Multiphase Bioreactor Design

require experiments at lab or pilot scale with extremely well controlled environmental
conditions. In the same way a new strain might require different operating strategies in
order to achieve a pre-established economic output.
One issue is the potential benefit of process control and the other is the practical
benefit achievable with the current state of the-art in theory, practice and hardware.
Process control has both benefits and costs associated. As mentioned by Royce (1993) the
cost/benefit ratio did not justify up to now investments in advanced process control. In
the present section we will go through some important concepts in bioprocess automation
and control while trying to focus on the practical usability of the methods in terms of
such ratio.

Optimal Open-loop Control

In open-loop control optimal time profiles for manipulated and state variables are
evaluated off-line according to some predefined economic profit function. The optimal
trajectories for the manipulated variables are implemented on-line using for instance
programmable controllers. No automatic corrective action is taken if the process deviates
from the expected optimal path. The central task for open-loop control is hence to
determine optimal trajectories for the most relevant process variables (relevant in respect
to the process performance) using appropriate design procedures.
Two important points should be noticed. The first is that the model must be
sufficiently detailed in order to describe the most important features of the process related
to the economic profit function. The optimal C-source feeding rate profile is often
evaluated in this manner in the industry. The second is that, considering that no on-line
corrective actions are taken, this control leads almost inevitably to sub-optimal process
operation due to process disturbances and parametric uncertainty. This question will be
discussed further in the next section.
Traditionally, the open-loop control problem is solved by applying mathematical
optimisation techniques based on Pontryagin’s maximum principle (e.g. Modak, 1993).
As pointed out by Simutis et al. (1996) this technique is difficult to apply and is subject
to some practical limitations:

1. Only simple models can be worked with Pontryagin’s maximum principle to keep the
   mathematical analysis workload at bearable costs. However sufficiently accurate
   process models are normally complex models.


2. Practical constraints in objective function and physical equipment hinders the
   application of the method.


3. High development times even for experienced scientists, and only a few specialists are
   able to properly apply this theory.

Some authors suggest the application of stochastic optimisation techniques that can be
used successfully with today’s availability in computing power (Montague and Ward
1994; Simutis and Lübbert 1997). In relation to classical optimisation techniques the
advantages are clear: the method is more robust, much simpler to apply and no
restrictions on model complexity and objective function constraints are imposed. The
only serious constraint is computation time. In the work of Simutis et al. (1996) it was

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