It is all highly dependant on your exact setup, the intelligence of the controllers and how they interact.
Yes, the bulk phase is when the batteries are not fully charged. With lead this is while the voltage is less than say 14.4V. I would hope that both controllers would be working together during this.
But this only brings the
battery up to say 80% charge, the last 20% goes in during the absorption phase when the controllers maintain the
battery voltage at 14.4V for a suitable period of time, then fall back to about 13.8V as a float charge. (These are general numbers, not necessarily correct).
This is where I foresee potential difficulties if one controller has a slightly different (higher) absorption voltage setting then the other one might decide that absorption had completed and fall back to float. When the controller left with all the load might not have the current to keep the
battery at the absorption voltage, voltage drops, triggers it back to bulk mode, maybe other controller sees the same thing happening, kicks in again, cycle repeats who knows ? Either way absorption is disrupted
Absorption is quite important, as I said it accounts for maybe the final 20% of the charging. So if say you have drained your
battery to no less than 50%, the bulk phase puts in 30% and the absorption the final 20%.
Different controllers manage the absorption phase in different ways, the most basic ones just for a set time period, more sophisticated ones monitor the current and when they see it tailing off go into float.
Then there is the question of when the
battery is at float but you start using power from it. The voltage drops to say the nominal 12.7V of a fully charged
battery, actually less under load. Does your controller now work as a power supply, as it should, to provide as much current as the
solar can deliver to add to that drawn from the
battery, or is it just a dumb one. How does it determine when to restart the bulk-absorption-float operation. Will both work together in harmony sharing the load ?
Basic ones just work on a 24 hour cycle. Once the sun comes up in the morning they attempt the bulk/absorption/float cycle. Might complete, might not. Then only get re-triggered and start again after a period of darkness (night).
That can actually be quite bad for the
battery if it doesn't really need charging, e.g. the van is not being used much, just parked up. or driven around without using much from the
battery. Pushing it into absorption mode every day when not needed is harsh. A decent controller will sense this and just keep it in float, until it decides a full cycle might be a good idea. Maybe once a week, or longer. Float is safe indefinitely, a periodic absorption charge is a good thing for a wet cell to stir up the acid which otherwise stratifies. But not every day. Other technologies do not require this at all.
Better controllers are more clever.
What really happens in a motorhome ? We drive around, the alternator kicks in possibly confusing a simple controller, we park up somewhere shaded, move on, a bird poos on our panel or some leaves fall on it knocking out some or all of the capacity, maybe we plug in to some EHU for a while, all very confusing for a simple controller.
Park up for a few days in one spot, set out the second panel, and it's simpler.
I can think of many other reasons why things might not work smoothly, but basically my advice would be to try rig up a connector for your folding panel to put it in parallel with the roof one, feeding a single controller that is rated for the combined capacity. That inexpensive one you have bought, at 20A,
might just cope with 250W combined, in practice you won't see 250W from your panels in the UK except in the most favourable conditions, and whilst your batteries are low.
Actually that £24 controller seems too good to be true. If it is genuinely an MPPT, not actually just
PWM (it looks just like many of the basic
PWM controllers available everywhere at similar prices and does mention
PWM whilst claiming to be MPPT) , and can say drop 24V down to 12 efficiently you could even rig your two panels in series to get the best from them.
Be cautious connecting and disconnecting them, you can get some very big sparks if the sun is shining that could damage the connectors and fry your controller, cover it with e.g a towel whilst doing so.