23 ms·

You need to know what right-half-plane zeros are

439 points by jbay808 4y ago

Linda703 4y ago
[dead]
cheeselip420 4y ago
This is fantastic.
GistNoesis 4y ago
Are they still important if you use something like model predictive control ?
- jbay808 4y ago
  They are certainly something that your MPC controller will need to account for, and they will constrain the theoretical maximum performance you can get out of the system no matter how optimal your control algorithm is.
lordnacho 4y ago
Shouldn't there be a diagram of the complex plane so that people can see what it's the right half plane of? On top of it, there's a picture of a plane which is confusing. Fascinating subject though, in engineering class it was quite surprising how this bunch of functions tracing lines and dots on the complex plane would be relevant to just about everything. 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.
- jbay808 4y ago
  > 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.
- rhn_mk1 4y ago
  I felt that the article ended just where it was ripe to dig into the maths.
- woojoo666 4y ago
  Not to mention, it's not just a complex plane. It's the s-domain, reached through the laplace transform.
nurettin 4y ago
So sometimes it is better to cut losses rather than double down because planes exist.
lb1lf 4y ago
My signals processing professor apparently knew one joke, and one joke only. "A LOT (Polish airline) airplane is about to land in New York City; as they align for final approach, the first officer notifies the passengers that those seated on the right can now see the Statue of Liberty. A number of passengers get up from their seats left of the aisle and lean over the people seated on the right to get a glimpse of the statue. Plane promptly crashes. Why? There were too many Poles in the right half of the plane. I'll lead myself out.
- gugagore 4y ago
  The article saying zeros (where the transfer function is 0) when it should be saying poles (where the denominator of the rational function is zero), right?
  - themeiguoren 4y ago
    Controls engineer here. The author’s control theory knowledge is correct - a RHP zero indicates that corrective action will begin in the wrong direction (which the article compares well with countersteering on a bike). The technical term is a “non minimum phase system”. It’s possible this will lead to instability, but in general the long term stability of a system is determined by the location of its poles (which is more applicable to the author’s ice cream example). Poles in the RHP will cause a system to blow up. My gripe with the article is that the author tries to wow you with some obscure technical points about a system which is unmodeled and he does not understand, to wave his hands at a vague conclusion. If he had made the same point using common English phrases that encapsulate the idea (“positive feedback loop”, “we have to let it get worse before it gets better”, etc), then it would be a lot clearer how wispy his argument is.
- l33t2328 4y ago
  I hate to be the guy to ask you to explain the joke, but why would that make the plane crash? I do know what a “pole” refers to, but I don’t follow the crash bit.
  - 4y ago
DeathArrow 4y ago
Something I don't understand: on the one hand, people on HN seems to enjoy this kind of articles. On the other hand, they upvote any article who decries interviews where candidates are asked things that involves knowing some theory. So, if we think knowing theory is useful in cracking hard problems, why is it wrong to asses its knowledge in an interview?
- deleted 4y ago
  [deleted]
- CamperBob2 4y ago
  HN's readership isn't homogeneous. There's room for both points of view. I've done a lot of useful work in feedback systems without ever really grokking Laplacian notation and the notion of complex frequency in general. A lot of the actual numerical methods used in real life boil down to a few canned formulas. But I know enough about the underlying theory to appreciate where the canned formulas come from, and fully intend to sit down some day and go through the whole process. Articles like this are interesting if only for the occasional gems in the comments, such as John N.'s pointer to Maxwell's 'On Governors' paper that I'd never run across before. At the same time, I don't see much upside in making hiring decisions on the basis of whether someone can regurgitate a bunch of textbook math. I'd rather spend the interview talking about control problems the candidate has dealt with personally, how they were handled, and what the candidate learned from them.
- genezeta 4y ago
  While I don't claim to have the answer to your question, I think there's a jump you're making that may not be so straightforward and somewhat explain things. You say "people on HN seems to enjoy this kind of articles" which seems reasonable, given the comments here. But then you jump to "we think knowing theory is useful in cracking hard problems". Going from the first to the second is not quite so clear. That is, someone may enjoy such an article and even learning some theory, but not necessarily because they think they will directly apply it. People sometimes just enjoy learning stuff or reading about it and then forgetting it. You also make a second jump, because other factors may be involved. Maybe the theory asked in the interviews is completely unrelated to the things involved in the job. The job may not even require cracking hard problems. These are frequent occurrences -in my experience, at least-, and clearly seem compatible with thinking that knowing theory is good in general.
Animats 4y ago
The classic paper, Maxwell's "On governors". (1869) [1] This is the first theoretical analysis of feedback. It will be seen that the motion of a machine with its governor consists in general of a uniform motion, combined with a disturbance which may be expressed as the sum of several component motions. These components may be of four different kinds:- (1) The disturbance may continually increase. (2) It may continually diminish. (3) It may be an oscillation of continually increasing amplitude. (4) It may be an oscillation of continually decreasing amplitude. The first and third cases are evidently inconsistent with the stability of the motion; and the second and fourth alone are admissible in a good governor. This condition is mathematically equivalent to the condition that all the possible roots, and all the possible parts of the impossible roots, of a certain equation shall be negative. That is, in the left half-plane. (Terminology has changed. Maxwell says "disturbance" where today, the term "error" would be used. Today, "disturbance" means an input which disturbs stability, while error is an output.) Maxwell got so much right in that paper, and it was a long time before anybody picked up on that result. Now, where it looks like the author is going is into economic territory. Basic economics talks about "economic equilibrium". The concept is that restoring forces will bring supply and demand into equilibrium. But basic control theory tells us that may not happen. Any system with delay in it can potentially be unstable. Too much delay, and even simple systems will not stabilize. [1] https://en.wikisource.org/wiki/On_Governors https://en.wikisource.org/wiki/On_Governors
- WanderPanda 4y ago
  In the real world all exponentials are sigmoids eventually, so what we actually get is is a recession with a drastic reallocation of resources (creative destruction).
  - duped 4y ago
    Not really, there are plenty that are sinusoids which are just complex exponentials. The real trouble with sigmoids is when the saturation point is beyond physically meaningful quantities of the system. See the tacoma narrows bridge collapse.
    - deleted 4y ago
d--b 4y ago
This is very well explained, but there should be a simpler name for this effect than right-half-plane zeros if the author wants to spread the concept beyond control theory.
duped 4y ago
The greatest sin of undergraduate engineering education is sequestering signals and systems into electrical engineering curricula. I understand why it's done that way (I even had to fight to take the course early, sidestepping some prereqs for reasons). But it's really so foundational to understanding concepts of stability, resonance, information/energy flow (from the conceptual perspective), and the simple analytical tools for building a solid conceptual base. It takes a semester to hammer home that step response matters, positive feedback bad, negative feedback usually good, and topologies are useful.
- Agentlien 4y ago
  I took some electrical engineering courses but mainly software engineering with a focus on low-level details and graphics. The more I specialize in graphics the more I realize I need much more knowledge about signal processing than we were taught at the university.
  - AB1908 4y ago
    Could you demonstrate with an example?
    - Agentlien 4y ago
      I can give a few. In general, the theory behind rendering generally treats what's on the screen as a discretization of a continuous visual signal. Post processing especially is largely about signal processing. Anti-aliasing (AA) is a very clear example where the lack of it leads to moiré patterns and jaggies. Understanding a lot of AA techniques is simplified by seeing the frame not as a discrete set of pixels but as a continuous signal being sampled (and can be sampled at multiple sub-pixel points per pixel). A lot of other screen effects are essentially filters applied to the graphical signal (sobel, gaussian blur, ...) and understanding them from a signal processing view helps understanding how to modify and optimize them. A good example here is identifying whether your effect is a separable filter which can be split into a horizontal and vertical pass. Seeing the image as a continuous signal/field being sampled is also the theoretical basis for a lot of visual effects used in physically-based rendering and things like screen-space ambient occlusion. Finally, if you want to write your own ray-tracer it really helps to be able to take this view of things once you get past the basics.
LolWolf 4y ago
Counterpoint: no you don’t. By the time you have a perfectly reasonable model of a system that is good enough such that computing the transfer function’s poles actually tell you something interesting about the system, there’s way more you can say about the system than “it is stable.” There are maybe some lessons to be drawn from basic “classical” control theory, but many are better stated by just analyzing the system directly. (As a side note, I’m not saying there’s Zero value in analyzing transfer functions, just that it’s a long way to the top from there.)
magneticnorth 4y ago
The follow-up article on inflation of shelter costs in response to mortgage interest rates is also fascinating and worth a read, imo [0]. The tl;dr is that in the medium and longer term, higher interest rates will decrease inflation, but there's a right-half-plane zero effect that will cause higher inflation rates in the short term in response to interest rate hikes (with a lot of simplifying assumptions). [0] https://jbconsulting.substack.com/p/on-shelter-futures-part-1 https://jbconsulting.substack.com/p/on-shelter-futures-part-...
- neilwilson 4y ago
  It's a little more complex than that because of the potential feedback loop via the main price channel. In other words if you can have a wage/price spiral you can have a profit/price spiral and an interest/price spiral for the same reasons. [0]:https://new-wayland.com/blog/interest-price-spiral/ https://new-wayland.com/blog/interest-price-spiral/ Once you abandon the concepts of general equilibrium and a fixed amount of money for what happens in reality, then the functional control mechanisms get a whole lot more interesting.
voldacar 4y ago
This is some of the best non-rigorous writing about math that I've encountered. Far superior to the awful quanta articles that sometimes get posted here.
eigart 4y ago
Great read. I’ve been thinking about how this applies to earth/climate change for a while, so I was surprised that the system he worries about is inflation/the economy.
- jbay808 4y ago
  Thank you for reading! I agree the Earth is a much worthier system to be worried about than the economy, for sure.
ilayn 4y ago
Always appreciate control theory articles. But this one needs some editing. Take ice cream example;that is not zero dynamics that's still pretty much convolution. Now zero dynamics examples must have no effect on the system. Thus it is not a zero if you continuously chugging ice cream. It is indeed a step input that you equilibriate at a constant ice cream input and some happiness comes out constantly. The moment you stop happiness goes away. That is not related to zero. Also a pure zero action is supposed to cancel the input completely. Not at first but completely (restricting the discussion to linear systems). Zeros effects are not so trivial to untangle as the article suggests unfortunately but fun read anyways and very nice flow.
- jbay808 4y ago
  > Now zero dynamics examples must have no effect on the system. Thus it is not a zero if you continuously chugging ice cream Thank you for your input! I wonder if you might have misread that example. In this system there's indeed a RHP0 in the transfer function from ice cream consumption happiness. A continuously increasing rate of ice cream intake results in exactly no effect on the output.
  - ilayn 4y ago
    Your happiness shouldn't change if ice cream input has a zero. Also it should be independent from the amount of ice cream. In other words if we have an ODE say ddot y + 2 dot y + y = dot u - 2 u As long as my input is pure C exp(2t) independent of C I see no happiness and it's not working on my mood. In your example input u effect is cancelled by decay of y cancelling the guilt. Making it not a zero. In my personal case eating celery is a zero i see absolute no point eating it :) no harm and no benefit just pointless chewing
once_inc 4y ago
For those wondering: this article is an introduction into inflation of house prices in Canada. You can easily find the next article (it's already online) by going to the substack's index. Very good article, and well worth your time to read.
- pcthrowaway 4y ago
  Link, because I assumed it wasn't out yet since the author hadn't provided it: https://jbconsulting.substack.com/p/on-shelter-futures-part-1 https://jbconsulting.substack.com/p/on-shelter-futures-part-...
- dools 4y ago
  It’s funny as soon as I read the ice cream but I knew where he was going with it. The interesting thing is that his modelling concludes that raising interest rates is inflationary which is what Warren Mosler also says. Anyone interested in what to do about inflation would enjoy the recent Macro n Cheese podcast episode featuring Randall Wray
  - selimthegrim 4y ago
    Let’s hope Erdogan doesn’t read this
parasti 4y ago
This is weird to say, but I've never had this happen before: as someone who's never heard of control theory, the initial illustrations and the leading icecream example seemed highly confusing and put me off from reading the rest.
tdubhro1 4y ago
It’s a bit disappointing that an article purporting to educate us about something we should know but may be unaware of, is completely wrong about the example of how an airplane climbs - you don’t climb by pitching up, you have to increase power.
- rocqua 4y ago
  Just pitching up will have you climb, but at the expense of losing velocity right?
  - jhugo 4y ago
    Briefly.
  - jacquesm 4y ago
    Right up to the stall speed limit. You can't just keep pitching up, you'd have to apply some power too if you don't eventually want to run out of forward (air)speed. In a glider you can't do that so there when in level flight you have a limited amount of forward momentum available to help you climb if the air itself isn't moving up, you are continuously trading altitude for speed and vv (easy to see in a dive: everybody expects you to gain speed in a dive because can all relate so something falling, it's obvious the reverse has to happen when you climb and the stall speed is a design parameter of the aircraft at a given altitude combined with a bunch of other factors). https://aviation.stackexchange.com/questions/27693/how-does-the-ias-stall-speed-vary-with-increasing-altitude https://aviation.stackexchange.com/questions/27693/how-does-...
- jbay808 4y ago
  Fair. Perhaps a glider would have been a better example.
  - nosianu 4y ago
    How? A glider climbs when the air it is in rises faster than the airplane sinks in that air to maintain its forward speed. If you pitch up you can only exchange speed for a little bit of altitude, briefly.
lagrange77 4y ago
Great article and blog! I would also mention, that we essentially design controllers to shift the poles and zeroes of the total system (which consists of the plant system and the controller system) to more desirable positions, than those of the plant system alone.
ali-preview 4y ago
I'm nX 1 too<p>;)\n
ali-preview 4y ago
jokabrink 4y ago
I am not sure what to take from this. The title certainly makes sense from a engineers perspective. But from a layman's? I don't know. It seems, that he tries to explain an important concept in control theory but does not explain the meaning of "plane" at all. Even worse: He uses airplanes as an example. Isn't it terribly confusing for non-control-theory people? If I don't know control theory, then how on earth would I know that he means a 2D-plane? And what's this "minimum-phase-system" he mentions once? Is a pole a number? And what about RHP poles? I would be interested in how readers without a background in control theory and higher maths understood that article and what questions arose.
- lagrange77 4y ago
  > He uses airplanes as an example. Oh wow, i didn't notice that. It's either pretty clever, or unfortunate wording.
- petesergeant 4y ago
  > I am not sure what to take from this I think the author is using a lot of words to say "things often need to get a bit worse in order to start getting better"
  - nbadg 4y ago
    That's only half of the story. The second half of the story is "if the getting worse temporarily cancels out the getting better, stop trying to correct, or you're going to crash!"
  - Perseids 4y ago
    And, critically, you potentially need to ignore the signal of "things getting worse". Otherwise you might creature a vicious cycle of more corrective action -> more things getting worse (at first) -> even more corrective action, until your system crashes and you never got into the phase where most of the desired result of the corrective action materialized. And a second important point: You mustn't ever get into a state where the "things getting worse at first" already pushes you over a red line (see the example of the plane that loses even more altitude before it rises again. If you hit the ground in between you don't care that you theoretically would have risen later on).
gsliepen 4y ago
> The danger of the right-half-plane zero is that it lures you into reacting to it, but that is precisely the wrong thing to do. Attempting to apply a new control input to cancel the inverse response only sets off an even worse chain of events, where the resulting secondary inverse reaction becomes even more severe, requiring even more corrective action, until finally you’ve slammed into the ground. > In this situation, the flight controller’s only option is to ignore the initial misdirection and wait patiently until the airplane eventually begins to climb as intended. Of course that is easier said than done; adding a sleep() to your control loop to ignore the initial misdirection is also very bad. The right way to solve this is to not just tell the control loop to "go up", but to plan a realistic trajectory that the control loop can execute. That way, the error between the desired trajectory and the actual trajectory will be much smaller, and the closer the error is to zero, the less chance of a control loop to go wild.
thaumaturgy 4y ago
The danger of "systems thinking" is that it misleads otherwise clever people into believing they've found a cheat sheet for subjects they don't have deep knowledge in. This article is a fine example of that. I didn't know what right-half-plane zeroes are. I knew some of the examples it gave (Veritasium has a fun video on the bicycle steering phenomenon), but not that there was a category they all fit into. Neat. But I got squinty when the author said the intended audience was everybody, and got a hunch it was going to wander into the current economy ... which it did, sort of, except that in this case, "wandering" into the subject meant, "wrap it up with a graph and then point at it and go, see! See! I can predict the economy now!" The follow-up at https://jbconsulting.substack.com/p/on-shelter-futures-part-1 https://jbconsulting.substack.com/p/on-shelter-futures-part-... goes into more detail and concludes that interest rate hikes will increase inflation over the next 5-ish years, but there's no "part 2" in the series to be found (paywalled?). There are lots of graphs and the author tries to build a case out of several arguments, buuuuut in the end it feels like that IASIP conspiracy board meme. I smell a faint whiff of gish galloping here and there, but one thing that stands out to me is that the author chooses to normalize housing costs against inflation, but there's no mention of wage stagnation anywhere. Rents and housing costs can't rise a whole lot more, certainly not to the extent the author seems to be predicting, because people can't afford them. This is already a conversation happening in every housing market in at least several countries. In the US, pick literally any local subreddit and ask if anyone knows of an affordable place to rent, I dare you. There's already a huge epidemic of unhoused people and van-dwelling is more popular than it has ever been, and consumers are currently getting squeezed in a lot of directions. Here, one of the things in my browser history before this article was this thread: https://old.reddit.com/r/news/comments/v8knl5/gas_prices_hit_5_national_average_after_rapid_rise/ibs341g/ https://old.reddit.com/r/news/comments/v8knl5/gas_prices_hit... So, if wages don't rise to meet these costs, then something big is going to break way before the cost increases the article is doomsaying.
- robertlagrant 4y ago
  > Rents and housing costs can't rise a whole lot more, certainly not to the extent the author seems to be predicting, because people can't afford them. House prices are passively controlled because there's only so much money to spend on housing?
bambax 4y ago
> the first important lesson of inverse response is: don’t ride your bicycle on the edge of a cliff I don't know if many people often ride their bicycle on cliff edges, but many plane (as in airplane) accidents occur because it's difficult / impossible to recover from a stall near the ground.
- LanceH 4y ago
  You can also get your weight to the inside of a turn for a bicycle by leaning while riding straight. Every time this comes up there is a big debate with a bunch of people saying counter steering is required. Please, go out and try it. Drive perfectly straight along a painted line. Lean left, turn left. Lean right, turn right. There is no requirement for counter steering.
  - bambax 4y ago
    I think it's somewhat speed-dependent. I ride motorcycles and bikes. On a motorcycle at high speed it's impossible (in my experience) to take a turn without counter steering. You sometimes have to push really hard on the handle on the side where you want to go. Also, leaning is very similar to counter steering; counter steering makes the bike "fall" on the side where you want to go. Interestingly, you can also steer a horse without doing anything on the reins; the horse will usually go where you put your weight; I think it's because it needs to compensate for the weight differential; or maybe it takes it as a hint about which way you're looking. In any case it works.
bob1029 4y ago
This stuff is fun. Surprised I haven't seen direct mention of state space representation yet: https://en.wikipedia.org/wiki/State-space_representation https://en.wikipedia.org/wiki/State-space_representation I recall going through this at university and it being a bit of a struggle. Looking back at it now, this stuff makes a lot more sense. A decade+ of practical experience probably helps.
raydiatian 4y ago
The footnote is nonsense. Needs revision, author is currently arguing that poles are indistinguishable from zeros.
- oh_my_goodness 4y ago
  The footnote currently appears to be correct.
- jbay808 4y ago
  I'm not aware of what you mean.
blauditore 4y ago
Can someone provide a TL;DR? I don't have time to read the whole article, and I don't even understand what's the topic based on title and reading a few paragraphs, nor from googling "right-half-plane zeros".
- a_imho 4y ago
  The plane refers to the plane of complex numbers (a+b*i), the right half is where the real part (a) is positive. If the zeros of your feedback loop are on the right hand side that means it is a unstable feedback loop, if they are on the left side it is stable feedback loop (this happens because the zeros eventually end up in exponents which either tend to infinity or to zero with time). If you squint a little bit most systems looks like a feedback loop and my not very confident interpretation is, judging from the last picture, that the author thinks we have a runaway inflation problem (zeros on the right hand side of the plane) and we might or might not have the controls to move them to the left hand side to tame it.
  - layer8 4y ago
    I thought this would be something about positive zero in a 2D coordinate system, but seeing drawings of airplanes in the article I concluded “bummer, it’s not” and immediately hit backspace. Thanks for the summary. :)
woojoo666 4y ago
I don't think they should use the term right-half-plane zero if they don't explain laplace transform and the s-domain. Just call it an unstable system, or unbounded growth.
- oh_my_goodness 4y ago
  The point of the article, perhaps not stressed enough, is that there are stable systems that can be very difficult to control. Zeros in the right half-plane don't indicate instability. They indicate nulls in the transfer function for unbounded inputs. Poles in the right half-plane indicate instability. Zeros in the right half-plane indicate something a little more subtle. I believe the article is about the latter.
  - woojoo666 4y ago
    Good point, I mixed up the two. However, the right-half plane still refers to the s-domain so it doesn't make sense to keep referring to the a right half plane without explaining what plane it is
- jbay808 4y ago
  That would be a right-half-plane pole. An explanation of the Laplace transform is coming! This is an article, not a book.
_moof 4y ago
Really should've run this by someone who knows how airplanes work, because they don't do what these hypothetical airplanes do. First off, "elevator flaps" is a howler. Elevators and flaps are two very different things. More importantly, you don't climb with the elevator; you climb with excess thrust. You can kinda sorta climb a little bit with just elevator, but unless you're making a very minor altitude correction, you'll slow way down and your climb rate will be really anemic, if you climb at all. But most importantly, an airplane won't just keep climbing and do a loop like that (unless you've got a thrust-to-weight ratio greater than one, which, to put it simply, you don't); the wing will stall way before you get anywhere near vertical, and the airplane will just stop flying until the angle of attack is reduced.
- tzs 4y ago
  > More importantly, you don't climb with the elevator; you climb with excess thrust. You can kinda sorta climb a little bit with just elevator, but unless you're making a very minor altitude correction, you'll slow way down and your climb rate will be really anemic, if you climb at all. So what happens to something like a jet fighter that is in level flight with the engines at maximum power if the pilot uses the elevators to raise the nose?
  - _moof 4y ago
    It will climb (and slow down), but again, it's the thrust that's producing the climb, and this is an extreme example that isn't illustrative. Fighter jets produce enormous thrust for their weight with many having thrust-to-weight ratios greater than one. If they weren't air-breathing, they could literally fly into space. A normal airplane, even if it weren't air-breathing, couldn't do that. Depending on the configuration an F-16 has a T/W a little under 1.1, while a transport category aircraft (an airliner) will have a T/W somewhere between 0.20 and 0.35. Totally different performance characteristics.
  - p_l 4y ago
    Powered airplanes hide the energy-management nature of climb/descent. Essentially, you have potential energy (altitude) and kinetic energy (speed), and you trade one for the other. For safe range of inputs, your lift is function of pitch and airspeed, with drag as result. Increasing pitch increases lift (most of the time) at expense of increased drag. Lift gets you higher raising your potential energy, which you can spend back on glide, exchanging it for kinetic energy necessary for airflow. With powered plane, you provide extra kinetic energy that can be spent on higher lift. You use your stick to manipulate energy/speed, and in fact it's common to descend while pulling the stick on purpose. A fighter jet with TWR above 1 has enough extra energy that it's going to be able to maneuver rapidly (afterburner/reheat exists for it, even, as jet engines are slow to spool up). Plane with lower TWR, or with significant mass, is going to behave closer to glider (heavy planes like airliners make energy management a big issue)
VogonPoetry 4y ago
I think this article is trying to make a political statement, "Our leaders have just done something that is going to cause a future problem, a crash". I have only read the linked article, I think the followup might be available, but I'm not going to read it before posting this -- because this article was meant to be clickbait, to get you hooked and possibly mis-informed. The article as it stands (incomplete) contains some classic argument fallacies. It is an "appeal to authority", by attempting to explain control theory. This person knows something. The examples all result in bad things, airplanes crashing, hard drives (crashing - perhaps a stretch). Bicycle at the edge of a cliff. Eating too much ice cream. Chernobyl. This is a possible "appeal to emotion". The final issue is an "incomplete comparison". The graph at the bottom of the article shows housing prices -- all of the previous examples have mathematical models which can explain the behavior. For the last graph no model (the equations) is presented. Without a model you cannot use control theory to analyze the zeros and poles. The last graph wants you to believe in a continuing upward trend, the fallacious argument, implies that whatever the Canadian political change that has been made is going to make this trend to zero, despite the intention to keep it trending upwards. Background: A long time ago, as a mathematics undergraduate, I did take a course in control theory, it was run out of the engineering department. It was somewhat awkward as quite a few mathematical terms were not-quite-the-same. I get the same unease when reading this for poles, zeros and right-half-planes. Any engineering textbooks that use j for sqrt(-1) instead of i (because that is taken) is an indicator. Yup, this could be construed as an "appeal to authority".
- any1 4y ago
  Textbooks that use j instead of i are an indicator of what? Why is slightly different notation awkward? It's not as if notation is always consistent within the field of mathematics, right?
  - VogonPoetry 4y ago
    The context of the writer. Apologies if I implied that the notation semantics were important -- letter exchange is free; concept change is not. What I indented to mean was the use of the terms poles and zeros is a bit wonky. Attempting to be cute with a physicist's hat, a pole is a "black hole", an entity you must not cross because the calculus will not work. It is a discontinuity, a singular value. There are worse things in mathematical generalizations; a cut / line in a manifold. But tools to cope.
iandanforth 4y ago
TLDR; If you want to make something go up (or down, or left or right) sometimes it goes down (or whatever the opposite is) a bit first. If you were to try harder to make it go up at that point, the problem gets worse, repeat until your system crashes. Times like these are called right-half-plane zeros and any control system you build has to be aware of them and designed to avoid causing a feedback loop.
civilized 4y ago
The article claims to be for a broad audience, and contains insinuations of political relevance. But right-half-plane zeros are a purely technical concept, and they're not explained with enough technical detail to be air-dropped into the middle of a broad audience piece. It's almost good. It would be good if it dropped the pretensions to technicality.
dhosek 4y ago
I lost interest before I got to his political point (about inflation), but the comments made me go back and while it’s an interesting point, it ignores the fact that the current bout of inflation is almost certainly a consequence of the Covid stimulus plus the supply chain disruptions with a dose of war in Ukraine. And it turns out that inflationary pressures seem to be declining outside of the volatile food and energy sectors (see https://jabberwocking.com/inflationary-pressure-seems-to-be-easing/ https://jabberwocking.com/inflationary-pressure-seems-to-be-...). I have a bit more faith in domain-specific analysis than abstract mathematical approaches.
- civilized 4y ago
  It's like "I know math so take me seriously" but then the posts don't use the math in any meaningful way. Not that I think they should use the math. Just skip the systems lectures and the "there is math behind this" and go straight to the analysis.
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dukeofdoom 4y ago
If you are going slow on a bicycle, and want to turn right, you might have to turn your front wheel left and then right, just so you don't fall over and maintain upright balance. Which would be a problem if you are riding along a cliff's edge.
deepsun 4y ago
> Countersteering on a bicycle is another example: To turn right, a cyclist will first steer slightly to the left. It's very visible and pronounced on heavier bikes, like motorcycles. Especially if you try riding a very heavy cruiser bike -- you'll immediately notice that countersteering is the only way to turn it. No matter how you try to lean it, it won't respond and will just go straight, but it'll respond very easly to handlebar inputs.
dukeofdoom 4y ago
I watched this video in preparation for a Drone license test. Really interesting stuff. Human Factors for Drone Pilots https://www.youtube.com/watch?v=UHYjl0u2UMA https://www.youtube.com/watch?v=UHYjl0u2UMA Based on what real pilates need to know about human physiology as it relates to steering airplanes.
oh_my_goodness 4y ago
OP: dy/dt = dx/dt + Ax Comments: The OP is a troubling covert political statement. The real issue here seems to be US midterm elections / climate change / COVID / appeal to authority.
- dqft 4y ago
  Everything is fine. We are prepared and can handle the situation(s). Everything is fine. It's fine. We have it under control. Fine. We have the metrics and they're fine. Okay?
- draw_down 4y ago
entropicgravity 4y ago
Not to mention poles in the unit circle.
bsedlm 4y ago
can anybody tell me what's f in this scenario? dy/dt = dx/dt + Ax is it the case that y = f(x,t)? thanks
sbf501 4y ago
Odd that OP would give a grim warning without an equation. I graduated in 1991 with BSEE and the curriculum was a rush to get us to diffeq and linear systems because 90% of the remaining three years of classes were taught using S and Z plane analysis. My engineering professors were incapable of introducing a concept without starting with a differential equation.[1] For the author to spend so much time explaining control theory, then sort of give up on it, was disappointing. Ironically, knowledge of control systems and warnings about them should pervade the thought process of the thinker and prevent them from making grandiose claims. Perhaps OP only has a topical knowledge but can spin a good yarn. [1] I'm a career programmer, but I always start my thoughts with a d/dt: whether it's an RTOS project, a graph GraphQL endpoint, or USB driver. I guess "if all you have is a hammer..."
mattmaroon 4y ago
I have a feeling this is going to be about interest rates and housing.
steve76 4y ago
shreyshnaccount 4y ago
My dynamical systems prof loved that xD
whycombinetor 4y ago
The author lost all credibility when he said I have to countersteer to turn my bike. The author is a "professional engineer and consultant, specializing in feedback systems and motors" too. There are >50 million cyclists in the US who would presumably immediately recognize this as a false statement and he didn't ask a single one of them to proofread. Edit since some people are confused by this apparently: You can steer your bike away from the edge of a cliff by leaning to initiate the turn instead of countersteering. This makes the author's advice of "Don’t ride your bicycle on the edge of a cliff" much less critical.
- jbay808 4y ago
  In the interest of defending my credibility, consider the challenge of explaining some concept to an audience using concrete examples, when any example has subtle associated details and exceptions that, while fun to explore on their own, do not further the goal of explaining the original concept. If you'd prefer, I can explain the concept of the right-half-plane zero using only abstract systems described by transfer functions. But I suspect that will be less effective from an education standpoint. I maintain that countersteering a bicycle is an excellent example of a RHP0, and it's no coincidence that a translating inverted pendulum also has an RHP0 in its control solution. I also am one of those cyclists and, at least prior to the pandemic, commuted by bicycle every day.
- mk12 4y ago
  I'm curious how you're so confident about this. I think if you ask most people (even most cyclists) what happens when you turn the handlebars to the right, they'd say you turn to the right. I cycle almost every day and I thought this for a long time. Have you actually tried it? When I tried it, I found that it forces me into a left turn.
  - whycombinetor 4y ago
    Have you tried leaning to the left while biking in a straight line? It results in you turning left without your front wheel ever having gone to the right (i.e., turning without countersteer).
f3rnando 4y ago
xg15 4y ago
As a layman, I had to think of drugs or other dopamine hits first - actions which increase well-being in the short term but are harmful in the long term. But what he really talks about seems to be the opposite: Actions which case some mild harm in the short term but increase well-being in the long term. So I guess something like working out or going on a diet or making a downpayment for a house? Except the failure mode is also counterintuitive: Normally, we tend to overvalue the short-term downsides of those actions and therefore shy away from them, missing out on the long-term benefits. But he talks about a situation where we overvalue the long-term benefits but ignore the short-term and overdo the action until the short-term harm becomes critical. So, e.g. someone working out, getting muscle-ache - and then working out more to counter the ache - which will only lead to more of it until the workout actually starts to become detrimental to their health. It's easy to see how this would trip up automated control loops, but I don't really see how this has practical application outside of control theory.
cyanydeez 4y ago
Economics is not a physical theory. Full stop.

439 points by jbay808 4y ago

Linda703 4y ago

[dead]

cheeselip420 4y ago

This is fantastic.

GistNoesis 4y ago

Are they still important if you use something like model predictive control ?

jbay808 4y ago
They are certainly something that your MPC controller will need to account for, and they will constrain the theoretical maximum performance you can get out of the system no matter how optimal your control algorithm is.

lordnacho 4y ago

Shouldn't there be a diagram of the complex plane so that people can see what it's the right half plane of? On top of it, there's a picture of a plane which is confusing. Fascinating subject though, in engineering class it was quite surprising how this bunch of functions tracing lines and dots on the complex plane would be relevant to just about everything. 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.

jbay808 4y ago
> 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.
rhn_mk1 4y ago
I felt that the article ended just where it was ripe to dig into the maths.
woojoo666 4y ago
Not to mention, it's not just a complex plane. It's the s-domain, reached through the laplace transform.

nurettin 4y ago

So sometimes it is better to cut losses rather than double down because planes exist.

lb1lf 4y ago

My signals processing professor apparently knew one joke, and one joke only. "A LOT (Polish airline) airplane is about to land in New York City; as they align for final approach, the first officer notifies the passengers that those seated on the right can now see the Statue of Liberty. A number of passengers get up from their seats left of the aisle and lean over the people seated on the right to get a glimpse of the statue. Plane promptly crashes. Why? There were too many Poles in the right half of the plane. I'll lead myself out.

gugagore 4y ago
The article saying zeros (where the transfer function is 0) when it should be saying poles (where the denominator of the rational function is zero), right?
- themeiguoren 4y ago
  Controls engineer here. The author’s control theory knowledge is correct - a RHP zero indicates that corrective action will begin in the wrong direction (which the article compares well with countersteering on a bike). The technical term is a “non minimum phase system”. It’s possible this will lead to instability, but in general the long term stability of a system is determined by the location of its poles (which is more applicable to the author’s ice cream example). Poles in the RHP will cause a system to blow up. My gripe with the article is that the author tries to wow you with some obscure technical points about a system which is unmodeled and he does not understand, to wave his hands at a vague conclusion. If he had made the same point using common English phrases that encapsulate the idea (“positive feedback loop”, “we have to let it get worse before it gets better”, etc), then it would be a lot clearer how wispy his argument is.
l33t2328 4y ago
I hate to be the guy to ask you to explain the joke, but why would that make the plane crash? I do know what a “pole” refers to, but I don’t follow the crash bit.
- 4y ago

DeathArrow 4y ago

Something I don't understand: on the one hand, people on HN seems to enjoy this kind of articles. On the other hand, they upvote any article who decries interviews where candidates are asked things that involves knowing some theory. So, if we think knowing theory is useful in cracking hard problems, why is it wrong to asses its knowledge in an interview?

deleted 4y ago
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CamperBob2 4y ago
HN's readership isn't homogeneous. There's room for both points of view. I've done a lot of useful work in feedback systems without ever really grokking Laplacian notation and the notion of complex frequency in general. A lot of the actual numerical methods used in real life boil down to a few canned formulas. But I know enough about the underlying theory to appreciate where the canned formulas come from, and fully intend to sit down some day and go through the whole process. Articles like this are interesting if only for the occasional gems in the comments, such as John N.'s pointer to Maxwell's 'On Governors' paper that I'd never run across before. At the same time, I don't see much upside in making hiring decisions on the basis of whether someone can regurgitate a bunch of textbook math. I'd rather spend the interview talking about control problems the candidate has dealt with personally, how they were handled, and what the candidate learned from them.
genezeta 4y ago
While I don't claim to have the answer to your question, I think there's a jump you're making that may not be so straightforward and somewhat explain things. You say "people on HN seems to enjoy this kind of articles" which seems reasonable, given the comments here. But then you jump to "we think knowing theory is useful in cracking hard problems". Going from the first to the second is not quite so clear. That is, someone may enjoy such an article and even learning some theory, but not necessarily because they think they will directly apply it. People sometimes just enjoy learning stuff or reading about it and then forgetting it. You also make a second jump, because other factors may be involved. Maybe the theory asked in the interviews is completely unrelated to the things involved in the job. The job may not even require cracking hard problems. These are frequent occurrences -in my experience, at least-, and clearly seem compatible with thinking that knowing theory is good in general.

Animats 4y ago

The classic paper, Maxwell's "On governors". (1869) [1] This is the first theoretical analysis of feedback. It will be seen that the motion of a machine with its governor consists in general of a uniform motion, combined with a disturbance which may be expressed as the sum of several component motions. These components may be of four different kinds:- (1) The disturbance may continually increase. (2) It may continually diminish. (3) It may be an oscillation of continually increasing amplitude. (4) It may be an oscillation of continually decreasing amplitude. The first and third cases are evidently inconsistent with the stability of the motion; and the second and fourth alone are admissible in a good governor. This condition is mathematically equivalent to the condition that all the possible roots, and all the possible parts of the impossible roots, of a certain equation shall be negative. That is, in the left half-plane. (Terminology has changed. Maxwell says "disturbance" where today, the term "error" would be used. Today, "disturbance" means an input which disturbs stability, while error is an output.) Maxwell got so much right in that paper, and it was a long time before anybody picked up on that result. Now, where it looks like the author is going is into economic territory. Basic economics talks about "economic equilibrium". The concept is that restoring forces will bring supply and demand into equilibrium. But basic control theory tells us that may not happen. Any system with delay in it can potentially be unstable. Too much delay, and even simple systems will not stabilize. [1] https://en.wikisource.org/wiki/On_Governors https://en.wikisource.org/wiki/On_Governors

WanderPanda 4y ago
In the real world all exponentials are sigmoids eventually, so what we actually get is is a recession with a drastic reallocation of resources (creative destruction).
- duped 4y ago
  Not really, there are plenty that are sinusoids which are just complex exponentials. The real trouble with sigmoids is when the saturation point is beyond physically meaningful quantities of the system. See the tacoma narrows bridge collapse.
  - deleted 4y ago

d--b 4y ago

This is very well explained, but there should be a simpler name for this effect than right-half-plane zeros if the author wants to spread the concept beyond control theory.

duped 4y ago

The greatest sin of undergraduate engineering education is sequestering signals and systems into electrical engineering curricula. I understand why it's done that way (I even had to fight to take the course early, sidestepping some prereqs for reasons). But it's really so foundational to understanding concepts of stability, resonance, information/energy flow (from the conceptual perspective), and the simple analytical tools for building a solid conceptual base. It takes a semester to hammer home that step response matters, positive feedback bad, negative feedback usually good, and topologies are useful.

Agentlien 4y ago
I took some electrical engineering courses but mainly software engineering with a focus on low-level details and graphics. The more I specialize in graphics the more I realize I need much more knowledge about signal processing than we were taught at the university.
- AB1908 4y ago
  Could you demonstrate with an example?
  - Agentlien 4y ago
    I can give a few. In general, the theory behind rendering generally treats what's on the screen as a discretization of a continuous visual signal. Post processing especially is largely about signal processing. Anti-aliasing (AA) is a very clear example where the lack of it leads to moiré patterns and jaggies. Understanding a lot of AA techniques is simplified by seeing the frame not as a discrete set of pixels but as a continuous signal being sampled (and can be sampled at multiple sub-pixel points per pixel). A lot of other screen effects are essentially filters applied to the graphical signal (sobel, gaussian blur, ...) and understanding them from a signal processing view helps understanding how to modify and optimize them. A good example here is identifying whether your effect is a separable filter which can be split into a horizontal and vertical pass. Seeing the image as a continuous signal/field being sampled is also the theoretical basis for a lot of visual effects used in physically-based rendering and things like screen-space ambient occlusion. Finally, if you want to write your own ray-tracer it really helps to be able to take this view of things once you get past the basics.

LolWolf 4y ago

Counterpoint: no you don’t. By the time you have a perfectly reasonable model of a system that is good enough such that computing the transfer function’s poles actually tell you something interesting about the system, there’s way more you can say about the system than “it is stable.” There are maybe some lessons to be drawn from basic “classical” control theory, but many are better stated by just analyzing the system directly. (As a side note, I’m not saying there’s Zero value in analyzing transfer functions, just that it’s a long way to the top from there.)

magneticnorth 4y ago

The follow-up article on inflation of shelter costs in response to mortgage interest rates is also fascinating and worth a read, imo [0]. The tl;dr is that in the medium and longer term, higher interest rates will decrease inflation, but there's a right-half-plane zero effect that will cause higher inflation rates in the short term in response to interest rate hikes (with a lot of simplifying assumptions). [0] https://jbconsulting.substack.com/p/on-shelter-futures-part-1 https://jbconsulting.substack.com/p/on-shelter-futures-part-...

neilwilson 4y ago
It's a little more complex than that because of the potential feedback loop via the main price channel. In other words if you can have a wage/price spiral you can have a profit/price spiral and an interest/price spiral for the same reasons. [0]:https://new-wayland.com/blog/interest-price-spiral/ https://new-wayland.com/blog/interest-price-spiral/ Once you abandon the concepts of general equilibrium and a fixed amount of money for what happens in reality, then the functional control mechanisms get a whole lot more interesting.

voldacar 4y ago

This is some of the best non-rigorous writing about math that I've encountered. Far superior to the awful quanta articles that sometimes get posted here.

eigart 4y ago

Great read. I’ve been thinking about how this applies to earth/climate change for a while, so I was surprised that the system he worries about is inflation/the economy.

jbay808 4y ago
Thank you for reading! I agree the Earth is a much worthier system to be worried about than the economy, for sure.

ilayn 4y ago

Always appreciate control theory articles. But this one needs some editing. Take ice cream example;that is not zero dynamics that's still pretty much convolution. Now zero dynamics examples must have no effect on the system. Thus it is not a zero if you continuously chugging ice cream. It is indeed a step input that you equilibriate at a constant ice cream input and some happiness comes out constantly. The moment you stop happiness goes away. That is not related to zero. Also a pure zero action is supposed to cancel the input completely. Not at first but completely (restricting the discussion to linear systems). Zeros effects are not so trivial to untangle as the article suggests unfortunately but fun read anyways and very nice flow.

jbay808 4y ago
> Now zero dynamics examples must have no effect on the system. Thus it is not a zero if you continuously chugging ice cream Thank you for your input! I wonder if you might have misread that example. In this system there's indeed a RHP0 in the transfer function from ice cream consumption happiness. A continuously increasing rate of ice cream intake results in exactly no effect on the output.
- ilayn 4y ago
  Your happiness shouldn't change if ice cream input has a zero. Also it should be independent from the amount of ice cream. In other words if we have an ODE say ddot y + 2 dot y + y = dot u - 2 u As long as my input is pure C exp(2t) independent of C I see no happiness and it's not working on my mood. In your example input u effect is cancelled by decay of y cancelling the guilt. Making it not a zero. In my personal case eating celery is a zero i see absolute no point eating it :) no harm and no benefit just pointless chewing

once_inc 4y ago

For those wondering: this article is an introduction into inflation of house prices in Canada. You can easily find the next article (it's already online) by going to the substack's index. Very good article, and well worth your time to read.

pcthrowaway 4y ago
Link, because I assumed it wasn't out yet since the author hadn't provided it: https://jbconsulting.substack.com/p/on-shelter-futures-part-1 https://jbconsulting.substack.com/p/on-shelter-futures-part-...
dools 4y ago
It’s funny as soon as I read the ice cream but I knew where he was going with it. The interesting thing is that his modelling concludes that raising interest rates is inflationary which is what Warren Mosler also says. Anyone interested in what to do about inflation would enjoy the recent Macro n Cheese podcast episode featuring Randall Wray
- selimthegrim 4y ago
  Let’s hope Erdogan doesn’t read this

parasti 4y ago

This is weird to say, but I've never had this happen before: as someone who's never heard of control theory, the initial illustrations and the leading icecream example seemed highly confusing and put me off from reading the rest.

tdubhro1 4y ago

It’s a bit disappointing that an article purporting to educate us about something we should know but may be unaware of, is completely wrong about the example of how an airplane climbs - you don’t climb by pitching up, you have to increase power.

rocqua 4y ago
Just pitching up will have you climb, but at the expense of losing velocity right?
- jhugo 4y ago
  Briefly.
- jacquesm 4y ago
  Right up to the stall speed limit. You can't just keep pitching up, you'd have to apply some power too if you don't eventually want to run out of forward (air)speed. In a glider you can't do that so there when in level flight you have a limited amount of forward momentum available to help you climb if the air itself isn't moving up, you are continuously trading altitude for speed and vv (easy to see in a dive: everybody expects you to gain speed in a dive because can all relate so something falling, it's obvious the reverse has to happen when you climb and the stall speed is a design parameter of the aircraft at a given altitude combined with a bunch of other factors). https://aviation.stackexchange.com/questions/27693/how-does-the-ias-stall-speed-vary-with-increasing-altitude https://aviation.stackexchange.com/questions/27693/how-does-...
jbay808 4y ago
Fair. Perhaps a glider would have been a better example.
- nosianu 4y ago
  How? A glider climbs when the air it is in rises faster than the airplane sinks in that air to maintain its forward speed. If you pitch up you can only exchange speed for a little bit of altitude, briefly.

lagrange77 4y ago

Great article and blog! I would also mention, that we essentially design controllers to shift the poles and zeroes of the total system (which consists of the plant system and the controller system) to more desirable positions, than those of the plant system alone.

ali-preview 4y ago

I'm nX 1 too<p>;)\n

ali-preview 4y ago

jokabrink 4y ago

I am not sure what to take from this. The title certainly makes sense from a engineers perspective. But from a layman's? I don't know. It seems, that he tries to explain an important concept in control theory but does not explain the meaning of "plane" at all. Even worse: He uses airplanes as an example. Isn't it terribly confusing for non-control-theory people? If I don't know control theory, then how on earth would I know that he means a 2D-plane? And what's this "minimum-phase-system" he mentions once? Is a pole a number? And what about RHP poles? I would be interested in how readers without a background in control theory and higher maths understood that article and what questions arose.

lagrange77 4y ago
> He uses airplanes as an example. Oh wow, i didn't notice that. It's either pretty clever, or unfortunate wording.
petesergeant 4y ago
> I am not sure what to take from this I think the author is using a lot of words to say "things often need to get a bit worse in order to start getting better"
- nbadg 4y ago
  That's only half of the story. The second half of the story is "if the getting worse temporarily cancels out the getting better, stop trying to correct, or you're going to crash!"
- Perseids 4y ago
  And, critically, you potentially need to ignore the signal of "things getting worse". Otherwise you might creature a vicious cycle of more corrective action -> more things getting worse (at first) -> even more corrective action, until your system crashes and you never got into the phase where most of the desired result of the corrective action materialized. And a second important point: You mustn't ever get into a state where the "things getting worse at first" already pushes you over a red line (see the example of the plane that loses even more altitude before it rises again. If you hit the ground in between you don't care that you theoretically would have risen later on).

gsliepen 4y ago

> The danger of the right-half-plane zero is that it lures you into reacting to it, but that is precisely the wrong thing to do. Attempting to apply a new control input to cancel the inverse response only sets off an even worse chain of events, where the resulting secondary inverse reaction becomes even more severe, requiring even more corrective action, until finally you’ve slammed into the ground. > In this situation, the flight controller’s only option is to ignore the initial misdirection and wait patiently until the airplane eventually begins to climb as intended. Of course that is easier said than done; adding a sleep() to your control loop to ignore the initial misdirection is also very bad. The right way to solve this is to not just tell the control loop to "go up", but to plan a realistic trajectory that the control loop can execute. That way, the error between the desired trajectory and the actual trajectory will be much smaller, and the closer the error is to zero, the less chance of a control loop to go wild.

thaumaturgy 4y ago

The danger of "systems thinking" is that it misleads otherwise clever people into believing they've found a cheat sheet for subjects they don't have deep knowledge in. This article is a fine example of that. I didn't know what right-half-plane zeroes are. I knew some of the examples it gave (Veritasium has a fun video on the bicycle steering phenomenon), but not that there was a category they all fit into. Neat. But I got squinty when the author said the intended audience was everybody, and got a hunch it was going to wander into the current economy ... which it did, sort of, except that in this case, "wandering" into the subject meant, "wrap it up with a graph and then point at it and go, see! See! I can predict the economy now!" The follow-up at https://jbconsulting.substack.com/p/on-shelter-futures-part-1 https://jbconsulting.substack.com/p/on-shelter-futures-part-... goes into more detail and concludes that interest rate hikes will increase inflation over the next 5-ish years, but there's no "part 2" in the series to be found (paywalled?). There are lots of graphs and the author tries to build a case out of several arguments, buuuuut in the end it feels like that IASIP conspiracy board meme. I smell a faint whiff of gish galloping here and there, but one thing that stands out to me is that the author chooses to normalize housing costs against inflation, but there's no mention of wage stagnation anywhere. Rents and housing costs can't rise a whole lot more, certainly not to the extent the author seems to be predicting, because people can't afford them. This is already a conversation happening in every housing market in at least several countries. In the US, pick literally any local subreddit and ask if anyone knows of an affordable place to rent, I dare you. There's already a huge epidemic of unhoused people and van-dwelling is more popular than it has ever been, and consumers are currently getting squeezed in a lot of directions. Here, one of the things in my browser history before this article was this thread: https://old.reddit.com/r/news/comments/v8knl5/gas_prices_hit_5_national_average_after_rapid_rise/ibs341g/ https://old.reddit.com/r/news/comments/v8knl5/gas_prices_hit... So, if wages don't rise to meet these costs, then something big is going to break way before the cost increases the article is doomsaying.

robertlagrant 4y ago
> Rents and housing costs can't rise a whole lot more, certainly not to the extent the author seems to be predicting, because people can't afford them. House prices are passively controlled because there's only so much money to spend on housing?

bambax 4y ago

> the first important lesson of inverse response is: don’t ride your bicycle on the edge of a cliff I don't know if many people often ride their bicycle on cliff edges, but many plane (as in airplane) accidents occur because it's difficult / impossible to recover from a stall near the ground.

LanceH 4y ago
You can also get your weight to the inside of a turn for a bicycle by leaning while riding straight. Every time this comes up there is a big debate with a bunch of people saying counter steering is required. Please, go out and try it. Drive perfectly straight along a painted line. Lean left, turn left. Lean right, turn right. There is no requirement for counter steering.
- bambax 4y ago
  I think it's somewhat speed-dependent. I ride motorcycles and bikes. On a motorcycle at high speed it's impossible (in my experience) to take a turn without counter steering. You sometimes have to push really hard on the handle on the side where you want to go. Also, leaning is very similar to counter steering; counter steering makes the bike "fall" on the side where you want to go. Interestingly, you can also steer a horse without doing anything on the reins; the horse will usually go where you put your weight; I think it's because it needs to compensate for the weight differential; or maybe it takes it as a hint about which way you're looking. In any case it works.

bob1029 4y ago

This stuff is fun. Surprised I haven't seen direct mention of state space representation yet: https://en.wikipedia.org/wiki/State-space_representation https://en.wikipedia.org/wiki/State-space_representation I recall going through this at university and it being a bit of a struggle. Looking back at it now, this stuff makes a lot more sense. A decade+ of practical experience probably helps.

raydiatian 4y ago

The footnote is nonsense. Needs revision, author is currently arguing that poles are indistinguishable from zeros.

oh_my_goodness 4y ago
The footnote currently appears to be correct.
jbay808 4y ago
I'm not aware of what you mean.

blauditore 4y ago

Can someone provide a TL;DR? I don't have time to read the whole article, and I don't even understand what's the topic based on title and reading a few paragraphs, nor from googling "right-half-plane zeros".

a_imho 4y ago
The plane refers to the plane of complex numbers (a+b*i), the right half is where the real part (a) is positive. If the zeros of your feedback loop are on the right hand side that means it is a unstable feedback loop, if they are on the left side it is stable feedback loop (this happens because the zeros eventually end up in exponents which either tend to infinity or to zero with time). If you squint a little bit most systems looks like a feedback loop and my not very confident interpretation is, judging from the last picture, that the author thinks we have a runaway inflation problem (zeros on the right hand side of the plane) and we might or might not have the controls to move them to the left hand side to tame it.
- layer8 4y ago
  I thought this would be something about positive zero in a 2D coordinate system, but seeing drawings of airplanes in the article I concluded “bummer, it’s not” and immediately hit backspace. Thanks for the summary. :)

woojoo666 4y ago

I don't think they should use the term right-half-plane zero if they don't explain laplace transform and the s-domain. Just call it an unstable system, or unbounded growth.

oh_my_goodness 4y ago
The point of the article, perhaps not stressed enough, is that there are stable systems that can be very difficult to control. Zeros in the right half-plane don't indicate instability. They indicate nulls in the transfer function for unbounded inputs. Poles in the right half-plane indicate instability. Zeros in the right half-plane indicate something a little more subtle. I believe the article is about the latter.
- woojoo666 4y ago
  Good point, I mixed up the two. However, the right-half plane still refers to the s-domain so it doesn't make sense to keep referring to the a right half plane without explaining what plane it is
jbay808 4y ago
That would be a right-half-plane pole. An explanation of the Laplace transform is coming! This is an article, not a book.

_moof 4y ago

Really should've run this by someone who knows how airplanes work, because they don't do what these hypothetical airplanes do. First off, "elevator flaps" is a howler. Elevators and flaps are two very different things. More importantly, you don't climb with the elevator; you climb with excess thrust. You can kinda sorta climb a little bit with just elevator, but unless you're making a very minor altitude correction, you'll slow way down and your climb rate will be really anemic, if you climb at all. But most importantly, an airplane won't just keep climbing and do a loop like that (unless you've got a thrust-to-weight ratio greater than one, which, to put it simply, you don't); the wing will stall way before you get anywhere near vertical, and the airplane will just stop flying until the angle of attack is reduced.

tzs 4y ago
> More importantly, you don't climb with the elevator; you climb with excess thrust. You can kinda sorta climb a little bit with just elevator, but unless you're making a very minor altitude correction, you'll slow way down and your climb rate will be really anemic, if you climb at all. So what happens to something like a jet fighter that is in level flight with the engines at maximum power if the pilot uses the elevators to raise the nose?
- _moof 4y ago
  It will climb (and slow down), but again, it's the thrust that's producing the climb, and this is an extreme example that isn't illustrative. Fighter jets produce enormous thrust for their weight with many having thrust-to-weight ratios greater than one. If they weren't air-breathing, they could literally fly into space. A normal airplane, even if it weren't air-breathing, couldn't do that. Depending on the configuration an F-16 has a T/W a little under 1.1, while a transport category aircraft (an airliner) will have a T/W somewhere between 0.20 and 0.35. Totally different performance characteristics.
- p_l 4y ago
  Powered airplanes hide the energy-management nature of climb/descent. Essentially, you have potential energy (altitude) and kinetic energy (speed), and you trade one for the other. For safe range of inputs, your lift is function of pitch and airspeed, with drag as result. Increasing pitch increases lift (most of the time) at expense of increased drag. Lift gets you higher raising your potential energy, which you can spend back on glide, exchanging it for kinetic energy necessary for airflow. With powered plane, you provide extra kinetic energy that can be spent on higher lift. You use your stick to manipulate energy/speed, and in fact it's common to descend while pulling the stick on purpose. A fighter jet with TWR above 1 has enough extra energy that it's going to be able to maneuver rapidly (afterburner/reheat exists for it, even, as jet engines are slow to spool up). Plane with lower TWR, or with significant mass, is going to behave closer to glider (heavy planes like airliners make energy management a big issue)

VogonPoetry 4y ago

I think this article is trying to make a political statement, "Our leaders have just done something that is going to cause a future problem, a crash". I have only read the linked article, I think the followup might be available, but I'm not going to read it before posting this -- because this article was meant to be clickbait, to get you hooked and possibly mis-informed. The article as it stands (incomplete) contains some classic argument fallacies. It is an "appeal to authority", by attempting to explain control theory. This person knows something. The examples all result in bad things, airplanes crashing, hard drives (crashing - perhaps a stretch). Bicycle at the edge of a cliff. Eating too much ice cream. Chernobyl. This is a possible "appeal to emotion". The final issue is an "incomplete comparison". The graph at the bottom of the article shows housing prices -- all of the previous examples have mathematical models which can explain the behavior. For the last graph no model (the equations) is presented. Without a model you cannot use control theory to analyze the zeros and poles. The last graph wants you to believe in a continuing upward trend, the fallacious argument, implies that whatever the Canadian political change that has been made is going to make this trend to zero, despite the intention to keep it trending upwards. Background: A long time ago, as a mathematics undergraduate, I did take a course in control theory, it was run out of the engineering department. It was somewhat awkward as quite a few mathematical terms were not-quite-the-same. I get the same unease when reading this for poles, zeros and right-half-planes. Any engineering textbooks that use j for sqrt(-1) instead of i (because that is taken) is an indicator. Yup, this could be construed as an "appeal to authority".

any1 4y ago
Textbooks that use j instead of i are an indicator of what? Why is slightly different notation awkward? It's not as if notation is always consistent within the field of mathematics, right?
- VogonPoetry 4y ago
  The context of the writer. Apologies if I implied that the notation semantics were important -- letter exchange is free; concept change is not. What I indented to mean was the use of the terms poles and zeros is a bit wonky. Attempting to be cute with a physicist's hat, a pole is a "black hole", an entity you must not cross because the calculus will not work. It is a discontinuity, a singular value. There are worse things in mathematical generalizations; a cut / line in a manifold. But tools to cope.

iandanforth 4y ago

TLDR; If you want to make something go up (or down, or left or right) sometimes it goes down (or whatever the opposite is) a bit first. If you were to try harder to make it go up at that point, the problem gets worse, repeat until your system crashes. Times like these are called right-half-plane zeros and any control system you build has to be aware of them and designed to avoid causing a feedback loop.

civilized 4y ago

The article claims to be for a broad audience, and contains insinuations of political relevance. But right-half-plane zeros are a purely technical concept, and they're not explained with enough technical detail to be air-dropped into the middle of a broad audience piece. It's almost good. It would be good if it dropped the pretensions to technicality.

dhosek 4y ago

I lost interest before I got to his political point (about inflation), but the comments made me go back and while it’s an interesting point, it ignores the fact that the current bout of inflation is almost certainly a consequence of the Covid stimulus plus the supply chain disruptions with a dose of war in Ukraine. And it turns out that inflationary pressures seem to be declining outside of the volatile food and energy sectors (see https://jabberwocking.com/inflationary-pressure-seems-to-be-easing/ https://jabberwocking.com/inflationary-pressure-seems-to-be-...). I have a bit more faith in domain-specific analysis than abstract mathematical approaches.

civilized 4y ago
It's like "I know math so take me seriously" but then the posts don't use the math in any meaningful way. Not that I think they should use the math. Just skip the systems lectures and the "there is math behind this" and go straight to the analysis.

deleted 4y ago

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dukeofdoom 4y ago

If you are going slow on a bicycle, and want to turn right, you might have to turn your front wheel left and then right, just so you don't fall over and maintain upright balance. Which would be a problem if you are riding along a cliff's edge.

deepsun 4y ago

> Countersteering on a bicycle is another example: To turn right, a cyclist will first steer slightly to the left. It's very visible and pronounced on heavier bikes, like motorcycles. Especially if you try riding a very heavy cruiser bike -- you'll immediately notice that countersteering is the only way to turn it. No matter how you try to lean it, it won't respond and will just go straight, but it'll respond very easly to handlebar inputs.

dukeofdoom 4y ago

I watched this video in preparation for a Drone license test. Really interesting stuff. Human Factors for Drone Pilots https://www.youtube.com/watch?v=UHYjl0u2UMA https://www.youtube.com/watch?v=UHYjl0u2UMA Based on what real pilates need to know about human physiology as it relates to steering airplanes.

oh_my_goodness 4y ago

OP: dy/dt = dx/dt + Ax Comments: The OP is a troubling covert political statement. The real issue here seems to be US midterm elections / climate change / COVID / appeal to authority.

dqft 4y ago
Everything is fine. We are prepared and can handle the situation(s). Everything is fine. It's fine. We have it under control. Fine. We have the metrics and they're fine. Okay?
draw_down 4y ago

entropicgravity 4y ago

Not to mention poles in the unit circle.

bsedlm 4y ago

can anybody tell me what's f in this scenario? dy/dt = dx/dt + Ax is it the case that y = f(x,t)? thanks

sbf501 4y ago

Odd that OP would give a grim warning without an equation. I graduated in 1991 with BSEE and the curriculum was a rush to get us to diffeq and linear systems because 90% of the remaining three years of classes were taught using S and Z plane analysis. My engineering professors were incapable of introducing a concept without starting with a differential equation.[1] For the author to spend so much time explaining control theory, then sort of give up on it, was disappointing. Ironically, knowledge of control systems and warnings about them should pervade the thought process of the thinker and prevent them from making grandiose claims. Perhaps OP only has a topical knowledge but can spin a good yarn. [1] I'm a career programmer, but I always start my thoughts with a d/dt: whether it's an RTOS project, a graph GraphQL endpoint, or USB driver. I guess "if all you have is a hammer..."

mattmaroon 4y ago

I have a feeling this is going to be about interest rates and housing.

steve76 4y ago

shreyshnaccount 4y ago

My dynamical systems prof loved that xD

whycombinetor 4y ago

The author lost all credibility when he said I have to countersteer to turn my bike. The author is a "professional engineer and consultant, specializing in feedback systems and motors" too. There are >50 million cyclists in the US who would presumably immediately recognize this as a false statement and he didn't ask a single one of them to proofread. Edit since some people are confused by this apparently: You can steer your bike away from the edge of a cliff by leaning to initiate the turn instead of countersteering. This makes the author's advice of "Don’t ride your bicycle on the edge of a cliff" much less critical.

jbay808 4y ago
In the interest of defending my credibility, consider the challenge of explaining some concept to an audience using concrete examples, when any example has subtle associated details and exceptions that, while fun to explore on their own, do not further the goal of explaining the original concept. If you'd prefer, I can explain the concept of the right-half-plane zero using only abstract systems described by transfer functions. But I suspect that will be less effective from an education standpoint. I maintain that countersteering a bicycle is an excellent example of a RHP0, and it's no coincidence that a translating inverted pendulum also has an RHP0 in its control solution. I also am one of those cyclists and, at least prior to the pandemic, commuted by bicycle every day.
mk12 4y ago
I'm curious how you're so confident about this. I think if you ask most people (even most cyclists) what happens when you turn the handlebars to the right, they'd say you turn to the right. I cycle almost every day and I thought this for a long time. Have you actually tried it? When I tried it, I found that it forces me into a left turn.
- whycombinetor 4y ago
  Have you tried leaning to the left while biking in a straight line? It results in you turning left without your front wheel ever having gone to the right (i.e., turning without countersteer).

f3rnando 4y ago

xg15 4y ago

As a layman, I had to think of drugs or other dopamine hits first - actions which increase well-being in the short term but are harmful in the long term. But what he really talks about seems to be the opposite: Actions which case some mild harm in the short term but increase well-being in the long term. So I guess something like working out or going on a diet or making a downpayment for a house? Except the failure mode is also counterintuitive: Normally, we tend to overvalue the short-term downsides of those actions and therefore shy away from them, missing out on the long-term benefits. But he talks about a situation where we overvalue the long-term benefits but ignore the short-term and overdo the action until the short-term harm becomes critical. So, e.g. someone working out, getting muscle-ache - and then working out more to counter the ache - which will only lead to more of it until the workout actually starts to become detrimental to their health. It's easy to see how this would trip up automated control loops, but I don't really see how this has practical application outside of control theory.

cyanydeez 4y ago

Economics is not a physical theory. Full stop.