Process Control 17 (2007) 595–606

6. Conclusions

The main outcome of this study is the cascade controllerfor dissolved oxygen. The proposed scheme efficiently reg-ulates the DO level, but a proper setpoint needs to be cho-sen to keep the process away from oxygen limitation. Theadvantage of the proposed control strategy is that it is sim-ple to apply and not specific to the strain of microorganismstudied in this paper. Thus, it is applicable to a wide varietyof fungal fermentations.

A mechanistic model of enzyme production by filamen-tous fungal fermentation has been extended to include rhe-ological considerations. The effect of medium viscosity onthe oxygen dynamics is described by empirically modelingthe dependence of the mass transfer coefficient kLa on vis-cosity and that of viscosity on biomass and dissolved oxy-gen concentration. The resulting model is used todetermine the optimal DO setpoint, while the insightgained from the model is also used to design a cascade con-

troller. This study has also indicated several model short-comings. The most important one is that the effect of pHis completely discarded. As a consequence, the model pre-dicts feasible operation at low dissolved oxygen values thatcould not be verified experimentally. Also, the model-basedoptimization is not capable of computing reliable DOsetpoints.

In future experiments, one could focus on determiningexperimentally the best setpoint for dissolved oxygen, e.g.using extremum-seeking techniques [11].

Acknowledgements

This paper presents the results of the Knowledge-drivenBatch Production (BatchPro) European Project HPRN-CT-2000-00039. The authors thank F. Lei and H. Jorgen-sen from Novozymes, Bagsvaerd, Denmark, for theirsuggestions and for making possible to carry out the exper-imental work.

Appendix A. Kinetic expressions and model parameters for

the fed-batch filamentous fermentation model

k1 ¼kbran � 104

p4ðd � 10�4Þ2ð1� wÞf q

ðA:1Þ

at ¼1

2

1

2d � 10�4

� �34p3ð1� wÞq

!�1

ðA:2Þ

k2 ¼ ktip;max � 10�4 p4ðd � 10�4Þ2ð1� wÞf q ðA:3Þ

d ¼1:1þ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1:21þ 135ktip;maxfsxe

ðsþKs2ÞðxeþxaþxhÞ

q2

ðA:4Þ

The parameter values are given in Table A.1.

Appendix B. Variables used in the fed-batch filamentousfermentation model

at number of tips per unit mass (tips/(kg DW))aDO regression coefficient (kg/(m s%))ax regression coefficient (kg DW kg/(g m s))b proportionality coefficient (L/mmol)c proportionality coefficient (1/mmol)CER carbon evolution rate (mmol/(L h))c0 regression coefficient (h�1)c1 regression coefficient (m s/(kg h))d hyphal diameter (lm)D[CO2] change in carbon dioxide concentration over the

reactor (%)D[O2] change in oxygen concentration over the reactor

(%)DO dissolved oxygen concentration (%)DO* equilibrium dissolved oxygen concentration (%)g viscosity (kg/(m s))g0 regression coefficient (kg/(m s))f fraction of the active region (%)

Table A.1Model parameter values

Parameter Value Measurement unit

aDO 0.04 kg/(m s %)ax 0.094 kg DW kg/(g m s)b 1 L/mmolc 1 1/mmolc0 67.2 h�1

c1 4.3816 m s/(kg h)DO* 100 %g0 4.185 kg/(m s)f 80 %Fevap 1.25 L/hk3 0.08 h�1

kbran 0.0017 tip/(lm h)kc 8 FAU kg DW/(L g h)Kcor 10�6 g/LKI 1.5 · 10�3 g glucose/LKDO 2.5 %Ks 0.0211 g glucose/LKs1 0.003 g glucose/LKs2 0.006 g glucose/Lktip,max 49 lm/(tip h)mo 0.01 % kg DW/(g h)ms 0.01 kg DW g glucose/(g L h)l0 227 FAU kg DW/(L g h)q 1 g/cm3

sf 430 g glucose/Lw 0.67 g/kg DWYXS 1.75 g glucose kg DW/L gYPS 1.88 · 10�4 g glucose/FAUYXO 57 % kg DW/gYPO 35 % L/FAU

L. Bodizs et al. / Journal of Process Control 17 (2007) 595–606 605

F feed flow rate (L/h)FAU 1 FAU is the amount of enzyme that hydrolyzes

5.26 g starch/h at 30 �CFevap evaporation rate (L/h)k1 specific branching frequency (tips/(kg DW h))k2 maximal tip extension rate (kg DW/(tips h))k3 rate constant (h�1)kbran specific branching frequency determined by image

analysis (tip/(lm h))kc constitutive a-amylase production rate (FAU kg

DW/(L g h))Kcor correction constant for the product formation

(g glucose/L)KDO limit value of dissolved oxygen concentration, be-

low which oxygen limitation occurs (%)KI Haldane parameter (g glucose/L)kLa specific gas–liquid mass transfer coefficient (1/

(L h))Ks Haldane parameter (g glucose/L)Ks1 saturation constant for branching (g glucose/L)Ks2 saturation constant for tip extension (g glucose/L)ktip,max maximal tip extension rate determined by image

analysis (lm/(tip h))mo maintenance coefficient (% kg DW/(g h))ms maintenance coefficient (kg DW g glucose/(g L h))l0 Haldane parameter (FAU kg DW/(L g h))

OUR oxygen uptake rate (mmol/(L h))p a-amylase concentration (FAU/L)pref reference pressure (atm)q1 rate of branching (g/(kg DW h))q2 growth rate of the active region (g/(kg DW h))q3 rate of hyphal cell formation (g/(kg DW h))R universal gas constant (L atm/(mmol K))rDO oxygen consumption rate (kg DW/(g h))rps specific a-amylase formation rate (FAU kg DW/

(L g h))rs substrate consumption rate (kg DW g glucose/

(g L h))q hyphal density (g/cm3)s substrate concentration (g glucose/L)sf feed substrate concentration (g glucose/L)Tref reference temperature (K)V volume (L)w hyphal water content (g/kg DW)xa concentration of active region (g/kg DW)xe concentration of extension zone (g/kg DW)xh concentration of hyphal region (g/kg DW)YPO stoichiometric coefficient for oxygen consumption

for product formation (% L/FAU)YXO stoichiometric coefficient for oxygen consumption

for growth (% kg DW/g)YPS yield coefficient for a-amylase on substrate (g glu-

cose/FAU)YXS stoichiometric coefficient for the uptake of sub-

strate (g glucose kg DW/L g)

References

[1] M. McIntyre, C. Muller, J. Dynesen, J. Nielsen, Metabolic engineer-ing of the morphology of Aspergillus, Adv. Biochem. Eng./Biotech.73 (2001) 104–128.

[2] Z.J. Li, V. Shukla, A.P. Fordyce, A.G. Pedersen, K.S. Wenger, M.R.Marten, Fungal morphology and fragmentation behavior in fed-batch Aspergillus oryzae fermentation at the production scale,Biotech. Bioeng. 70 (2000) 300–312.

[3] R. Oliveira, R. Simutis, S.F. de Azevedo, Design of a stable adaptivecontroller for driving aerobic fermentation processes near maximumoxygen transfer capacity, J. Process Contr. 14 (2004) 617–626.

[4] L. Simon, M.N. Karim, Identification and control of dissolvedoxygen in hybridoma cell culture in a shear sensitive environment,Biotechnol. Prog. 17 (2001) 634–642.

[5] J.D. Chung, Design of metabolic feed controllers: application to high-density fermentations of Pichia pastoris, Biotech. Bioeng. 68 (2000)298–307.

[6] T. Agger, B. Spohr, M. Carlsen, J. Nielsen, Growth and productformation of aspergillus oryzae during submerged cultivations:Verification of a morphologically structured model using fluorescentprobes, Biotech. Bioeng. 57 (1998) 321–329.

[7] J.K. Rasmussen, S.B. Jorgensen, Experimental investigation of data-driven modelling for control of fed-batch cultivation, in: IFAC WorldCongress, Prague, Czech Republic, 2005.

[8] C. Herwig, On-line exploitation tools for the quantitative analysis ofmetabolic regulations in microbial cultures, Ph.D. thesis, EcolePolytechnique Federale de Lausanne (2001).

[9] A.G. Pedersen, kLa characterization of industrial fermentors, in: 4thInternational Conference on Bioreactor and Bioprocess FluidDynamics, Edinburgh, UK, 1997.

606 L. Bodizs et al. / Journal of Process Control 17 (2007) 595–606

[10] L. Bodizs, B. Srinivasan, D. Bonvin, Optimal feeding strategy forbioreactors with biomass death, in: Proc. CAB9, Nancy, France, 2004.

[11] M. Titica, D. Dochain, M. Guay, Adaptive extremum-seeking controlof enzyme production in filamentous fungal fermentation, in: Proc.CAB9, Nancy, France, 2004.

[12] A. Moser, Bioprocess Technology. Kinetics and Reactors, Springer-Verlag, 1988.

[13] M. Titica, L. Bodizs, F. Lei, B. Srinivasan, D. Dochain, D. Bonvin,Modeling and optimization of fed-batch filamentous fungal fermen-tation, in: BatchPro Symposium, Poros, Greece, 2004, pp. 55–65.

[14] D. Dochain, State and parameter estimation in chemical andbiochemical processes: a tutorial, J. Process Contr. 13 (2003) 801–818.

[15] B. Srinivasan, S. Palanki, D. Bonvin, Dynamic optimization of batchprocesses: I. Characterization of the nominal solution, Comp. Chem.Eng. 27 (2003) 1–26.

[16] Ph. Mullhaupt, B. Srinivasan, J. Levine, D. Bonvin, Cascade controlof the toycopter, in: ECC’99, Karlsruhe, Germany, 1999.

[17] D.E. Seborg, T.F. Edgar, D.A. Mellichamp, Process Dynamics andControl, Wiley, 1989.