Y'know those stories about accidental discoveries?

I think I've caught a glimpse of what that must feel like. Here's the first page or so of my report b/c it's just text. Feel free to check out the whole thing here.

The birth of a control system

As I start to type up this lab, I continually glance back at my levitating object in wonder. I also glance up at the whiteboard and think that math is truly beautiful. I think my controller can best be explained by a story.

I was attempting to figure out a way to get the step response of the original system. It was not going terribly well. I could add a step, but I couldn't see anything at all through the noise from the system moving just a little at equilibrium (I'm currently thinking that a levitated object is not the best way to get the starting point that I then disturb with a step). Anyhow, I tried to stabilize the system by using a plastic rod to hold things together at the set point. That got rid of the high-amplitude, low-frequency noise, but high-frequency was still killing me. So I tried just adding a low-pass filter so that I might be able to see the step response better despite the noise. There was sadly too much noise. At this point I started poking around for a bit and one of the things I tried was changing the system to open-loop for a bit. I then took a look at the signal coming from the hall effect sensor. Importantly, I did this by touching the output of the hall-effect sensor to the place where my probe was at the time (after the low-pass filter). Then things moved and I was confused (I hadn't meant to change anything by probing the sensor's output). In my attempt to figure out what was going on, I inserted the sensor output into the row with the probe and (I guess out of habit?) went to set up the levitated object. It stayed. It stayed for a long, long time. And it had learned damping. It was incredible. I drew up the circuit on the board. I did math. It makes sense. It's absolutely incredible. I love math. I should still do that step response and system characterization thing, but I'll write up the math for why this works and include a block diagram first. So my design process was rather lacking, but I did figure everything out and fully understand it post facto. I was planning on doing the same thing with active elements, but this is actually more elegant. I'm glad I happened upon it.