The R_RAMP = 436257.10 which would be 436.25 kOhm with Rds(on) = 0.002 which would be worst case in temp for the mosfet

 

That MOSFET is only rated for 30v, it's too low for operation at 24v, you need something rated at 50v or more. But the ADP1850 is only rated for 20v so can't be used on a 24v supply.

But I sense you're blindly following the design guide without understanding what it's telling you. You don't calculate for every gain, you make intelligent informed decisions based on output power, efficiency, etc about the values you're going to use for the current sense resistor and based on that you choose a feedback loop gain that works, keeping the feedback voltage within the limits specified so it doesn't go out of regulation. But that only applies to a fixed output voltage variable current load. That NOT what you have, you have a constant current, variable voltage load. You can't use the design guide verbatim, you need to understand how to reconfigure that to work as a constant current supply. Otherwise you are just wasting your time, and your money, on what will be a big smoking pile of ex-supercaps.

 

I try to search on the internet for the answers. Some are easier to understand because they expect others to learn while some write to put-out what's in their mind. I find it hard to understand some then there are forums to ask. People seek answers to questions but the others decide if they need to know it or not.

 

That's because it takes years of experience to learn to design systems of this nature, and you are trying to jump in at the very deep end of high-current, indeed constant current, systems for high-speed charging of supercaps, which few, myself included, have any experience of. I do, however, have 10y+ of designing charging systems for large scale LiPo and LiFePO4 packs so I do understand the pitfalls and I can translate the requirement. My concern is you are picking at different SMPS chips based on headline figures of current capability without any in-depth understanding of how they work or how to apply them in your specific requirement. Most of these will not deliver what you need without extensive experimentation on how to coerce them into providing constant-current regulation. On top of that you have no effective balancing scenario which must be integrated into the charging regime. All the balancing solutions you've investigated so far deal with balancing post charging to handle the self-discharge due to leakage current. Irrelevant in your scenario since this isn't for long term energy storage.

I've said all the above on several occasions in the last 3 pages. Most people on AAC (with one or two notable exceptions) won't answer questions about a subject they have no knowledge of, and as I said, you're asking some very detailed questions about a device 99.999% of users here, myself included, won't have come across or used. There will be some here who can, but probably won't, after reading the thread.

Sorry to be blunt. I'm happy to help you work through the design, though I do have some reservations about your basic understanding of electronics. We do need to work from the ground up on this. There are no short cuts.