Automatic Control of Bioprocesses - Measurement, Monitoring, Modelling, and Control of Bioprocesses - page 44

V 0 X 0

F 0 ð t Þ¼ l sp
Y XS

C feed e l sp t t 0

ð Þ

þ m ð 2 Þ

X 0 ¼ Xt ¼ 0 ð Þ V 0 ¼ V ð t ¼ 0 Þ

Using such a controller, the cultivation feed is performed following a prede-
fined trajectory. Knowledge of the inoculum size as well as the specific growth rate
and the yield factors is obviously needed to perform this kind of open-loop control,
which is called feed forward control. Advantages and disadvantages of open-loop
control are presented by Gnoth et al. [ 13 ]. In case of disturbances (e.g., wrong pH
value as a result of a failure), the system's behavior will differ from the prediction.
In this case, the feed is predicted incorrectly and the result of the cultivation is not
as designated, resulting in a waste of resources. To prevent this, the plainest
closed-loop control approach is to add a feedback to the feed forward term for
regulatory action. These feed forward/feedback controllers are usually a class of
single-input single-output (SISO) controller. The control law Eq. ( 4 ) is the sum of
the feed forward part F 0 , which is the estimation of the approximately needed feed
rate Eq. ( 2 ) at time t, and the feedback part F b , in this case delivered by a PI
algorithm Eq. ( 3 ).

F b ð t Þ¼ K P e ðÞþ K i Z t
0

e ð s Þ ds ð 3 Þ

u ð t Þ¼ F b ðÞþ F 0 ðÞ ð 4 Þ

3.2 PID Control Based on Soft Sensors Measurements

Controllers with more than one input value are classified as multiple-input single-
output (MISO) or multiple-input multiple-output (MIMO) and are represented as
multiloop PID or cascade PI controllers. MIMO systems couple their input values
according to the interaction and are therefore able to map higher complexities of
the controlled process. They are supposed to be more accurate in their control
action than SISO systems. The structures of both controllers (SISO and MIMO)
are shown in Fig. 2 .
Applications of these controller types for bioprocess automation are discussed
in the following sections.

3.2.1 Single-Input Single-Output Control

The combination of a Kalman filter, whose measurements came from a glucose FIA
system, and a PI controller is presented by Arndt and Hitzmann [ 14 ]. The system was
applied to S. cerevisiae cultivation to control the glucose concentration. The Kalman