3 ms·

It is a fundamental law. Systems theory has the concepts of "gain margin" and "phase margin" -- how much you can amplify feedback or delay feedback, respective

It is a fundamental law. Systems theory has the concepts of "gain margin" and "phase margin" -- how much you can amplify feedback or delay feedback, respectively, before your self-adjusting feedback mechanism fails to find equilibrium and turns into an oscillator. Even though most non-engineering systems don't fit the mathematical theory, the idea that only a finite amount of gain + delay is available, and that the two are somewhat inter-convertible, generalizes astoundingly well.

bschne 6y ago
Do you happen to know a good introduction to that? I‘d love to read up more on it!
- dboreham 6y ago
  https://books.google.com/books/about/Modern_Control_Theory.html?id=OPFQAAAAMAAJ&source=kp_book_description https://books.google.com/books/about/Modern_Control_Theory.h... ?
- p-funk 6y ago
  This youtube channel has (seemingly good quality) Khan Academy style lecture videos on control systems, if you just want a quick introduction to the concepts. https://www.youtube.com/watch?v=ThoA4amCAX4 https://www.youtube.com/watch?v=ThoA4amCAX4
- acidbaseextract 6y ago
  Steve Brunton, a University of Washington professor has a sweet lecture series called the Control Bootcamp that dives deep into control fundamentals while still being approachable. Great production values too: https://www.youtube.com/watch?v=Pi7l8mMjYVE&list=PLMrJAkhIeNNR20Mz-VpzgfQs5zrYi085m https://www.youtube.com/watch?v=Pi7l8mMjYVE&list=PLMrJAkhIeN...
throwaway815190 6y ago
> It is a fundamental law. > Systems theory I'm confused. Is it a law or a theory? And no, it can't be both. Laws are proved. Theories are unproven.
- Jtsummers 6y ago
  Well, those two statements aren't referring to the same thing. The law they reference is something found in Systems Theory. It may be useful, also, for you to read these two pages: https://en.wikipedia.org/wiki/Scientific_law https://en.wikipedia.org/wiki/Scientific_law https://en.wikipedia.org/wiki/Scientific_theory https://en.wikipedia.org/wiki/Scientific_theory The difference between Law and Theory (in scientific discourse) is not what you believe it to be.
  - throwaway815190 6y ago
    > The difference between Law and Theory (in scientific discourse) is not what you believe it to be. ELI5?
    - Jtsummers 6y ago
      Well, I'm not interested in explaining this to a five-year old, but I'll treat you as an adult and use words over two syllables. > Laws are proved. Theories are unproven. This is not what is used to identify something as either a law or a theory in scientific discourse. First, "laws" may be disproven, or falsified: Newton's Law of Gravity could actually be considered disproven as it is not accurate at all scales, but it's accurate enough within its scope to continue using it. It's considered a law in the sense that it matches empirical, observed data (within certain bounds). See [0] for details on that. So that, right there, is a flaw in your understanding. Second, laws do not attempt to offer an explanation of the phenomenon they describe, they offer predictive value like "a ball dropped from 50 meters will, at time t, have velocity ...". Again, Newton's Laws do not explain why gravity works, only offering a model to calculate the effect of it. This brings us to theories. Theories are, again, falsifiable via empirical evidence (like laws), but they offer an attempt at explanation. A Theory of Gravity would try to explain why objects are attracted to each other and why the mass effects the amount of attraction. The theory can be shown as false, but like a law it can only be shown to match empirical data. This is not the same as proven. TLDR: The distinguishing characteristic is that both attempt to predict, but theories attempt to explain. Both are falsifiable, and neither are considered proven only to match empirical data (possibly within some constraints). [0] https://en.wikipedia.org/wiki/Newton%27s_law_of_universal_gravitation#Limitations https://en.wikipedia.org/wiki/Newton%27s_law_of_universal_gr...
themeiguoren 6y ago
Yeah, as a controls engineer I’ve worked on systems where the main requirement was not gain or phase margin, but a root sum square of the two. Nichols plots drive home the idea that it’s not really the margin at two discrete points that matter, but the close approach to the critical point.

bschne 6y ago

Do you happen to know a good introduction to that? I‘d love to read up more on it!

dboreham 6y ago
https://books.google.com/books/about/Modern_Control_Theory.html?id=OPFQAAAAMAAJ&source=kp_book_description https://books.google.com/books/about/Modern_Control_Theory.h... ?
p-funk 6y ago
This youtube channel has (seemingly good quality) Khan Academy style lecture videos on control systems, if you just want a quick introduction to the concepts. https://www.youtube.com/watch?v=ThoA4amCAX4 https://www.youtube.com/watch?v=ThoA4amCAX4
acidbaseextract 6y ago
Steve Brunton, a University of Washington professor has a sweet lecture series called the Control Bootcamp that dives deep into control fundamentals while still being approachable. Great production values too: https://www.youtube.com/watch?v=Pi7l8mMjYVE&list=PLMrJAkhIeNNR20Mz-VpzgfQs5zrYi085m https://www.youtube.com/watch?v=Pi7l8mMjYVE&list=PLMrJAkhIeN...

throwaway815190 6y ago

> It is a fundamental law. > Systems theory I'm confused. Is it a law or a theory? And no, it can't be both. Laws are proved. Theories are unproven.

Jtsummers 6y ago
Well, those two statements aren't referring to the same thing. The law they reference is something found in Systems Theory. It may be useful, also, for you to read these two pages: https://en.wikipedia.org/wiki/Scientific_law https://en.wikipedia.org/wiki/Scientific_law https://en.wikipedia.org/wiki/Scientific_theory https://en.wikipedia.org/wiki/Scientific_theory The difference between Law and Theory (in scientific discourse) is not what you believe it to be.
- throwaway815190 6y ago
  > The difference between Law and Theory (in scientific discourse) is not what you believe it to be. ELI5?
  - Jtsummers 6y ago
    Well, I'm not interested in explaining this to a five-year old, but I'll treat you as an adult and use words over two syllables. > Laws are proved. Theories are unproven. This is not what is used to identify something as either a law or a theory in scientific discourse. First, "laws" may be disproven, or falsified: Newton's Law of Gravity could actually be considered disproven as it is not accurate at all scales, but it's accurate enough within its scope to continue using it. It's considered a law in the sense that it matches empirical, observed data (within certain bounds). See [0] for details on that. So that, right there, is a flaw in your understanding. Second, laws do not attempt to offer an explanation of the phenomenon they describe, they offer predictive value like "a ball dropped from 50 meters will, at time t, have velocity ...". Again, Newton's Laws do not explain why gravity works, only offering a model to calculate the effect of it. This brings us to theories. Theories are, again, falsifiable via empirical evidence (like laws), but they offer an attempt at explanation. A Theory of Gravity would try to explain why objects are attracted to each other and why the mass effects the amount of attraction. The theory can be shown as false, but like a law it can only be shown to match empirical data. This is not the same as proven. TLDR: The distinguishing characteristic is that both attempt to predict, but theories attempt to explain. Both are falsifiable, and neither are considered proven only to match empirical data (possibly within some constraints). [0] https://en.wikipedia.org/wiki/Newton%27s_law_of_universal_gravitation#Limitations https://en.wikipedia.org/wiki/Newton%27s_law_of_universal_gr...

themeiguoren 6y ago

Yeah, as a controls engineer I’ve worked on systems where the main requirement was not gain or phase margin, but a root sum square of the two. Nichols plots drive home the idea that it’s not really the margin at two discrete points that matter, but the close approach to the critical point.