It depends a lot on what your source water is if distilled is needed ....
Thinking about it some more ... Algae is not going to thrive in just distilled water + buffer. It is going to need nutrients. If your tap water isn't too bad (ie liquid rock!) you can prob use tap + nutrient as your control.
Eg. You can decide to use a complete hydroponics fertilizer as your nutrient base. Mix up an appropriate concentration of the fert + tap & call that your control #1. That will have an intrinsic pH. The fert solution is a buffer in its own right, so might keep that pH relatively steady. However, as the nutrients are used up, the pH might shift. You are going to have to monitor that & may have to do some additional dosing to keep things constant. <You will have to dose all your experimentals the same way if dosing is needed. ... This si going to depend on length of the experiment ... you prob have to dose the ferts if it lasts more than a few weeks.>
Now that you ahve your control, you will have to vary the pH somehow. Altering the buffering system (eg adding crushed coral = CaCO3, etc) is the most fool proof way. But I really can't think of any buffering system that is also not physiologically active & skew your result. Even HCO3 may have a effect if the algae is capable of biogenic decalcification. You could do a double control ... Eg adding NaHCO3 to one to raise the pH & H2CO3 to another to decrease it, that controls for the HCO3, but not the Na ....
You might try maintaining the different pH by adding strong acid or base. Ideally, you would need a constant feedback loop & some form of auto dosing equipment, but with the fert solution acting as buffer, you might get decent stability if you manually adjust things daily. Say, you add Ca(OH)2 to raise the pH (vary the amount to increase to different pH ranges) & HCl to decrease pH. Check daily & adjust your experimental tanks so the pH is within range. To account for Ca & Cl, you would need a second control - fert + CaCl2 only. <Since Ca & Cl are both in the balanced fert solution, chances are this will be the same as control 1, but do it just to be through.>
I don't know if the daily pH adjustment is adequate, nor if your tap water is suitable for this. <Some miniciple water is already doctored with CaO or Ca(OH)2 +/- HCl. Others are way too hard (too high KH) for you to easily change the pH with acid/base.> You might want to do some preliminary tests on the various water combinations to see how it pans out.