Pros , Please help me on DIP(Double Inverted Pendulum)

[ntwagent]

Hi Geeks! ;-)
I am trying to simulate a controller for DIP (two stage linear one) using fuzzy techniques. I have faced a problem. I calculate the desired force for the move of cart by means of fuzzy, but don't have any idea about how to calculate the dynamical response of each pole to that force (using crisp techniques).
I have surfed in the internet for the solution but couldn't have found any thing useful.
can you pros help me out on the subject?
I would me really thankful.
cheers,

[Reedbeta]

I've never heard of fuzzy physics before. Would you mind explaining what these "fuzzy techniques" are that you're using?

[ntwagent]

Well, the field of fuzzy is so vast. Fuzzy logic is not any less precise than any other form of logic: it is an organized and mathematical method of handling inherently imprecise concepts.
in use of it for some controlling problems, instead of modeling a system in precise and confusing equations, some appropriate rules, simply showing the behavior of the system, are defined. this imprecision gives a high flexibility to the model, and because of this has a wide use in artificial intelligence.

For example, an extremely simple temperature regulator that uses a fan might look like this:

"IF variable IS set THEN action":

IF temperature IS very cold THEN stop fan
IF temperature IS cold THEN turn down fan
IF temperature IS normal THEN maintain level
IF temperature IS hot THEN speed up fan



the question that i have asked is not dealing with fuzzy. I have problem with obtaining the dynamical response of the poles to the force applied to the cart. I mean how the angles will be changed after applying the force to te cart? is there any equations?

please help me out.

[Reedbeta]

I know what fuzzy logic is. But I don't understand how you'd apply it to physics simulation.

Anyway, if you're looking for equations of the pendulum's motion, they shouldn't be too hard to work out, should they? Here (http://en.wikipedia.org/wiki/Double_pendulum) is an article with the equations for an ordinary double pendulum; to get an inverted one I think you would use the same Lagrangian and just reverse the signs of the y coordinates of the two bodies. Also you'd have to add terms for the cart, but that shouldn't be hard, and this (http://en.wikipedia.org/wiki/Inverted_pendulum) shows you the Lagrangian for an inverted single pendulum with the cart, so you should be able to combine the two.

[ntwagent]

On my own simulation I have used fuzzy as follows:

I have considered 3 fuzzy systems, two ones have the angles of the first and the second poles and their velocity as inputs and the forces needed to be applied on the them as outputs. and the final fuzzy system by means of the values obtained from the first two, computes the proper force for the cart. all are done by rules such as:
"if (betha1 is zero) and (betha1d is positive) then forc1 is positivebig"
in which "zero", "positive", and "positivebig" are fuzzy terms that are defined by a fuzzy set.
these rules can be made by use of the knowledge of an expert and simplifying the equations.
now after defining the rules, its ready. i give the state of the system as an input to these fuzzy system, the steps of fuzzification of the inputs, applying inference rules, and finally defuzzification of the result is carried out. now i have a crisp value for the force that helps me to update the state of the pendulum.
since everything is fuzzy it helps the result be flexible.
thats all.
i hope i have explained clear enough.

BTW, Thank you for the help. it was really useful.
cheers.

[Reedbeta]

two ones have the angles of the first and the second poles and their velocity as inputs and the forces needed to be applied on the them as outputs.

I see what you mean. The actual physics is not fuzzy, you're talking about the *control* system as employing fuzzy logic to make its decision about what to do. That is what I was confused about.