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Analyses of various control schemes for continuous bioreactors

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Bioprocess Parameter Control

Part of the book series: Advances in Biochemical Engineering/Biotechnology ((ABE,volume 30))

Abstract

A common framework is laid through which the feasibilities and efficacies of various control schemes for continuous bioreactors can be evaluated using only the steady state information. It is shown that many important and practical conclusion can be drawn based on the steady state growth models. For this purpose two well known steady state growth models are used, the Monod model and the substrate inhibition model. The control schemes that are reviewed and theoretically analyzed in terms of potential advantages as well as disadvantages, include turbidostats, nutristats, pH-auxostats and those based on various rates such as the base addition rate, the oxygen absorption rate, the oxygen uptake rate, and carbon dioxide evaluation rate. The feasibility of these control schemes is tested by cheking the local controllability and/or stability criteria, while the practical effectiveness is evaluated by analyzing the steady state gains. Existence of input multiplicity is also checked to point out potentially poor static and/or dynamic performances. Finally, a new control scheme is proposed, which is superior to the conventional continuous bioreactor operations and which allows for a multivariable control scheme.

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Abbreviations

A:

system matrix or the Jacobian matrix [Eqs. (7) and (11)]

Am :

the Jacobian matrix [Eq. (76)]

a:

constant in model-3

B:

m × n matrix [Eqs. (7) and (77)]

BAR:

base addition rate, mmoles per h

BARd :

set point value of BAR

BC:

buffering capacity, mmoles per 1

b:

∂f/∂D [Eq. (12)]

b:

constant in model (3)

C:

l × n matrix [Eq. (8)]

c T :

vector defined in Eq. (58)

CER:

carbon dioxide evolution rate, mmole per l

c:

constant in model (3)

D:

dilution rate h−1

Ds, Ds1, Ds2 :

steady state dilution rates, h−1

Dc :

Fc/v h−1

Dm :

Fm/v h−1

DOC:

dissolved oxygen concentration

F:

total flow rate of medium, l h−1

Fc :

flow rate of concentrated stream, l h−1

Fm :

flow rate of medium or water stream, l h−1

f:

defined in Eq. (5)

f m :

defined in Eq. (71)

H+ :

hydrogen-ion concentration, moles per h

H +d :

set point value of H+

K:

proportional controller matrix [Eqs. (15)–(18)]

Kt T :

defined by Eq. (26)

K n T :

defined by Eq. (39)

Kb :

steady state gain of BAR-controlled bioreactor, mmoles

Kc, Kcb, Kcn, Kct :

proportional controller constants

Km :

constant in the Monod Model, g l−1

Kmx :

steady state gain of the modified turbidostat, (% w/v), h

Ks :

steady state gain of a nutristat, (% w/v), h

Kx :

steady state gain of a turbidostat, (% w/v), h

Ky :

steady state gain

Lc :

controllability matrix [Eqs. (9) and (13)]

L 0c :

output controllability matrix [Eqs. (10), (57) and (59)]

m:

maintenance constant, h−1

OAR:

oxygen absorption rate, moles per h

OOC:

off gas O2 concentration

OCC:

off gas CO2 concentration

OUR:

oxygen uptake rate, moles per h

(OH−):

hydroxide-ion concentration, moles per l

\(r_{H^ + }\) :

rate of acid production per unit volume moles H+ per h

\(r_{OH^ - }\) :

rate of base production per unit volume moles OH− per h

s:

substrate concentration, g l−1 or % w/v

sc :

concentration of substrate in the stream Fc, g l−1

sd :

setpoint value of S

sE :

effective feed substrate concentration, g l−1

sF :

feed substrate concentration, g l−1

t:

time, h

U:

vector of controls

v:

volume, l

X:

vector of states

x:

cell mass concentration, g l−1 or % w/v

xd :

setpoint value of x

Y:

vector of outputs

y:

cell mass yield, g cell per g substrate

y0 :

yield constant in the maintenance model

\(y_{H^ + /x}\) :

yield of acid, moles H+ per g cell mass

z:

defined in Eq. (19)

z(0):

initial value of z

α, Β:

constants

Μ:

specific growth rate, h−1

Îœm :

maximum specific growth rate, h−1

Τi, Τd :

controller constant

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Authors and Affiliations

  1. School of Chemical Engineering, Purdue University, 47907, West Lafayette, Indiana, USA

    Pramod Agrawal & Henry C. Lim

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  1. Pramod Agrawal
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  2. Henry C. Lim
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© 1984 Springer-Verlag

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Agrawal, P., Lim, H.C. (1984). Analyses of various control schemes for continuous bioreactors. In: Bioprocess Parameter Control. Advances in Biochemical Engineering/Biotechnology, vol 30. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0006380

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  • DOI: https://doi.org/10.1007/BFb0006380

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-13539-5

  • Online ISBN: 978-3-540-39004-6

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