Elektromagnetic levitation system with simulink

[pcwortex]

Hi
I am trying to make Elektromagnetic levitation system with simulink (Matlab). I create system and it you can to see below. I want to ask whether I make correct system with simulink? Coil induction is constant, because metal ball is very small and don't have influence on magnetic field.

I used this equation show below.

And magnetic system you see below

Thank everybody for advice

 

[FvM]

A "levitation system" would need a kind of position control feedback manipulating the electromagnet current current. The present equations of motion make the ball either fall down or jump up and stick on the magnetic pole.

 

[pcwortex]

Yesterday, I tryed to make this system with state space, but I confronted with problem, because need linearization equations around working point. I don't know how need do it.

 

[BradtheRad]

Years ago I saw someone's website telling how he made a similar levitation project.

He used a lightweight globe about 2 inches diameter. It had a magnet at the top.

However he found it was impossible to adjust the pulses so finely that the globe would float. It either fell or popped up to the electromagnet.

He tried positioning an LED to send a narrow optical beam under the globe to a light detector.

As the globe fell it interrupted the beam. The light detector activated power to the electromagnet. The globe rose. When it exposed the light beam, the electromagnet was turned off.

This took place many times a second. The globe was automatically suspended in midair. That was the idea anyway.

Now I remember it wasn't so simple. The feedback circuit did not act quickly enough. The globe still fell.

I seem to remember the designer found a way to anticipate the globe's up-and-down motion. He found he could take advantage of a capacitor's current-lead characteristic with AC.

He made a circuit which automatically adjusted to the frequency of motion, and took a current sense through the capacitor at the right moment, to send a pulse to the electromagnet just before the globe could fall too far.

It worked. His project may still be on the internet somewhere.

 

[FvM]

I took as granted, that the magnetic levitation apparatus is a common playground for applied control engineering, together with some other advanced problems like inverted pendulum. It's of course technically feasible. I was however surprized, that the above system diagram is missing any control loop.

 

[pcwortex]

I made this system. The feedback system I made from one IR diode and 2 IR tranzistors. I am using atmega8 two ADC and one PWM schannels. PWM control MOSFET tranzistor which working how transistor switch and it activated power to the elektromagnet. Now I think to use liner hall-effect sensor.
Curently need to make mathematical model this system with simulink (Matlab). I have problem with linearization.

---------- Post added at 23:50 ---------- Previous post was at 23:44 ----------

Maybe you know how need make control loop in this system?

 

[FvM]

I made this system.

Your initially post would have been clearer if you mentioned this connection to control system design.

Curently need to make mathematical model this system with simulink (Matlab). I have problem with linearization.

I don't excatly understand the problem. The shown model can be expected to represent the behaviour of the real system (with some simplifications). It's obviously non-linear. A linear controller can be only adjusted to control process parameters in a particular state. Or try to compensates control process non-linearities in part.An easy compensation can be made for the quadratic F = f(i) magnet characteristic, F = f is more complicated.