Also I am curious how one modifies a PID controller to keep the RPM of the reaction wheel low. With a standard PID controller you would eventually exceed Max RPM, wouldn't you
the reaction wheel works because of the large moment of inertia of the wheel. when the bike begins to tip over, it applies a torque to the wheel. you can imagine trying to get that wheel turning with your hands, it would offer a lot of resistance at first before getting up to speed. the bike is applying torque against that resistance and this moves the bike. this means that, if the moment of the wheel is large enough, and the correction small enough, you could make a correction without even spinning the wheel very much at all.
when the bike is making a correction, it can overshoot and then stop the wheel suddenly, which would ultimately result in the bike becoming perfectly upright and the wheel not accumulating any speed from one correction to the next.
if the momentum of the correction you need to make is greater than the momentum of the wheel spinning at max RPM, then the bike will fall over. this means that the system will fail if the bike is pushed too hard, becomes too off-balance or if there is something heavy, like a person, on top of it. with a wheel that was heavy enough, and a motor strong enough, the bike would be able to make itself upright from laying on the ground or keep itself upright with a person and cargo on top.
You change the target lean angle based on RPM. Let's say there's a side wind from the right, the wheel keeps spinning faster, so it'll set the desired lean further to the right until the RPM starts dropping.
when the bike is making a correction, it can overshoot and then stop the wheel suddenly, which would ultimately result in the bike becoming perfectly upright and the wheel not accumulating any speed from one correction to the next.
if the momentum of the correction you need to make is greater than the momentum of the wheel spinning at max RPM, then the bike will fall over. this means that the system will fail if the bike is pushed too hard, becomes too off-balance or if there is something heavy, like a person, on top of it. with a wheel that was heavy enough, and a motor strong enough, the bike would be able to make itself upright from laying on the ground or keep itself upright with a person and cargo on top.