Inverted Pendulum

[iceburging]

Hi all,

Not sure if this is the correct place to post this question but it is loosly robotics related. If anyone has any other suggestions I am open to ideas.

Basically I am working on a classic inverted pendulum control problem, the rig consists of a dc motor to which is connected a fixed rod forming a rotating arm (link 1). A second link (link 2) is connected on a piviot to the end of the arm. Rotational sensors report the position of the links with respect to the vertical position.

Through carrying out a frequency sweep on the motor I have obtained a mathematical model relating the input to the motor to the angle of the arm. What I would like to do next is obtain from first principles a model relating the angle of the first arm from the zero point to the angle of the second arm from teh zero point and devise a controller to stabilise the pendulum in the inverted position.

Unfortunatly nearly all of the information I have found on this topic talks about the cart type inverted pendulum or the horizontal rotary type of inverted pendulum.

Does anyone have any advice as to how I can obtain a model for the pendulum?

 

[akg]

the microchip has an AN related to this topic , searching that would be helpful

 

[iceburging]

The Microchip? is that a website or something? whats the link?

 

[phalanx]

www.microchip.com

 

[dknguyen]

You can only get the model of the inverted pendulum by drawing a diagram and a few free body diagrams and so some mechanics on it to work it out. You need to come up with an equation that is of a familiar form to what you have seen in your control systems class.

For now, try not to think about the electronics and only think about the mechanical aspect of it (to come up with transfer function or polynomial of the system so you can relate it to your control systems class). THen worry about the electronics. You may need to linearize your equation

Best bet is to find a textbook with a sample deriviation and very carefully study it (even if it is for the cart inverted pendulum).

If you can derive the equations for a cart inverted pendulum, I imagine it wouldn't be too hard to do the same with your pivot inverted pendulum.

 

[guyfn]

I suppose you are talking about this:
**broken link removed**
Just go to Google and type Rotary Inverted Pendulum, you will get a lot of pdf links with all the information you need for your project

 

[sobia]

i myself is doing the same project

 

[MrAl]

Hello,


For a lot of problems like this the approximation:

sin(angle)=angle {small angles in rads}

becomes very very useful, and makes the whole thing a bit simpler and linear.
This would mean there would be less difference between this problem and the
cart problem as both would be using a linear horizontal movement as the control
actuator action. For small angles the horizontal distance becomes equal to the
angle times a constant.

 

[oem_odm]

there is a video software call Phun, it allows you to make animations which simulate reality (i think) - i saw it and breifly read about it but didnt try it (all in 15 seconds).

Phun - 2D physics sandbox - Home

try it...you might be able to make your penduluim and test it out in their software - its free

 

[birdman0_o]

Wow thanks for the link!

Edit: Its not free, only a demo version

 

[oem_odm]

also try Physics Help and Math Help - Physics Forums for help

but you have to partly solve/attempt your problem yourself.