Automatic Control of Bioprocesses - Measurement, Monitoring, Modelling, and Control of Bioprocesses - page 49

to tune a PID controller are described in many publications [ 19 , 20 , 31 - 33 ] where
the authors use, e.g., genetic algorithms to obtain the optimal parameters.
Online estimation of control parameters is described by Bastin and Dochain
[ 30 ] as well as by Perrier et al. [ 34 ]. This is used in various control strategies
[ 35 - 38 ], where the upper bound of the estimation error is minimized online and
the resulting parameters are considered to be the optimal ones. Another approach
in this direction is given by Kansha et al. [ 39 ], introducing a self-tuning PID design
applying just-in-time learning. This algorithm compares a given database with the
state of the process online and adjusts the gain parameter according to the obtained
results, performing self-tuning derived from the Lyapunov method [ 40 ] to guar-
antee convergence of the given gain parameters.
3.3 Model Linearization-Based Control
Due to the inherent complexity, nonlinearity, and nonstationarity of bioprocesses,
Renard et al. [ 41 ] proposed a so-called RTS control scheme with Youla parame-
terization to overcome these problems. They develop their control approach for
S. cerevisiae cultivation, controlling the ethanol concentration to a nonzero value.
For substrate concentrations higher than the critical substrate concentration S crit ,
the occurrence of overflow metabolism is assumed. Since S crit for yeast fermen-
tations is 0.1 gL -1 , the authors suggest respirofermentative conditions and a
quasisteady state of the substrate concentration (considering no accumulation of
substrate and instantaneous consumption, as long as the process does not deviate
dramatically from the predetermined operation conditions). They obtain a model
for the relation between the feed F in and the measured ethanol concentration as
well as a discrete time transfer function mapping the feeding rate to the ethanol
concentration, which is linearized for the purpose of control law application. The
controller considers cell growth as an unstable exponential disturbance. This
control method is based only on online measurement of ethanol. For the yield
coefficient, a rough estimation (e.g., from literature) seems sufficient. They identify
the state between fermentative and respirative operation as another way to control
the specific growth rate close to the critical value when overflow metabolism
occurs. They initially employed the controller in laboratory-scale fermentation
[ 41 ] with a set-point of 0.7 gL -1 ethanol concentration, achieving very small
errors in the controlled variable. Later in the cultivation, they observe an accu-
mulation of ethanol, considering the limitation of oxygen. This is considered in a
subsequent investigation [ 42 ], leading to a redesign in the controller scheme
employing a feedforward term and determination of the OTR from exhaust gas
measurements. The performance of the new proposed controller is evaluated via
simulation studies of the process with offline data. The same control algorithm was
later [ 43 ] employed in an industrial fermentation process. The authors claim 40 %
increased productivity using their algorithm compared with the previously used
open-loop control.