Robust cascaded control of an animal cell culture
Mihaela Sbarciog a, Daniel Coutinho b, Alain Vande Wouwer aa Automatic Control Laboratory, University of Mons, Boulevard Dolez 31, B-7000 Mons, Belgium
b Department of Automation and Systems, Federal University of Santa Catarina, 476 Florianopolis, 88040-900, Brazil
MihaelaIuliana.Sbarciog, Alain.VandeWouwer@umons.ac.be, Coutinho@das.ufsc.br
1 Introduction
Perfusion operation of cell growing systems provides con-
sistent culture conditions, high productivity and low prod-
uct residence times. In spite of the increased productivity
of the culture, perfusion operation with partial cell retention
is hardly used at industrial scale because of the complexity
raised by the multivariable nature of the process. Althoughseveral studies exist regarding the necessity and the influ-ence of the bleed stream on the cells growth, not much isknown on how to set this process input or how to use it
for control and optimization purposes. Therefore, the ex-isting control implementations on perfusion cultures try to
Figure 1: Control structure
achieve the control goal by only manipulating the perfusion
rate. We present here a multivariable robust control structure
for an animal cell growth process, in which the dilution and
the bleed rates are manipulated to control the cell and sub-
strate concentrations. The control structure combines a par-
tial feedback linearizing control, designed to ensure robust-
ness with respect to parametric uncertainty and uncancelled
nonlinear dynamics, with predictive control principles. 2 The process model
The animal cell culture used in this study is described by a
model, which considers that the cells grow on glucose and
glutamine and their death is governed by lactate, ammonia
and glutamine concentrations. The model equations are:
ξ1 = −bl · Dξ1 + r1(ξ) − r2(ξ)
2) − ar1(ξ ) − r3(ξ )
Figure 2: Closed loop response
goal is achieved by a two-layer control structure as illus-
4 = −Dξ4 + cr1(ξ ) + dr3(ξ )
trated in Figure 1: i) a partial feedback linearizing controller
is designed such that the inner loop has approximately a de-
coupled linear dynamics; ii) two linear MPC controllers are
1, ξ2, ξ3, ξ4, ξ5 respectively represent the concen-
trations of viable cells, glucose, glutamine, lactate and am-
used in the outer loops to compute the inputs of the inner
glutamine in the influent; D = F/V is the dilution/perfusion
The robust performance of the closed loop is illustrated in
rate and bl ∈ [0, 1] is the bleed ratio; ri(ξ ), i = 1, 2, 3 are
Figure 2, where the controlled outputs follow their respec-
reaction rates and a, b, c, d, e > 0 are the stoichiometric co-
tive setpoints in spite of a 20% uncertainty on the maximum
3 Control structure and simulation results References
The control goal is to manipulate the dilution rate D and
M. Sbarciog and I. Saraiva and A. Vande Wouwer, Acceler-
the bleed ratio bl (or bleed rate defined as Db = bl · D) such
ating animal cell growth in perfusion mode by multivariable con-
that the biomass concentration ξ1 and the glucose concen-
trol: Simulation studies, Bioprocess and Biosystems Engineering,
tration ξ2 follow their setpoints defined by ξ re f , ξ re f . This
flected power and SWR simultaneously. stances you’ll be concerned with average test gear you’ll ever own is your watt-power, leaving it up to you to “ask” fordo an adequate job in this department. the output of your transceiver and adjusta calibration knob. Other wattmeters dis-at 2, 14, 28, 50 and, for those meters withit accordingly. A wattmeter can alert youplay only forwa
Vom Schöpfer 10/96 geadelt zu: Yesuja dem Wittelsbacher (der, der Artikel wird grammatikalisch angepasst) Mein Leben mit JHWHIch bin verzweifelt weil es so viel ist sollte ich das in einen Computer eingeben. Meine rhetorische Frage 2001 Weil ich zu viel um die Ohren hatte und nicht aufgeschrieben konnte, kurz später hatte ich Probleme, mit meinem Erinnerungsvermögen. Erst nach einer Gift- und