So if we do an example here, that's my unmodeled torque in the body frame.
It's a fixed number.
Just pretend some valve didn't close properly,
you've got some outgassing out of that valve, that's a particular problem.
Now you've got this disturbance.
And we want to do a maneuver just bringing it to rest, regulation problem,
as we're predicting our status rate error should go to zero.
So my rate error should go to zero.
And my status state attitude error should be this divided by,
I think I have a gain of one.
Yep.
So it's easy to do the math.
This should be my attitude error in MRPs.
If you run it through the simulation then, you will see my rate errors,
I'm tumbling at the beginning getting things going with the control.
But it stabilizes and my write errors do go to 0 as predicted, so that's nice.
And the attitude errors of MRPs, they start out with here.
They try to drive into 0.
But if I have 0 added to my control basically turns off.
I have 0 rate, 0 attitude and
the unmodeled disturbance keeps moving you away from where you want to be.
Once you move far enough away, the feedback says no, move right and
the disturbance says no move left, and they find their balance.
That's the new equilibrium, and that's what's happening here.
It gets close to it, but you get precisely the predicted offsets.
If you're not happy with that performance,
you would have to increase K if you're keeping the same control structure.
Make it ten times bigger, this would shrink ten times.
But that's kind of nice, you can see now we've got nice analytic guarantees,
with at least constant disturbances.
And if you can bound them, you can get a feel for just how much of an offset you
can have, even if they're time-varying, and go in there.
>> This is assuming that you're constantly in control of feedback, right?
It's not- >> Yes, continuous control.
Yep, not impulsive implementations, or on and off.
If you turn it off again you would start to drift,
this would then, without the control this would accelerate infinitely.
Fact, it would go off to infinity.
In fact, if you look at asteroid stuff that's the york effect you have
a torque that's always there, and no control in an asteroid.
>> Fall apart.
>> Fall apart, exactly.
They'd become binary systems, and tertiary systems, and fun things happen.