Multiphase Bioreactor Design

shown that stochastic optimisation techniques may provide results of the same quality as
Pontryagin’s maximum technique with much less development cost.
Considering that stochastic approaches are not limited to simple models and that
computing power is less and less a constraint, this represents an attractive solution for
industrial applications of open-loop control.

Closed-loop Control

In general terms closed-loop control aims at forcing the process state to follow some
predetermined path (reference). This path may be defined heuristically or mathematically
and can be kept unchanged along the operation or subject to periodic adaptation.
Going back to open-loop control discussion, an obvious application of closed-loop
control is to enforce the optimal trajectories evaluated within the open-loop procedures.
The viability of closed-loop control is constrained by the availability and robustness of
on-line measurement devices for the control quantities. This poses currently the most
serious impediment for closed-loop control in the industrial environment. In many
situations the problem can be circumvented by implementation of estimation models that
provide on-line and real time estimates of the control quantities. Not surprisingly most of
the many control studies reported in the literature rely on linear or non-linear estimation/
predictive (adaptive) models. Several control strategies can be implemented ranging from
classical PID control to non-linear control. In the present section we look to some of the
most pertinent issues in bioprocess closed-loop control.

Compensation of measurement dynamics

It is often the case in industrial installations that measurements are available but process
conditions under which they are performed and/or the intrinsic sensor dynamics lead to
distorted information on relevant process properties. Common practical situations are
related to the design of the process production line, to sensor location and to spécific
operating conditions. As a simple practical example, process measurements, namely of
quantities such as concentrations, may have to take place quite distant from the source of
interest. In such cases, and merely for reasons of process layout and operating conditions,
measurements are corrupted by a first order dynamics with a transportation lag, (e.g.
Tham et al., 1989). This limitation in the quality of these measurements may lead to
unnecessary difficulties even in the simplest regulatory problem where control set-points
are kept constant. Such difficulties are particularly meaningful for time varying
reference-tracking control problems (with rapidly changing outputs) or in naturally
unstable process operations where the precise knowledge of the output transient
trajectory is essential for control purposes.
In general terms and whatever the causes, for those measurement systems where
significant time constants and transportation lags are observed, sensor outputs will not
(instantaneously) be representative for the real process. This may hinder the
implementation of efficient operation control policies.
Recently, Georgieva and Feyo de Azevedo (2000) studied the application of neural
networks (NN) for recovering process outputs from sensor signals, e., for modelling
sensor inverse dynamics so that once the trained NN is placed in series with the

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