Automatic Control of Bioprocesses - Measurement, Monitoring, Modelling, and Control of Bioprocesses - page 43

Fig. 1 General schematic of different (alternative) closed-loop control schemes

3 State-of-the-Art Control Algorithm

The most common closed-loop control algorithm is the PID controller. Here, e(t),
the difference between the controlled variable and the set-point at time t, is used to
calculate the control action. Equation (1) is the general form of a PID controller,
with K p as the proportional gain, K i the integral gain, K d the derivative gain
parameter, and u(t) as the control action.

d
dt e ðÞ :

u ðÞ¼ K p e ðÞþ K i Z t
0

e ðÞ ds þ K d ð 1 Þ

Basic PID control is an algorithm responding to current changes with constant
parameters, in which the knowledge of the process is presented. A special form of
the PID controller is the PI controller, which lacks the derivative part (i.e.,
K d = 0), leading to a steadier system in the presence of noisy measurement data.
This type of controller can be found most frequently.

3.1 Open Loop-Closed Loop Controller

The simplest control action for a cultivation process is open-loop control. One can
rearrange typical mass balance equations describing a cultivation process in a
stirred tank reactor to obtain, e.g., Eq. ( 2 ), representing the feeding law for sub-
strate. This is basically an assumption of a known, constant substrate consumption
rate as well as a predetermined constant specific growth rate l sp , which is smaller
than the maximal specific growth rate.