Automatic Control of Bioprocesses - Measurement, Monitoring, Modelling, and Control of Bioprocesses - page 42

the Kalman filter [ 9 ] is minimization of the error covariance of the estimation of
the state variables. Therefore, not only the process model, but also the estimated
error covariance differential equations have to be integrated online. If a nonlinear
state model is used, the filter is called an extended Kalman filter (EKF). A con-
tinuous-discrete EKF uses a continuous nonlinear state model and a discrete
measurement model. The differential equations are integrated as long as no new
measurement value is available. If a new measurement is available, the filter
equation is applied. As a result, the estimation error covariance is minimized and
the estimated values of the state variables are adjusted to the measurements. By
using a Kalman filter, the time-varying characteristics of cultivation processes can
be implemented in a control algorithm.
A general overview of specialized state observers is given by Kawohl et al.
[ 10 ], who compared different optimization-based state estimation algorithms to
judge their estimation quality. The Bayesian maximum, an a posteriori-based
constrained extended Kalman filter, the moving-horizon state estimation, and the
classical unconstrained extended Kalman filter are compared through Monte Carlo
simulation experiments. The authors conclude that the moving-horizon state
estimation shows greater potential for state estimation in small systems. For
higher-order systems, the adjustments of the filter parameters as well as the
numerical optimizations were more difficult.
2.3 Control Action
The control action (actuating variable) is the resulting action that the controller
performs corresponding to the control law, e.g., setting the substrate flow rate to
the appropriate value. Figure 1 shows the principle of a closed-loop controller. The
control action is the result of the feedback given by the process measurement,
which might be further processed by a soft sensor, and the control algorithm. The
overall goal is to minimize the deviation between the set-point and the controlled
variable.
The next sections discuss a wide variety of state-of-the-art control applications
for bioprocess automation. First, PID-based controllers in combination with dif-
ferent soft sensors are presented, and then model linearization approaches are
discussed. This is followed by fuzzy logic- and artificial neural network-based
controllers, a model predictive controller, as well as combinations of the three
latter methods. Lastly, probing feeding, extremum-seeking control, and a heuristic
control strategy are discussed.
A very basic approach is presented by Lindgren et al. [ 11 ] and Kriz et al. [ 12 ]
based on a real-time in situ SIRE biosensor system combined with a two-step
controller (on/off control) for yeast cultivation at different biomass concentrations.
Their controller could manage a set-point of 10 mM glucose for 60 min with
standard deviation of 0.99 mM at biomass concentration up to 80 gL -1 .