Modelling Inverted Pendulum With 2 Propellers (Control Engineering)

[Pipsqueakalchemist]

TL;DR Summary

I'm trying to model an inverted pendulum attached to cart system with 2 propellers at the top of the pendulum. The 2 propellers are meant to be controlled by a controller (PID and pole placement) to keep the pendulum in an upright position. Impulse disturbances are applied to the cart both at the top of the pendulum as well as to the cart.

Hello so as the summary suggests I'm trying to develop a controls system model of an inverted pendulum cart system with 2 propellers on top of the pendulum. I'm trying to obtain the equations of motion and I was wondering if I should include the impulse disturbances forces when trying to develop the equation of motion of the system. I have an image below just missing the 2 propellers on top of the pendulum. Also any advice into designing the controller to better react to impulse disturbance is appreciated. Also my derivation skills aren't good so if there's any resources such as software (matlab or python) to help me derive the equation of motion, that would also be appreciated. Thank you

 

[scottdave]

Matlab has a symbolic package, which can help with arranging formulas, when working on the derivations. I would create some free body diagrams to account for the forces and motions involved to start. An inverted pendulum can be balanced with just a moving cart. Once you have that solved then could try adding more complexity such as propellers.

 

[Pipsqueakalchemist]

Matlab has a symbolic package, which can help with arranging formulas, when working on the derivations. I would create some free body diagrams to account for the forces and motions involved to start. An inverted pendulum can be balanced with just a moving cart. Once you have that solved then could try adding more complexity such as propellers.

Hello, I think I obtained the equations of motion of my system. I'm trying to perform pole placement control so for that I need to obtain the transfer function. But the problem is that the equations are very nasty and large so by hand is very difficult, would it also be possible to use Matlab to obtain the transfer function so I can use pole placement?

Thanks

 

[scottdave]

Are you working with it in the time domain? If so, you'll need to perform a Laplace transform. I'm not sure how Maylab does that (it's been awhile) but they have help and a forum.

Also, you could use Maple or probably Mathematica to do this, as well.

 

[Pipsqueakalchemist]

[Mentor Note: Duplicate thread start merged into the original thread]

Hello so as the summary suggests, I'm trying to develop a controls system to control the angular position of an inverted pendulum. After doing some experiment today using a PID controller to control both propellers to keep the pendulum upright. I found that the propeller required a lot of thrust to move the pendulum especially when the pendulum was falling to one side, the propeller on the side the pendulum was leaning required a lot of thrust to move the pendulum back to the upright position. I felt the thrust caused a lot of overshoot and oscillation around the upright position rather then slowly settling into the upright position. I want the pendulum to smoothly settle down back into the angular position when pushed to one side, not just overshoot and oscillate.

I hypothesize that it would be easier if I reduced the moment of inertia of the pendulum hence reducing its resistance to motion and hence required less thrust to move and hence easier to control. Any experienced controls engineering can confirm if this is a viable solution or have any other alternatives solution, I'm all ears.

Thank you.

Edit : Forgot to mention, the way I was planning to reduce moment of inertia of pendulum was to drill holes through it. I feel like I should drill the holes at the top of the pendulum, that just seems intuitively better to improve ease of control using propellers. Is this correct or not?