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Biochemical Engineering Journal 53 (2010) 26–37

Contents lists available at ScienceDirect

Biochemical Engineering Journal

journa l homepage: www.e lsev ier .com/ locate /be j

inear robust control of S. cerevisiae fed-batch cultures at different scales

. Dewasmea,∗, A. Richelleb, P. Dehottayc, P. Georgesc, M. Remya, Ph. Bogaertsb, A. Vande Wouwera

Service d’Automatique, Faculté Polytechnique de Mons, Boulevard Dolez, 31, 7000 Mons, BelgiumService de Chimie Générale et Biosystèmes, Université Libre de Bruxelles, Av. F.-D. Roosevelt, 50 CP 165/61, 1050 Bruxelles, BelgiumGlaxoSmithKline Biologicals, Rue de l’Institut, 89, 1330 Rixensart, Belgium

r t i c l e i n f o

rticle history:eceived 30 June 2009eceived in revised form9 September 2009ccepted 5 October 2009

a b s t r a c t

In this paper, experimental investigations of an adaptive RST control scheme for the regulation of theethanol concentration in fed-batch cultures of S. cerevisiae is presented. Our main objective is to proveefficiency and robustness of this controller in experimental applications ranging from laboratory to indus-trial scales. The controller only requires one on-line measurement signal, making it easily implementablein an industrial environment. Disturbance rejection is ensured thanks to an on-line parameter adaptationprocedure, which delivers as a side product an estimate of the growth rate that can be used for process

eywords:ioreactor systemstirred tankontrol systems & optimizationn-line fed-batch

monitoring purposes. The robustification of the controller is achieved in a simple way, using the observerpolynomial.

© 2009 Elsevier B.V. All rights reserved.

etabolic controlecombinant technology

. Introduction

S. cerevisae is one of the most popular host microorganismsor vaccine production. The possibility to easily express a vari-ty of different recombinant proteins explains its important rolen the pharmaceutical industry. In order to maximize productiv-ty, a common strategy is to regulate the ethanol concentration at

low value, thus ensuring an operating point close to the edgeetween the respirative and respiro-fermentative regimes wherehe yeast respirative capacity is exactly filled (bottleneck assump-ion of Sonnleitner and Käppeli’s model [1]). Several applicationsf this principle can be found, for instance in [2–4]. These controlchemes all require the on-line measurement of the ethanol con-entration, implying the availability of an ethanol probe or the usef alternative strategies based on more basic measurement signals,uch as the dissolved oxygen concentration, as proposed in [5,6], or

oftware sensors reconstructing ethanol from the measurements ofasic signals as designed in [7]. In this paper, the focus is placed onhe design of a control scheme and the ethanol signal is assumedvailable (either via an ethanol probe as it is the case in our exper-

∗ Corresponding author. Tel.: +32 65374131.E-mail addresses: laurent.dewasme@umons.ac.be (L. Dewasme),

hilippe.Dehottay@gskbio.com (P. Dehottay), Patrice.a.Georges@gskbio.comP. Georges), Philippe.Bogaerts@ulb.ac.be (Ph. Bogaerts),lain.VandeWouwer@umons.ac.be (A. Vande Wouwer).

369-703X/$ – see front matter © 2009 Elsevier B.V. All rights reserved.oi:10.1016/j.bej.2009.10.001

imental set-up or by any other efficient means, including softwaresensors).

In a recent study by Renard et al. [8], a RST controller with Youlaparametrization is developed for the regulation of the ethanol con-centration and tested successfully in real-life experiments. One ofthe main advantages of this approach is that it is based on a simplelinear model linking the feed flow rate to the ethanol concentra-tion, and a simple linear model of the disturbance, which representsthe substrate demand for cell growth. The prior knowledge of onlyone stoichiometric coefficient is required, whereas the apparentgrowth rate can be easily estimated on-line (in order to ensure agood disturbance rejection).

In [9], an alternative and simpler formulation of the RST controlscheme based on the observer polynomial is introduced.

The objective of this study is to consider additional factors influ-encing the controller performance, such as the existence of latencyphases, sensor dynamics and the selection of the sampling period.In addition, a large set of experimental results ranging from labora-tory to industrial scales are discussed, demonstrating the potentialof the controller and its usefulness in scaling-up.

2. Modeling yeast fed-batch cultures

The yeast strain S. cerevisiae presents a catabolism that can bemacroscopically described by the following three main reactions:

Substrate oxidation : S + k5Or1X−→k1X + k7P (1a)

L. Dewasme et al. / Biochemical Engin

Fig. 1. Representation of Sonnleitner’s bottleneck assumption [1]. The cellsmetabolism is ruled by their respiratory capacity represented by the bottleneck.Iwes

S

E

wcdcs

r

r

r

wto

r

r

r

wsK

i

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n the first pathway, glucose and the remaining quantity of ethanol are consumedhile, in the second pathway, a limited quantity of glucose is consumed and the

xcess part produces ethanol by fermentation. Optimal operating conditions areituated at the edge of these two regimes.

ubstrate fermentation : Sr2X−→k2X + k4E + k8P (1b)

thanol oxidation : E + k6Or3X−→k3X + k9P (1c)

here X, S, E, O and P are, respectively, the concentration in theulture medium of biomass, substrate (typically glucose), ethanol,issolved oxygen and carbon dioxide. ki (i = 1, . . . , 9) are the yieldoefficients and rjX (j = 1, . . ., 3) are the reaction rates in which, thepecific growth rates rj (j = 1, . . ., 3) are defined as:

1 = min(rS, rScrit) (2a)

2 = max(0, rS − rScrit) (2b)

3 = max

(0, min

(rE,

k5(rScrit− rS)

k6

))(2c)

hich are highly non-linear functions of the main components dueo the switch mechanisms and the expressions of the substrate,xygen and ethanol consumption rates in the form of Monod laws:

S = �SS

S + KSwith rScrit

= �SScrit

Scrit + KS= ro

k5(3a)

O = �OO

O + KO

KiEKiE + E

(3b)

E = �EE

E + KE(3c)

ith the constants �S, �O and �E being the maximal values of thepecific growth rates (for instance, when S is very large, rS ≈ �S) andS, KO and KE expressing the saturation of the respective elements.

This kinetic model, which is often encountered in the literature,s based on Sonnleitner’s bottleneck assumption [1] (see Fig. 1).

During a culture, the yeast cells are likely to change theiretabolism because of their limited respiratory capacity. When

he substrate is in excess (concentration S > Scrit), the yeast cellsroduce ethanol through fermentation, and the culture is said inespiro-fermentative (RF) regime. Ethanol has a detrimental effectn the cells growth because it directly inhibits the cells respira-ory capacity [10]. On the other hand, when the substrate becomesimiting (concentration S < Scrit), the available substrate (typically

lucose), and possibly ethanol (as a substitute carbon source), ifresent in the culture medium, are oxidized. The culture is thenaid in respirative (R) regime. Thus, the optimal operating condi-ions that maximize the biomass productivity are at the boundary ofhe two regimes. In these conditions, the fermentation and ethanol

eering Journal 53 (2010) 26–37 27

oxidation rates are equal to zero and, from (2a):

rS = rO

k5(4)

Consequently, after some mathematical manipulations, a rela-tion between the critical substrate concentration level and the cellrespiratory capacity is obtained as:

Scrit = KSrO

k5�S − rO(5)

Unfortunately, even if this substrate critical level can be esti-mated through (3b) with the oxygen and ethanol measurements,the substrate concentration measurement is a difficult task as theorder of typical concentration levels (O(10−2) g/l) are below or,at least, too close to the resolution of currently available probes(O(10−1) to O(10−2) g/l)).

This is why an alternative solution based on ethanol measure-ment is presented in this paper in Section 4.

Component-wise mass balances give the following differentialequations:

dX

dt= (k1r1 + k2r2 + k3r3)X − DX (6a)

dS

dt= −(r1 + r2)X − D(S − Sin) (6b)

dE

dt= (k4r2 − r3)X − DE (6c)

dO

dt= −(k5r1 + k6r3)X − DO + OTR (6d)

dP

dt= (k7r1 + k8r2 + k9r3)X − DP − CTR (6e)

dV

dt= Fin (6f)

where Sin is the substrate concentration in the feed, Fin is the inletfeed rate, V is the culture medium volume and D is the dilution rate(D = Fin/V). OTR and CTR represent respectively the oxygen transferrate from the gas phase to the liquid phase and the carbon transferrate from the liquid phase to the gas phase. Classical models of OTRand CTR are given by:

OTR = kLaO(Osat − O) (7a)

CTR = kLaP(P − Psat) (7b)

where KLaO and KLaP, and Osat and Psat are respectively the vol-umetric transfer coefficients and concentrations at saturation ofdissolved oxygen and carbon dioxide.

3. Materials and methods

3.1. Operating conditions

A genetically modified strain of S. cerevisiae is cultivated. Yeastscultures are carried out at laboratory and industrial scales (witha scaling-up factor of about 100). For the sake of confidentiality,the exact bioreactor volumes and gene composition of the yeaststrain are not detailed here. For both scales, a control unit allows theculture conditions to be set: pH is controlled at 5 by adding NH4OH25%, temperature is maintained at 30 ◦C thanks to a water jacket,and dissolved oxygen, which is initially set at 100%, is controlledaround 20% by acting on the stirrer speed.

The air flow is used in backup if the maximum stirrer speed isreached (approximately 1000 rotations per minute or RPM). Oth-erwise, the air flow is set at 20 l/min.

As the initial volume V0 is known and the proposed controllerdoes not require an accurate measurement of V (this point will

2 Engine

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8 L. Dewasme et al. / Biochemical

ecome clear in Section 4), the latter is assessed by integrating theeed rate (alternatively the on-line measurement of the weight ofhe feed tank could be used).

A fed-batch is started from a precultured inoculum contained inhake flasks generally presenting a biomass optical density aroundat 650 nm, a quite high ethanol concentration above 5 g/l (which,

fter inoculation in the bioreactor, decreases to more or less 1 g/ly dilution effect) and a low glucose concentration below 0.1 g/l.

The added feed medium contains 350 g/l of glucose. Otheromponents of the feed and the culture media are not given foronfidentiality reasons.

.2. Measurements systems

Cell growth is estimated off-line thanks to optical density mea-urements at 650 nm. Glucose concentration is measured off-liney high-performance liquid chromatography (HPLC).

Ethanol concentration is measured on-line with a FringsTM

lcosens methanol probe between 0.01 and 0.6% (v/v) (i.e., approx-mately between 0.1 and 4.5 g/l). This probe is immersed directlyn the culture medium liquid phase and ethanol flows through a

embrane into a carrier gas which is led to a semi-conductor.The resistance variation is then measured and recorded. This

ariation is mathematically linked to the measured temperaturenote that this last measurement is also achieved by the ethanolrobe between 20 and 143 ◦C) and leads to the estimation of thethanol concentration. The response time of this probe is theoret-cally smaller than 5 min and experimentally estimated between

and 3 min so that a measurement sampling period of 6 min ishosen.

Ethanol concentration is also measured off-line by gashromatography for comparative purposes (validation). Usually,ff-line and on-line measurements slightly deviate, but this has aegligible effect on the controller performance.

This deviation is generally increasing with the medium volumend, indirectly the stirrer speed, supporting the idea that the accu-acy decreases because of the disturbances created by high stirrerpeeds.

. Simple design of an adaptive controller

The basic principle of the controller is to regulate the ethanol atconstant low setpoint, leading to a self-optimizing control in the

ense of [11] and ensuring that the yeast culture operates in theespiro-fermentative regime, close to the biological optimum, i.e.,lose to the edge with the respirative regime.

The control structure is defined based on the following obser-ations:

The most evident choice of a manipulated variable in a fed-batchsystem is the feed flow rate Fin. Considering that we are lookingfor the simplest way of modeling the bioreactor, we assume thatFin appears as the sole input of the system.As explained in [4], the maximum of productivity is obtainedat the edge between the respirative and respiro-fermentativeregimes, where the quantity of ethanol is constant and equal tozero (VE = 0); see (3a), (3b) and Fig. 1. Unfortunately, evaluatingaccurately the volume is a difficult task as it depends on the inletand outlet flows including Fin but also the added base quantityfor pH control and several gas flow rates. Moreover, maintaining

the quantity of ethanol constant in a fed-batch process meansthat the ethanol concentration has to decrease while the vol-ume increases. So, even if the volume is correctly measured, VEbecomes unmeasurable once E reaches the sensitivity level of theethanol probe. For those practical limitations, a sub-optimal strat-

ering Journal 53 (2010) 26–37

egy is elaborated through the control of the ethanol concentrationaround a low value depending on the sensitivity of commerciallyavailable ethanol probes (a general order is 0.1 g/l), and requir-ing only an estimation of the volume by integration of the feedrate.

- A linear control framework is chosen as it makes the design ofrobust controllers easier than in a non-linear framework.

- A RST (2-degree-of-freedom) controller is selected as it offers agreat decoupling of the servo/regulation tasks (desired perfor-mance specifications and rejection of disturbances).

4.1. Model linearization

Expressions (2) and (3) recall that model (4) is highly non-linearin the macroscopic key components. The linear controller designrequires a linearization along the proposed sub-optimal trajectorywhere the ethanol control reference Eref is chosen sufficiently lowso as to stay in the neighborhood of the optimal trajectory but alsosufficiently high to avoid probe sensitivity limitations. As proposedin [8], two partial linear models representing each regime, respec-tively, can be derived and have the interesting property that theyshare the same structure.

The following linearization is first performed consideringrespiro-fermentative culture conditions (S > Scrit, r3 = 0). Substrateconsumption represents one of the fastest dynamics of the sys-tem. As the theoretical value of Scrit is very small (below 0.1 g/l)and, on the basis of the singular perturbation principle, assuminga quasi-steady state of S (i.e. considering that there is no accumu-lation of glucose in the bioreactor while working not far from theoptimal operating conditions), the very small quantity of substrateVS is almost instantaneously consumed by the cells (d(VS)/dt ≈ 0and S ≈ 0).

Using this assumption, the differential Eq. (4b) reduces to

r2X = Fin

VSin − r1X (8)

Then (8) and (6c), related to the ethanol mass balance, are com-bined to give:

dE

dt= Fin

V(k4Sin − E) − k4r1X (9)

This equation can be linearized along a nominal trajectory definedby E*(t), F∗

in(t), V*(t), X*(t) and O*(t). As long as the process is oper-ated in the neighborhood of this trajectory, E*(t) can be consideredas a constant variable Eref, the control set point (or reference),while F∗

in(t) and V*(t), respectively corresponding to the necessaryfeed-rate and the related volume (dV∗(t)/dt = F∗

in(t), see (6f)) tomaintain E at Eref, are linked by the following relation:

F∗in = V∗

k4Sin − E∗ k4r∗1X∗ (10)

Setting:

E = E∗ + ıE

Fin = F∗in + ıFin

V = V∗ + ıV

X = X∗ + ıX

O = O∗ + ıO

(11)

where ı denotes a very small variation, a first-order Taylor seriesdevelopment can be achieved:

dıE

dt= k4Sin − E∗

V∗ ıFin − F∗in

V∗ ıE − F∗in

V∗k4Sin − E∗

V∗ ıV

− k4X∗ ∂r∗1

∂OıO − k4r∗

1ıX (12)

L. Dewasme et al. / Biochemical Engineering Journal 53 (2010) 26–37 29

Table 1Order evaluation of each term of (12).

Culture start Culture end

k4Sin−E∗V∗ O(101) O(101)

X∗k S −E∗ k4r∗

1 O(10−3) O(10−1)

oogsa

r

cfoa

a

k

tf

V

at

w

d

cfdt

E

d

Table 2Parameters of the linear discrete-time model (18).

Parameter RF regime R regime

b TSk4Sin−E

V TSk5/k6Sin−E

V

by:

Hm(q−1) = B(q−1)Am(1)B(1)Am(q−1)

(23)

4 in

X∗V∗ k4r∗

1 O(10−2) O(100)

k4r∗1 O(10−1) O(10−1)

Along the nominal trajectory, it is assumed that the process isperated not far from the optimal conditions (i.e., close to the edgef the two regimes) so that r∗

1 ≈ rO/k5. Moreover, when the oxy-enation is not limiting and the ethanol quantity is not sufficient toignificatively inhibit the respiratory capacity (i.e. (3b) with KO � Ond KiE � E), the following simplification holds:

∗1 ≈ rO,max

k5= �O

k5→ ∂r∗

1∂O

≈ 0 (13)

Now, considering (10) and (13), (12) can be written as follows:

dıE

dt= k4Sin − E∗

V∗ ıFin − X∗

k4Sin − E∗ k4r∗1ıE − X∗

V∗ k4r∗1ıV − k4r∗

1ıX

(14)

From the contributions brought by �Fin, �E, �V and �X, usingonstant values of E* and r∗

1, different values of V* and X* goingrom the start to the end of the culture and considering realisticperating parameters, the order of magnitude of the “�Fin term” islways significantly larger than the others as shown in Table 1.

From this on, it is legitimate to neglect these latter contributionsnd to consider the following model in variations:

dıE

dt= k4Sin − E∗

V∗ ıFin (15)

Moreover, defining the biomass specific growth rate1r1 + k2r2 + k3r3 as �, (6a) is written:

d(VX)dt

= �VX (16)

By integrating (16) over the culture period, we obtain the evolu-ion of the biomass quantity along the nominal trajectory (where,rom (13), �∗ ≈ k1r∗

1 can also be considered as constant):

∗X∗ = V0X0 exp(�∗t) (17)

Replacing �E and �Fin respectively by E − E* and Fin − F∗in in (15)

nd taking into account (10) and (17), the linear model betweenhe measured state E and the input Fin is obtained:

dE

dt= k4Sin − E∗

V∗ (Fin − dX) (18)

here:

X = k4r∗1

k4Sin − E∗ V0X0 exp(�∗t) (19)

Finally, a discrete-time transfer function linking the ethanoloncentration to the feed rate can be obtained for the respiro-ermentative regime on the basis of (19) and, using similarevelopments, also for the respirative regime. A general discrete-ime model representing both regimes can be described by:

(k) = bq−1

1 − q−1(Fin(k) − dX(k)) (20a)

X(k) = c

1 − �q−1ı(k) (20b)

c k4r1k4Sin−E

V0X0rO,max/k6

k5/k6Sin−EV0X0

� exp(�TS) exp(�TS)

where q−1 is the backward shift operator (x(k − 1) = q−1x(k)), theparameters b and c are functions of the operating regime and dXis seen as the perturbation representing the cells growth (� is animage of the cells growth rate). All the parameter values are listedin Table 2 where TS represents the sampling period.

4.2. Controller design

For the sake of clarity, we call B the polynomial bq−1, A thepolynomial 1 − q−1, C the polynomial c and DX is the polynomial1 − �q−1.

Potentialities of application of conventional PID controllersare unfortunately limited since the biomass grows exponentially.Indeed (20a) shows that the unstable disturbance, which is animage of the biomass growth, needs to be rejected. In [12–14],the tuning of a PID controller regulating the ethanol concentra-tion is investigated. Despite the integral part of the controller, anexponentially growing error is observed, showing that this type ofcontrollers is inappropriate. Moreover, the derivative action, whichusually improves the stability margin, has bad robustness withrespect to the process parameters [14].

Consequently, an adaptive RST controller based on the internalmodel principle in order to reject the unstable disturbance is cho-sen. A great advantage of this kind of controllers is presented in thefollowing design method using a pole placement procedure whichallows to easily impose the tracking behaviour independently ofthe robustness performance.

The two-degree-of-freedom RST controller, applied to the lin-earized model of the bioreactor (see Fig. 2), is designed to controlthe ethanol concentration at Eref and reject the disturbance dX.

The control law can be written as:

R(q−1)Fin(k) = −S(q−1)E(k) + T(q−1)Eref (21)

and, omitting the backward-shift operator, the closed-loop equa-tion takes the form

E(k) = BTAR + BS

Eref + BRAR + BS

dX(k) (22)

The RST controller polynomials are then computed using a pole-placement procedure [15,16], in which the reference model is given

Fig. 2. Closed-loop control of the bioreactor model. B, A, R, S and T are polynomialsin backward-shift operator q−1.

3 Engineering Journal 53 (2010) 26–37

waAt

A

wp

oDeR(

d

Ro

E

c

T

5

5

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0 L. Dewasme et al. / Biochemical

here Am is chosen to tune the tracking performance and, Am(1)nd B(1) are respectively the continuous gains of the polynomialsm and B. R and S are found by solving a diophantine equation ofhe form:

R + BS = A0Am (24)

here A0 is the observer polynomial, which can be selected inde-endently of Am so as to confer some robustness to the controller.

Following the internal model principle [17], the unstable pole �f the disturbance dX should be included into the R polynomial (i.e.,X is a factor of R). This disturbance will be canceled out if a correctstimation of the parameter � is available, for instance through aecursive Least Squares algorithm [15]. Indeed, after the initial time,20b) can be written as:

X(k) − �dX(k − 1) = 0 (25)

By replacing the closed-loop transfer function denominator andby their new expressions and the disturbance dX by (20b), we

btain:

(k) = BT

A0AmEref(k) + BDXR′

A0Am

c

DXı(k) (26)

It appears that the disturbance is compensated and T is onlyhosen to ensure the setpoint tracking:

= A0Am(1)B(1)

(27)

. Simulation results

.1. Controller performance

The simulation study is carried out using MATLABTM. The firstimulation run illustrates the ethanol regulation based on theinearized model (20), theoretical parameter values taken from

onnleitner’s kinetic model [1] and the RST controller defined in21) and applied in closed-loop as in (22). An initial ethanol con-entration of 0.8 g/l is chosen so that the process has to operaten the respiro-fermentative regime (this point will be detailed inection 6), and the only yield coefficient whose knowledge is a

Fig. 4. Simulation results with the RST controller defined in (21), (22), (24), (25

Fig. 3. Robust behavior analysis of the proposed controller in the Black–Nicholsdiagram. Upper and lower gain margins are represented by the OB and OC arrowsand the phase margin by the OD arrow.

priori required, is k4 = 0.48 (see (6c) and Table 2). Initial and oper-ating conditions are chosen as follows: kLa = 300 h−1; Sin = 350 g/l;X0 = 0.4 g/l; S0 = 0.012 g/l; E0 = 0.8 g/l; O0 = 100%; TS = 6 min.

The biological reactions occur on such a time scale that a sam-pling period of 6 min is acceptable. A first-order tracking behaviorwith a time constant of 1 h can be selected, which corresponds toAm = 1 − 0.9q−1.

The tuning of the observer polynomial A0 is generally achievedby loop-shaping, i.e., by modifying the shape of the corrected open-loop transfer function in a Black–Nichols diagram (Fig. 3). Followingthe general Nyquist theorem transposed to this diagram, the stabil-ity of the closed-loop system is verified if the corrected open-loopcurve surrounds the point (0, −180◦) by the right side (i.e., the curve

cuts the phase axis on the right side of (0, −180◦)). Three mar-gins are defined (see Fig. 3): an upper gain margin (OB), a lowergain margin (OC) and a phase margin (OD). Stability robustnesscan then be analyzed through these criterions, defining an ellipsoid

) and (27). Evolution of the ethanol concentration and the feed flow rate.

L. Dewasme et al. / Biochemical Engineering Journal 53 (2010) 26–37 31

F nd (2E

aeala([rprei

ipat

5p

nlit

o1ifc

E

n(s

× (Fin(k) − dX(k)) (29)

where � = e(TS/Tmes)

ig. 5. Simulation results with the RST controller defined in (21), (22), (24), (25) avolution of the ethanol concentration and the feed flow rate.

rea that the curve should not enter. Actually, an equivalent math-matical expression can be stated through the moduli of the directnd complementary sensitivity functions. Ensuring a modulusower than 6 dB for the direct sensitivity function (�d = AR/AR + BS)nd lower than 3 dB for the complementary sensitivity function�c = BS/AR + BS) provides a good stability robustness. This analysis9] leads to the conclusion that while those last criteria are notespected without robustification (A0 = 1), a first order observerolynomial (A0 = 1 − a1q−1) is indeed sufficient to ensure a goodobustification. The value a1 = 0.7 is obtained by trial and error andnsures a comfortable gain margin at high frequencies, correspond-ng to the frequency range of the neglected glucose dynamics (6b).

The tracking performance is tested in Fig. 4 where the reference,nitially set to 1 g/l is changed to 2 g/l. As E reaches the previous set-oint within 4 h from the start, the new set-point is also reachedfter 4 h. This last observation is expected as Am is chosen in ordero impose a time constant of 1 h.

.2. Controller improvements considering a delayed output androbe dynamics

Experimentally, it is sometimes observed that the ethanol sig-al does not respond instantaneously to feed variations so that a

atency phase, estimated between 6 and 12 min, has to be takennto account in model (20a). Chosing a sampling period of 6 min,his latency phase correspond then to 1 or 2 sampling periods.

A second test considers the performance of the same controllerf Fig. 5 when facing a process model incorporating a delay of2 min. In this case, the regulation is not designed taking this delay

nto account and it can be observed in Fig. 5 that the tracking per-ormance is affected by oscillations. Note that initial and operatingonditions remain unchanged.

Taking the time delay into account, the discrete model becomes:

bq−3

(k) =

1 − q−1(Fin(k) − dX(k)) (28)

ecessitating the use of a second order observer polynomial A0 =1 − 0.85q−1)(1 − 0.15q−1), following the same analysis as the onehown by Fig. 3 (see Fig. 6).

7), when presented with a process incorporating a non-modeled delay of 12 min.

Note that with a relatively large sampling time, the probedynamics can generally be neglected. However, reducing the sam-pling period can be interesting to improve the performance ofthe recursive least squares algorithm and, in turn, the disturbancerejection. Modeling the ethanol probe dynamics can be achievedby a first-order transfer function with a time constant Tmes (gener-ally in a range from 1 to 3 min). Including this second refinementin (28), the discrete model becomes:

E(k) = bq−3((TS + Tmes(� − 1)) + (Tmes − �(TS + Tmes))q−1)(1 − q−1)(1 − �q−1)

Fig. 6. Robust behavior analysis of the improved controller in the Black–Nicholsdiagram.

32 L. Dewasme et al. / Biochemical Engineering Journal 53 (2010) 26–37

F d (27E

riptTcttt

ig. 7. Simulation results with the RST controller defined in (21), (22), (24), (25) anvolution of the ethanol concentration and the feed flow rate.

Nevertheless, these performance improvements, inducing aeduction of the sampling period, can be detrimental to the systemn terms of stability robustness as the delay, estimated in samplingeriods, dramatically increases. Consequently (28) will be preferedo (29) and only a 2-sampling-period delay is taken into account.he sampling period must then be carefully chosen to estimate

orrectly the delay in a minimum of sampling periods. Still usinghe same initial and operating conditions as in Fig. 4, we obtainhe results shown in Fig. 7 where the oscillations vanish and theracking performance is better.

Fig. 8. Influence of the noise on the measured ethanol con

), when presented with a process model incorporating a modeled delay of 12 min.

5.3. Robustness against measurement noise and modeluncertainties

In the first hours of culture, when the biomass concentration isvery low, the cells are likely to alternatively switch between thetwo metabolic pathways, leading to hard sollicitations and satura-

tions (to 0 when the controller calculates negative feed rates) of theinput actuator (i.e., the feed pump). Indeed, the quasi-steady stateassumption of the substrate concentration is generally verified dur-ing the cells exponential growth in the neighborhood of the optimal

centration with a non-robust RST controller (A0 = 1).

L. Dewasme et al. / Biochemical Engineering Journal 53 (2010) 26–37 33

conce

obpFirSslt

rttfr

FE

Fig. 9. Influence of the noise on the measured ethanol

perating conditions but not in the starting transient period. Theest way to illustrate this idea is to challenge the controller in theresence of measurement noise, amplifying the saturation effect.ig. 8 shows a new simulation where a white noise (�2 = 0.005 g2/l2)s added to the ethanol concentration measurements and where noobustification by the observer polynomial is considered (A0 = 1).tarting with the same initial conditions as in Figs. 4, 5 and 7, theet-point is now kept at 1 g/l during 20 h in order to observe thearge divergence that occurs during the first 10 h, consequence ofhe multiple actuator saturations generated by the noise.

On the other hand, Fig. 9 shows the same simulation with the

obustufied controller of Fig. 4 (A0 = 1 − 0.7q−1). It appears clearlyhat the noise on the input Fin is attenuated, limiting the actua-or saturations and the divergence of the ethanol concentrationrom the set-point. The same observations can be made with theobustified controller of Fig. 6 in the presence of delay.

ig. 10. Experimental results of the ethanol regulation applied to laboratory-scale fed-baref = 1 g/l, the feed flow rate Fin expressed in percentage of the maximal pump speed and

ntration with a robust RST controller (A0 = 1 − 0.7q−1).

The only a priori knowledge on the system is the yield coefficientk4 in the RF regime and the ratio k5/k6 in the R regime (see Table 2).Considering that the order of the products k4Sin and k5/k6(Sin) aregenerally higher than E, uncertainties on these last products have aproportionnal influence on the gain b. Finally, simulations present-ing absolute errors going from 50% to 100% of the theoretical valuesof k4Sin and k5/k6(Sin) produce similar results to Figs. 4, 7 and 9(where the controller is robustified) which are not reproduced. Insummary, once the controller is robustified by the observer poly-nomial, very large intervals of model uncertainties are toleratedthanks to the increased stability margin (see Figs. 3 and 6).

6. Experimental results

Experimental investigation of the control scheme to fed-batchcultures of S. cerevisiae is performed with laboratory-scale and

tch cultures of S. cerevisiae. Evolution of the ethanol probe measurement E aroundthe parameter � , image of the cells growth rate.

34 L. Dewasme et al. / Biochemical Engineering Journal 53 (2010) 26–37

F fed-bat ation bd

i2pm

6

iLwv

F(

ig. 11. Experimental results of the ethanol regulation applied to laboratory-scalerations (off-line measurements are represented by circles and the spline interpolashed line the ethanol concentration set-point.

ndustrial-scale bioreactors. For all these experimental tests, only a-sampling-period delay is taken into account. Indeed, a samplingeriod of 6 min appears sufficient to ensure good control perfor-ance so that the ethanol probe dynamics is neglected.Consequently, model (28) is used in the following.

.1. Control interface

The on-line ethanol concentration measured by a Frings probes acquired through the Ethernet network and transfered into aabVIEWTM (National Instruments, USA) virtual instrument (vi)here the controller is implemented in a block diagram and super-

ised through the corresponding front control panel. Every 6 min

ig. 12. Experimental results of the ethanol regulation applied to laboratory-scale fed-bstars), both based on the spline interpolation of the off-line biomass measurements, and

tch cultures of S. cerevisiae. Evolution of the biomass, glucose and ethanol concen-y stars). The continuous line represents the ethanol probe measurement and the

(which correspond to the sampling period), the feed-rate is updatedby the controller on the basis of the process value (the ethanol mea-surement), and converted into the corresponding percentage of themaximum speed of an ISMATEC peristaltic pump.

6.2. Laboratory-scale results

Fig. 10 shows a typical run with a regulation of the ethanol at

1 g/l.

Fig. 11 shows the biomass, substrate (glucose) and ethanol off-line concentrations (circles) and a spline interpolation of thesemeasurements (stars, sampled every hour) providing an imageof the evolution of these key components when no off-line mea-

atch cultures of S. cerevisiae. Evolution of the growth rate � and the parameter �estimated � (continuous line).

Engineering Journal 53 (2010) 26–37 35

sNo(lp

�

�

�

wr

ttc

ec(gttcbmoumaetai

pt

FE

L. Dewasme et al. / Biochemical

urement is available (typically during the evening and the night).ote also that a slight off-set between the off-line measurementsbtained by HPLC and the online ethanol probe measurementsdelivered every 2 s and so, almost appearing as a continuous blueine) is increasing with time but does not really affect the controllererformance as both concentrations are approximately constant.

In Fig. 12, the measured cell growth rate and the corresponding= f(�) are calculated using a discrete approximation of the form:

≈ X(k + 1) − X(k)X(k)TSext

(30)

≈ exp

(X(k + 1) − X(k)

X(k)TSext

TS

)(31)

here TS is the controller sampling period and TSext = 1 h is theesampling period after interpolation of the experimental data.

The least squares estimate (sampled every 5 min) needs 10 ho converge to the real value of � and is almost perfectly main-ained during the 15 following hours until the “culture end phase”,haracterized by an important decrease of �, starts.

Consequently, the ethanol concentration stays around the refer-nce value of 1 g/l during the first 10 h and, when the estimate of theells growth rate converges, the regulation becomes more accurateas the disturbance, which represents the substrate demand for cellrowth, can be almost exactly compensated). This demonstrateshe efficiency of the controller, which is able to reject an unstableime-varying exponential disturbance. After 20 h, the ethanol con-entration deviates slightly from the setpoint. This can be explainedy an apparent decrease of the cell growth as reflected by the esti-ated value of � . This limitation phenomenon can be due to a lack

f oxygenation (see Fig. 13) in the last hours, resulting from annsufficient air flow following a saturation of the stirrer speed to itsaximum value. Nevertheless, the encountered metabolic changes

re robustly limited by the controller which prevents the suddenthanol increase. Note that the culture was stopped before the con-roller manages to reset more accurately the ethanol concentration

t 1 g/l. Anyway, other results presented in the next figures betterllustrate this missing part.

Initial process conditions play an important role in terms ofroductivity. As the controller only regulates the ethanol concen-ration around the set point (which is chosen by the user), and

ig. 14. Experimental results of the ethanol regulation applied to laboratory-scale fed-baref = 1 g/l (when E0 > Eref), the feed flow rate Fin expressed in percentage of the maximal p

Fig. 13. Experimental results of the ethanol regulation applied to laboratory-scalefed-batch cultures of S. cerevisiae. Evolution of the dissolved oxygen (circles) andthe stirrer speed (squares) respectively in percents of the phase saturation concen-tration and the maximum speed.

as the initial ethanol concentration in the culture medium (E0)depends on the residual concentration at the end of the precul-ture (which is a priori unknown), the initial difference between theset point and the initial concentration can be crucial for the culturetime.

Moreover, the ethanol concentration in the feed medium (Ein)plays also a determinant biological role. Indeed, it is possible toforce the cells to evolve through a preselected pathway by adjust-ing the ethanol concentration (Ein) in the feed medium (note that inthis paper, Ein is always equal to zero). When Ein < Eref, the controllerconstrains the cells to evolve in the respiro-fermentative path-way (as ethanol is always produced to cancel the dilution effectsand maintain the concentration around Eref) while when Ein > Eref,the cells are constrained to evolve in the respirative pathway (as

ethanol is never produced and only consumed).

If the ethanol set point is chosen so that Eref > E0, the cells areevolving through the respiro-fermentative pathway during the firsthours (as the controller constrains the cells to produce ethanol

tch cultures of S. cerevisiae. Evolution of the ethanol probe measurement E aroundump speed and the parameter � , image of the cells growth rate.

36 L. Dewasme et al. / Biochemical Engineering Journal 53 (2010) 26–37

F : expeo s, gluc

iadtwr

ttorE1

Ft

ig. 15. Experimental runs of industrial-scale fed-batch cultures of S. cerevisiae. Starsf the ethanol controller to the same process. Evolution of the feed rate and biomas

n order to reach the set point), which is beneficial as the cellsre driven through the same pathway in the future growth con-itions (indeed, Ein < Eref). On the other hand, if Eref is chosen sohat Eref < E0, the cells are evolving through the respirative path-ay during the first hours as ethanol has to be consumed until E

eaches Eref (note that at this moment, Fin = 0).The bad resulting consequences are (1) a lost time induced by

he growth on ethanol which is very slow in comparison with

he growth on glucose and (2) a latency which is experimentallybserved when the cells are switching from the respirative to theespiro-fermentative pathway (this is actually the case here, asin < Eref). In Fig. 14, the waste of time can be estimated to about0–15 h as the final batch time is 50 h (instead of 35 h, resulting

ig. 16. Experimental results of the ethanol regulation applied to industrial-scale fed-batche feed flow rate Fin expressed in percentage of the maximal pump speed and the param

rimental realization of a recipe based on heuristics. Circles: experimental applicationose and ethanol concentrations.

in a decreased productivity). Note that the oxygen limitation dis-cussed in Fig. 13 is still present (see the small deviation between30 and 40 h in Fig. 14).

6.3. Industrial-scale results

Industrial-scale fermentation is generally so costly that biotech-nological industries establish some very strict security norms that

should never be overridden. An open-loop protocol is generallydefined. The same feeding profile optimized through previous runs(their number and so, the efficiency of the method, being limitedby the financial provisions) is imposed, as a recipe based on heuris-tics, for each run of the production campaign. For confidentiality

h cultures of S. cerevisiae. Evolution of the ethanol concentration E around Eref = 1 g/l,eter � , image of the cells growth rate.

Engin

rd

(aTram

FltTsetd

7

cicpvaunuaaa

waoioop

[

[

[

[

[

[15] K.J. Astrom, B. Wittenmark, Computer Controlled Systems Theory and Design.

L. Dewasme et al. / Biochemical

easons, the operating conditions of these experiments cannot beetailed.

Fig. 15 shows two different experiments realized in open-loopthe principal constraints being the security norms and a limitedccumulation of ethanol) and with closed-loop control on ethanol.he aim of each run is to reach a fixed biomass concentration (rep-esented in percentage for confidentiality reasons). Obviously, 30 hre spared in the second case, leading to a productivity improve-ent estimated to 40%.On-line results obtained with the controller are presented in

ig. 16. The only scaling parameter that has been adapted from theaboratory-scale control settings is the initial volume (rememberhat V is used to adapt the gain in the expression of b, see Table 2).he observations are very similar to those made at laboratory-cale except for a more important noise magnitude observed on thethanol signal. An explanation to this phenomenon is that whereashe probe, and particularly its size, remain unchanged, the noiseisturbances due to the stirring increase with the scale.

. Conclusion

Based on singular perturbation and model linearization, a RSTontroller is designed to regulate the ethanol concentration at anmposed setpoint. This design is based on a pole placement pro-edure (for setpoint tracking) and the selection of an observerolynomial (for loop robustification), which can be achievedery easily and independently. The controller requires the onlinedaptation of the varying cells growth rate, considered as annstable exponential disturbance to be rejected, justifying theon-applicability of controllers such as PID. The estimation of thenstable pole is achieved through a simple recursive least squareslgorithm. The influence of latency phases and sensor dynamics canlso be taken into account. Robustness against measurement noisend model uncertainties can also be easily handled.

In all the experimental validations, the controller performedell independently of the bioreactor scale, demonstrating its reli-

bility under various conditions. As compared to conventional

pen-loop operation in industrial productions and previous exper-mental results using closed-loop PID-like control, the applicationf the presented particular closed-loop control can ensure a robustngoing control all along the culture and leads to very significantroductivity gain.

[

[

eering Journal 53 (2010) 26–37 37

Acknowledgements

This work presents research results of the Belgian NetworkDYSCO (Dynamical Systems, Control, and Optimization), funded bythe Interuniversity Attraction Poles Programme, initiated by theBelgian State, Science Policy Office.

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