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schemes such as DMC use a linear model to calculate the required future changes in the manipulated variable that will result in optimum set point tracking for a specified performance index. This linear model, normally obtained from the initial dynamic response of the bioreactor, is used by the controller to guide the control actions during the whole fermentation run.

However, for this fermentation, when this is allowed to happen, the controller makes large control actions in the latter stages of the process, which cause large and frequent oscillations in the manipulated variable, that is, in the temperature of the inlet air (Fig. 28.7(a)) and of course these oscillations cause similar oscillations in the temperatures within the substrate bed (Fig. 28.7(c)). Such large oscillating control actions are undesirable, especially if they are not necessary. The problem is that the controller had worked out its control strategy based on the initial part of the process during which growth was accelerating and temperature control was becoming ever more difficult. The controller worked out that it is necessary to apply large "preventative" control actions and when growth decelerates in the latter stages of the process, it still applies such large control actions, even though they are not necessary. This problem can be overcome by instructing the controller to establish a new linear model after each mixing event. Since there are three mixing events, four different linear models are used (i.e., the original one plus a new one after each mixing event). In other words, the controller changes its control strategy during the fermentation and this minimizes the oscillations in the inlet temperature (Fig. 28.7(b)) and therefore also the oscillations in the temperatures measured in the bed (Fig. 28.7(d)).

The necessity for the use of multiple linear models can be explained in a different way. The behaviour of the fermentation process is history dependent, that is, the evolution of the system from a particular point relies on what happens before this point. This can be easily understood when it is recognized that the rate of growth at any instant depends to a significant degree on the amount of biomass that was produced in the fermentation from the time of inoculation up until that instant. Since the underlying behaviour of the system (the rate of growth) varies significantly during the process, then the dynamics of the control system need to be changed.

As shown by comparing Figs. 28.7(e) and 28.7(f), it actually makes no difference to the biomass growth curve whether a single linear model or multiple linear models are used, however, it is obvious that multiple linear models should be used since the same performance is achieved, but without large and frequent control actions.

Note that the predicted growth with DMC control is superior to that predicted for PID control (Figs. 28.7(e) and 28.7(f)).

As a final point, this case study has shown that mathematical models of SSF bioreactors are useful tools in the initial stages of the development of control strategies and in the initial tuning of controllers.

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