Adding bang-bang control algorithm

[wca747]

First draft of a page covering the bang-bang control algorithm. Looking for feedback!

[ntindle]

If we want to go into signals and such here, the discrete form of the unit step function would be applicable as a mathematical example as well

[leios]

Yeah, I think having something we could abstract out to a signal processing section makes sense. Do you have something specific in mind @ntindle ?

[ntindle]

I've referred to this as signals and systems but it's based on control theory. I think a catch all signals and systems top level chapter would be good.

Edit: reread the question. The example above would work. I'm not super familiar with latex so I can't type it out but the example above would be something like this

X[n], where n is temperature, exhibits the following behavior for discrete values of n.

X[n]= {0, n>=50
      {1, n<=45

When this is in the presence of an external factor (such as what is being controlled) it will often oscillate causing that characteristic sawtooth graph in the chapter

[leios]

I agree with that, although "signals" and "control theory" seem a bit too distinct for me right now, maybe just "control theory"?

When I think of signals, I think signal processing with FFTs and things like that.

I think this chapter is a nice way to lead into PID controls. I wonder if we can revive the #346 PR? That one was close to being done, so we could fork it and open it up again with @Gathros co-authoring it.

[ntindle]

I think @wca747 's goal was using this as a stepping stone to the much harder PID chapter

Also for signal processing in computer engineering (not sure other places), FFTs are taught using things like bang bang as the introduction to why they are needed. It's a part of a much larger array of signal processing techniques

[leios]

Hey, it's been a while. Were you at all able to look at this chapter? I think example code is essential to understanding how the plots were generated. I am happy to continue the review from that stage!

[ntindle]

I could probably pick this up in your place @wca747 if you'd like

[leios]

I think the chapter needs some work right now, but it's definitely in the right direction. Namely, I would really like to see some code for the plots. Once that is there, I think I will have a better understanding of what they were supposed to show and we can finish the chapter from there.