If the voltage is fixed then it should not fluctuate. If you are finding fluctuations this is probably because the current demand at times can not be met by the power supply and as a result is dropping. So there should be a strong correlation between current demand and voltage drop.
Oddly enough I did supervise an MSc student making a detector to try and measure the difference between sewage and sludge, so that when pumping sludge into a tanker for disposal, they knew when to stop the transfer and not pump sewage. We tried detection plates similar to that described in that link and we found the cell actually generated a voltage when in the sewage / sludge mixture.
My worry about the PWM method of controlling the voltage is, it is not actually controlling the voltage, as that will always be the peak voltage. Rather it is turning the voltage on and off and altering the duty cycle. This will change the average voltage but not the peak voltage. The physicist in me is wondering about the importance of the actual voltage and the effect it has on the electrolysis process, which in the end you are trying to investigate.
By the way the student doing the sewage / sludge detector was not very popular with other users of the lab.