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> Shouldn't there be a diagram of the complex plane so that people can see what it's the right half plane of? Author here. Yes! Very fair criticism. I was tryi

> Shouldn't there be a diagram of the complex plane so that people can see what it's the right half plane of? Author here. Yes! Very fair criticism. I was trying to strike a balance between making the concept approachable for those who don't have a background involving complex numbers, but that certainly leaves the name of the concept more confusing. I should add it in a footnote at least. And I did honestly not think about the potential for confusion between plane // airplane. An airplane was the most familiar example system I could think of to explain the concept. Oops! > Perhaps the first lesson is that even if you know how a system works, you can't just take the inverse function to control what comes out. That's a great point too. It probably even deserves its own article.

lordnacho 4y ago
I'd definitely read a series about control theory. The first time round was very badly presented at my university. A lot of math, motivation hidden. Stuff like Nyquist criterion just sort of appears out of nowhere as functions. I guess the big one is feedback being the magic, and then the complex plane tells you where that blows up.
- pid-1 4y ago
  I went down this rabbit hole in grad and my opinion is that Control Theory is good for writing academic papers, but has few applications besides the classical ones (mostly in mechanics). Techniques often need very strong assumptions about the systems being modeled, which severely limits their usefulness. In fact, CT is sort of the antitheses of the currently most hyped way of modeling systems: Machine Learning.
  - jbay808 4y ago
    I hope I will be able to change your mind!
  - alanbernstein 4y ago
    I think you're sweeping a ton of valuable applications under the rug by saying "few applications besides the classical ones" ?
  - lagrange77 4y ago
    Interesting username for such an opinion. Also systems modeling is not the same as control theory. You could indeed utilize machine learning to model a system, which you could then control by classical controllers. On the other hand, control algorithms that use machine learning are a thing.
    - metaphor 4y ago
      > Interesting username for such an opinion. Perhaps just a coincidental namespace collision: Process ID, not Proportional-Integral-Derivative.
      - lagrange77 4y ago
        Yes, probably.
- metaphor 4y ago
  > Stuff like Nyquist criterion just sort of appears out of nowhere as functions. Black's canonical 1934 paper[1] Stabilized Feedback Amplifiers, which had an outsized influence on EE classical control theory, may have something to do with that: Results of experiments, however, seemed to indicate something more was involved and these matters were described to Mr. H. Nyquist, who developed a more general criterion for freedom from instability applicable to an amplifier having linear positive constants. ...which directly cites Nyquist's canonical 1932 paper[2] Regeneration Theory. [1] http://archive.org/details/bstj13-1-1 http://archive.org/details/bstj13-1-1 [2] http://archive.org/details/bstj11-1-126 http://archive.org/details/bstj11-1-126
l33t2328 4y ago
> the potential for confusion between plane // airplane This reminds me of the famous (possibly apocryphal) story of the algebraic geometer of middle eastern descent who was brought aside by Air Marshals for talking about how a particular problem could be solved by “blowing up points on a plane”
- wbl 4y ago
  At Berkeley the legend is that there was a class on blowing up with special application to local problems.
ehvatum 4y ago
If you haven’t read it, I recommend: https://www.gutenberg.org/files/6949/6949-h/6949-h.htm https://www.gutenberg.org/files/6949/6949-h/6949-h.htm
yesenadam 4y ago
The main thing missing for me: presumably if there's a plane, you're graphing something vs something. What are the X and Y? (or, uh, the x and y in the x+iy) Talk of a plane remains rather vague without knowing that. Maybe I missed it, but I looked twice, and read the comments on this page, and couldn't see it mentioned at all. There are a couple of graphs/planes, but they seem to be a different kind of thing.
- stephen_g 4y ago
  Wikipedia has it highlighted on the graph: https://en.wikipedia.org/wiki/Right_half-plane https://en.wikipedia.org/wiki/Right_half-plane Also see page 4 here: https://web.mit.edu/2.14/www/Handouts/PoleZero.pdf https://web.mit.edu/2.14/www/Handouts/PoleZero.pdf
  - yesenadam 4y ago
    Uh that first link is just a picture of a right complex half-plane... I know what that is, having done quite a bit of complex maths, but the kind that uses i, not the kind that uses j, e.g. I love Visual Complex Analysis. I just don't know what things are being graphed in the article! Sorry I didn't explain better. Ok thanks for the 13pp article, I will have a look sometime soon. I was hoping someone could just tell me the answer. edit: I looked at the first few pages of the paper but I feel none the wiser, at all. edit2: Ah... "the poles and zeros of a transfer function may be complex, and the system dynamics may be represented graphically by plotting their locations on the complex s-plane". The transfer function (whatever that is) is a rational function of the complex variable s, i.e. (in my words) it's a fraction with complex polynomials for numerator and denominator. The zeros are the roots of the numerator and the poles are the roots of the denominator. Ok, I still don't know what the transfer function is or means or comes from, but am much less in the dark, thank you! :-)
    - metaphor 4y ago
      > I know what that is, having done quite a bit of complex maths, but the kind that uses i, not the kind that uses j Some things in life leave a lasting impression[1]. :eye_roll: It sounds like what you're looking for is an explanation of root locus analysis[2]. In the simplest control case, a transfer function is nothing more than the expression of a continuous closed-loop LTI system's output Y(s) over its input X(s) in the Laplace domain, conveniently abstracted as its forward path G(s) and negative feedback path H(s). From there, Routh-Hurwitz method[3] can be used to determine stability of the system. ...and I will continue to use j, thanks. [1] https://youtu.be/1rqJl7Rs6ps?t=1828 https://youtu.be/1rqJl7Rs6ps?t=1828 [2] https://en.wikipedia.org/wiki/Root_locus https://en.wikipedia.org/wiki/Root_locus [3] https://en.wikipedia.org/wiki/Routh%E2%80%93Hurwitz_stability_criterion https://en.wikipedia.org/wiki/Routh%E2%80%93Hurwitz_stabilit...
LeonB 4y ago
Really good article. Make changes and corrections to it, sure, but be careful not to over react to the criticism and make too many changes such that you then get even more critical feedback and make more corrections and get worse feedback and bigger corrections and oh god help me worse feedback and bigger changes and stop me please worse feedback and help bigger changes seriously kill me bigger feedback worse changes arggggh
levi_n 4y ago
Thank you for this article and the follow up. The information is fascinating, and I eagerly await your next installments.

lordnacho 4y ago

I'd definitely read a series about control theory. The first time round was very badly presented at my university. A lot of math, motivation hidden. Stuff like Nyquist criterion just sort of appears out of nowhere as functions. I guess the big one is feedback being the magic, and then the complex plane tells you where that blows up.

pid-1 4y ago
I went down this rabbit hole in grad and my opinion is that Control Theory is good for writing academic papers, but has few applications besides the classical ones (mostly in mechanics). Techniques often need very strong assumptions about the systems being modeled, which severely limits their usefulness. In fact, CT is sort of the antitheses of the currently most hyped way of modeling systems: Machine Learning.
- jbay808 4y ago
  I hope I will be able to change your mind!
- alanbernstein 4y ago
  I think you're sweeping a ton of valuable applications under the rug by saying "few applications besides the classical ones" ?
- lagrange77 4y ago
  Interesting username for such an opinion. Also systems modeling is not the same as control theory. You could indeed utilize machine learning to model a system, which you could then control by classical controllers. On the other hand, control algorithms that use machine learning are a thing.
  - metaphor 4y ago
    > Interesting username for such an opinion. Perhaps just a coincidental namespace collision: Process ID, not Proportional-Integral-Derivative.
    - lagrange77 4y ago
      Yes, probably.
metaphor 4y ago
> Stuff like Nyquist criterion just sort of appears out of nowhere as functions. Black's canonical 1934 paper[1] Stabilized Feedback Amplifiers, which had an outsized influence on EE classical control theory, may have something to do with that: Results of experiments, however, seemed to indicate something more was involved and these matters were described to Mr. H. Nyquist, who developed a more general criterion for freedom from instability applicable to an amplifier having linear positive constants. ...which directly cites Nyquist's canonical 1932 paper[2] Regeneration Theory. [1] http://archive.org/details/bstj13-1-1 http://archive.org/details/bstj13-1-1 [2] http://archive.org/details/bstj11-1-126 http://archive.org/details/bstj11-1-126

l33t2328 4y ago

> the potential for confusion between plane // airplane This reminds me of the famous (possibly apocryphal) story of the algebraic geometer of middle eastern descent who was brought aside by Air Marshals for talking about how a particular problem could be solved by “blowing up points on a plane”

wbl 4y ago
At Berkeley the legend is that there was a class on blowing up with special application to local problems.

ehvatum 4y ago

If you haven’t read it, I recommend: https://www.gutenberg.org/files/6949/6949-h/6949-h.htm https://www.gutenberg.org/files/6949/6949-h/6949-h.htm

yesenadam 4y ago

The main thing missing for me: presumably if there's a plane, you're graphing something vs something. What are the X and Y? (or, uh, the x and y in the x+iy) Talk of a plane remains rather vague without knowing that. Maybe I missed it, but I looked twice, and read the comments on this page, and couldn't see it mentioned at all. There are a couple of graphs/planes, but they seem to be a different kind of thing.

stephen_g 4y ago
Wikipedia has it highlighted on the graph: https://en.wikipedia.org/wiki/Right_half-plane https://en.wikipedia.org/wiki/Right_half-plane Also see page 4 here: https://web.mit.edu/2.14/www/Handouts/PoleZero.pdf https://web.mit.edu/2.14/www/Handouts/PoleZero.pdf
- yesenadam 4y ago
  Uh that first link is just a picture of a right complex half-plane... I know what that is, having done quite a bit of complex maths, but the kind that uses i, not the kind that uses j, e.g. I love Visual Complex Analysis. I just don't know what things are being graphed in the article! Sorry I didn't explain better. Ok thanks for the 13pp article, I will have a look sometime soon. I was hoping someone could just tell me the answer. edit: I looked at the first few pages of the paper but I feel none the wiser, at all. edit2: Ah... "the poles and zeros of a transfer function may be complex, and the system dynamics may be represented graphically by plotting their locations on the complex s-plane". The transfer function (whatever that is) is a rational function of the complex variable s, i.e. (in my words) it's a fraction with complex polynomials for numerator and denominator. The zeros are the roots of the numerator and the poles are the roots of the denominator. Ok, I still don't know what the transfer function is or means or comes from, but am much less in the dark, thank you! :-)
  - metaphor 4y ago
    > I know what that is, having done quite a bit of complex maths, but the kind that uses i, not the kind that uses j Some things in life leave a lasting impression[1]. :eye_roll: It sounds like what you're looking for is an explanation of root locus analysis[2]. In the simplest control case, a transfer function is nothing more than the expression of a continuous closed-loop LTI system's output Y(s) over its input X(s) in the Laplace domain, conveniently abstracted as its forward path G(s) and negative feedback path H(s). From there, Routh-Hurwitz method[3] can be used to determine stability of the system. ...and I will continue to use j, thanks. [1] https://youtu.be/1rqJl7Rs6ps?t=1828 https://youtu.be/1rqJl7Rs6ps?t=1828 [2] https://en.wikipedia.org/wiki/Root_locus https://en.wikipedia.org/wiki/Root_locus [3] https://en.wikipedia.org/wiki/Routh%E2%80%93Hurwitz_stability_criterion https://en.wikipedia.org/wiki/Routh%E2%80%93Hurwitz_stabilit...

LeonB 4y ago

Really good article. Make changes and corrections to it, sure, but be careful not to over react to the criticism and make too many changes such that you then get even more critical feedback and make more corrections and get worse feedback and bigger corrections and oh god help me worse feedback and bigger changes and stop me please worse feedback and help bigger changes seriously kill me bigger feedback worse changes arggggh

levi_n 4y ago

Thank you for this article and the follow up. The information is fascinating, and I eagerly await your next installments.