no, no Joe. on this
JoeJ wrote:It looks like the top should fall to the floor pretty quickly, but doesn't. After some seconds the bodies stop, but the top one keeps levitating in air although the bottom ball is way off of the com, so it should fall.
that part is what is right and expected. what is wrong is that the effector keeps trying to apply control after is find the equilibrium. and that where I believe I either have a bug or something is missing.
it is important to get a clear definition of what is that we are trying to get.
Basically we are trying to make a system that is on unstable equilibrium to become stable.
There are three type of equilibrium:
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stable is when the system reaches a point where any perturbation makes gain potential energy so it restore back to is position of minimal energy.
the secund, indifferent is when a perturbation does not add energy.
these two are un-interesting, because cause is very little that can be done with a system like that.
the third one is the interesting one, it is when the is a point where any deviation from that point makes the system lose potential energy so it will just keep falling.
this of a ball on the top of a mountain, a gust of wind will make go downhill. now think of that ball having a small rocket that can pointed in the direction opposite to the wind direction, is the rocket can match the wind force the ball will state in equilibrium, is it can't it will lose it for tow reasons.
1-the wind is too strong, and the rocket can't match it.
2-the wind is no strong, be the rocket overreact and push it to the oversize.
Unstable equilibrium is the cores of everything in control theory and even nature. for a system to keep that equilibrium is mean that is need a source of energy to generate internal force that can counter act the of potential energy, meaning is most consume energy
in control theory as I expressed before the equation reduce to this, in some space the variable of the system will be determine by the linearization of the equation at that state,
so teh equation will be
Y = A x
but on A there will be a positive coefficient
so to make a system like that stable, engineer add a control variable
y = A x + B u
when the coefficient of B added to A makes all values negative and the system becomes stable.
u, is the input variable. and B is determined by the control that we are trying to model with a PD, and now with a PID.
the problem is that for anything more complex that a pendulum in 2d or a ball running downhill the values of A are very hard to find analytically, however engineers has been downing it for hundreds by trial and errors, that what control theory really is. Now people are trying to doing with neural
networks. the point is, that it very intuitive to get a measure of the system and apply a counter action to correct it, what is hard is to gage how strong or week that action has to be.
but anyway, the test do shows sign that is down the work at least for few seconds, but it is obvious that there is something either wrong and missing that nee to be determined.
finally, imaging a person standing in one leg. if someone give a lithe push, depend on how strong the push is, any person is capable to keeps its balance but tilting its body a little,
we can see that the upper box does lilt, to match the com, but what happen is that in order to do that it adding angular momentum, but once that is reach it does no know how to stop and keep adding more and more, but in doing that each perturbation becomes larger and larger until it can't keep it anymore.
what I expect, is that is tilt and after a while stops correcting. and will be floating