The time-dependent pH value in a fermentation I want to know if someone has supporting tips or solutions to my problem:
In biotechnology, fermentations are used to grow microorganisms. These need a specific media/broth in which temperature, pH, substrate and many other factors conclude to an optimum. Only if the surrounding broth is in optimal condition for the individual microorganism, the microorganism will grow as best as possible.

In my media the broth is buffered with $[\ce{HA}] = \ce{H2PO4^-}$ and $[\ce{A-}] = \ce{HPO4^2-}$.

While the fermentation is running the pH is corrected by $2\ M\ \ce{NaOH}$ which is pumped into the broth. Via balances, the weight is recorded and the input can be calculated.

I know the initial concentrations of my buffer solutions and the concentration of the base that is dropped into at every minute of record.

How can I calcute the pH for an individual timepoint in my aqueous fermentation? My tries via the Henderson-Hasselbach-formula did not work so far...
(Neglecting other surroundings such as stirring, the other media components, the biomass' metabolites, temperature influence on the pKs, etc.),

Thanks in advance!
The pH is not corrected mathematically, it is stabilized chemically by addition of NaOH when the pH sensors get out of range. Your pH is controlled to be constant over the fermentation period (+/- a little bit).

The acid produced by the fermentation is neutralized by addition of NaOH to keep the pH constant. What you can calculate from the data you get is the rate of acid production. The moles of acid produced will equal the number of moles of NaOH added, to a good approximation. The pKa of H2PO4- is 7.2 and the pKa of acetic acid (a typical carboxylic acid) is 4.76, so the acid produced will be "strong" - i.e., fairly acidic in your medium, which appears to be aimed for about pH = 7 - and the NaOH is strongly basic, so they will balance out (approximately).

Interestingly, sodium acetate has a pH range of 8.5 - 9.9 in real life, according to SDS. Calculation is so much more pleasant, where you can calculate pH to three decimals and feel good about it (until you test it in real life and have to calibrate your meter, etc, etc.)