This is a really cool toy example of one of my favorite algorithms. For an algorithm that predates the transistor, I'm constantly blown away at its modern use cases. For example, dynamic pricing, used everywhere from airline tickets to parking meters, is nothing more than a variant of the pid algorithm.

It is also used quite a bit in capacity allocation in a wide variety of industries. Instead of using NP Complete scheduling and discrete optimization that might not terminate, you take a page out of Hayek and use the PID algorithm to set a price on the capacity of each independent asset. Then, scheduling and allocation often becomes a matter of convex linear optimization.

In terms of practical use, I have zero doubt in my mind that the PID algorithm accounts for more economic impact than Page Rank or many other HN-popular algorithms. Just adding up the value of applications that I personally know about, it saves its users > $10B/year. I would wager that the only algorithm that surpasses its economic impact would be Simplex.

It is also incredibly extensible. I've seen variants where the integral term is swapped out with fourier transforms, or the derivative term is swapped out with ARIMAs or Hierarchical Forecasting algorithms or Neural Networks. You can hack the shit out of it, tailoring it to even the most obscure use cases if you wanted to. Like, for example, cooking an egg.