Forcing Functions for Microorganisms

It is usually impractical to force full-scale processes while in normal operation. An unintended upset may generate a useful forcing from which the Forier Series treatment can provide useful frequency response information. For example, a flood, lightning storm, or power failure can force the process in terms of flow rates, temperatures, nutrients, or the like. Usually, the higher sine frequencies are poorly excited, and the frequency response analysis becomes seriously inadequate shortly after the frequency corresponding to the time constant. With sine forcing you insure that a given frequency is studied, but the gain ratio at high frequency may be too small to measure. Step and pulse forcing tend to excite a wide range of frequencies, but again the high frequency information may not be decipherable.

Forcing of biosystems is not at all straightforward. Most research focusses on the CSTR (continuous stirred tank reactor). The forcing with which we are familiar applies the forcing to some input to the well-stirred tank. This is not the forcing that the microorganisms encounter. The response to the forcing of the reactor is the forcing function of the organisms. In other words, when we change the concentration of sugar entering the bioreactor suddenly from one concentration to another, this is step forcing. The sugar concentration in the bioreactor responds but probably not in the expected first-order manner because sugar is being consumed by the microorganisms. Analysis of sugar concentration with time can provide the actual forcing function for the microorganisms. The problem is that the change in sugar concentration tends to be quite smooth with very little excitation of high frequencies.

A much better way to force sugar concentration is to add some suddenly right into the bioreactor. Because the uptake by the organisms is slow relative to the sudden dumping, the initial part of the forcing should be very close to the front edge of a step. The sugar concentration will then decline as it is consumed by the organisms, but we can counter this by controlling its concentration. It is not so easy to devise an on-line controller for sugar concentration.

In summary, a sudden increase in something sensed by microorganisms is relatively easy. A sudden decrease is technically quite difficult. Forcing the bioreactor is not the same as presenting a well-defined forcing to the microorganisms.