Re:PID Without a PhD (2016) [pdf]
by patrick5415 on Thursday April 02, 2020 @12:31AM
(#22756215)
I did my PhD in controls too, and I’d pretty much agree with all of that. There is a ton of really heavy math flying around with little to show for it. If your system is anything beyond weakly nonlinear, you are basically screwd. The best and effectively only tool we have otherwise was invented over a 100 years ago by lyapunov. And using it requires, I’m not joking, nearly divine inspiration.
Magnetic bearings for example, are an entertaining system to control.
Can you expand on what this tool is?
Re:PID Without a PhD (2016) [pdf]
by creatornator on Thursday April 02, 2020 @01:14AM
(#22756410)
Lyapunov functions indicate Lyapunov stability. A system that is Lyapunov Stable will settle into a global minimum state and stay there stably indefinitely. Kind of like a ball in a bowl, where all gradients point in to the middle. Non linear systems can "refuse to settle". I may be misremembering something from my controls courses
Re:PID Without a PhD (2016) [pdf]
by dreamcompiler on Thursday April 02, 2020 @01:09AM
(#22756384)
Process control definitely seems like one of those disciplines where the old adage
There are two kinds of problems in the world, problems that are linear, and problems I can't solve.
holds true.
Re:PID Without a PhD (2016) [pdf]
by lambda-11235 on Thursday April 02, 2020 @03:40AM
(#22756982)
This is an interesting point. I was recently working on research for how to apply model predictive control theory to TCP congestion control. We basically wanted to minimize latency while maximizing throughput. One of the challenges was that, while we could match latency and throughput set-points if known apriori, actually determining what the set-points should be was very difficult.
Here's an early paper on it https://arxiv.org/abs/2002.09825. Note that if some of our control theory concepts seem a bit screwy, it's because we come from networking, not control theory :).
Re:PID Without a PhD (2016) [pdf]
by senderista on Thursday April 02, 2020 @03:11PM
(#22762469)
Sounds like an optimal control problem?
He’s not wrong, but the fundamental problem is that control theory has a very limited view of “correct behavior”: stability around a desired point or trajectory. If you can define your desired system state as a fixed or time varying value that can be determined ahead of time, and you would like to prove that your system stays close to that point for some definition of “close”, then this tool may be for you.
But if you can’t, it’s much harder to see how to apply it. And a lot of software problems can’t be defined in such strictly mathematical terms.
Also, if your system is linear or approximately linear then we have good tools. If your system is really honestly nonlinear it gets more dicey. You have to either hope that somebody has already derived a controller for systems of the class you are using, or you have to do novel numerical analysis in order to derive a controller that will stabilize it.