I'm using a Allen Bradley Ultra 5000 to control a Rotory Inverted Pendulum. The Ultra5000 is programmed using C language. I need the formula to dynamically calulate the distance and speed to catch the pendulum if it is physically moved from the vertical position. An Excell macro or similar would help. Please post a reply.

 

Speed and distance don't really matter it's the acceleration that does.
If the pendulum is L long and is tilted by alpha degrees, g=gravity acceleration =9.81
then you need a acceleration a
a=g*L/tan(alpha)
this acceleration will keep the pendulum stationary if you want it to become vertical you need to increase a and the sample the angle constantlly and control a with a control loop like PID.

 

a=g*L*tan(alpha)

I modified te formula as above and tried it in a spreadsheet and it looks like what I need as a starting point. I will use a PID to increase the error over time to try to stableise it a bit beter. Thanks for the input.
Dave.

 

What you meant to say was "I'm taking a motion control and advanced dynamics class. I have a practical application thesis for which I've been given a brand-spanking new Allen-Bradley controller. I know some of the math to analyze the system, but don't know how to express it in C inside the controller."

If you're interested in the math, go read through this excellent tutorial at UM:

"http://www.engin.umich.edu/group/ctm/examples/pend/invpen.html":http://www.engin.umich.edu/group/ctm/examples/pend/invpen.html

Unfortunately, all the stock demo programs for the Ultra5000 are for real industrial applications like web tensioning and flying shears.

Because you posted as anonymous and didn't provide any evidence you've gone further than this site researching the problem, that's where my contribution is going to stop. Give some information about the physical and electrical setup of your system and you might get some more response.

 

Responding to Bruzze's Fri, Jun 28, 2:19 pm, query:

A technical correction.... the equation you presented is valid only for small deflection angles, say less than 10 degrees. Appreciable error can be introduced if the deflection angle is, for example, greater than 15 degrees!

Regards,
Phil Corso, PE
(Boca Raton, FL)