[HN Gopher] What is a control system anyway?
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What is a control system anyway?
Author : feltarock
Score : 248 points
Date : 2020-05-18 13:27 UTC (9 hours ago)
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| davedx wrote:
| I'm working on this exact problem except for an autonomous boat,
| so probably it's completely transferable, so this is nice timing.
| For now though I think I'm going to use a much simpler autopilot
| system (that I've already coded): Accelerate towards target at
| maximum speed; if within a certain distance of target, slow to
| approach speed (10%); if within "arrived at target" distance, cut
| speed to 0 (station keeping). This seems to work "well enough" in
| my JavaScript simulator, but I really wonder how it will do on
| actual water.
| carapace wrote:
| Huh, I once plugged a 2D physics engine into Tkinter and made a
| little floaty PID drone sim. I added balls that spawned from
| above it and fell on it, and it would stay on point. I'll see if
| I can find it later today if anyone's interested?
| roland35 wrote:
| PID loops are simple and effective control solutions and are
| relatively easy to incorporate into embedded controllers as well.
| Generally I have left out the integration step because it can
| easily cause instabilities, even with a wind-up preventer.
|
| When things get more complicated like with flight controllers or
| advanced motor drives PID is not recommended. Another problem
| I've seen is people gloss over tuning a PID controller properly
| too.
| ChuckNorris89 wrote:
| _> Generally I have left out the integration step because it
| can easily cause instabilities, even with a wind-up preventer._
|
| Funny, in automotive we always left out the derivative
| component not the integral which IMHO is the most useful
| component of the controller.
| dls2016 wrote:
| A quick intuition for this is: d/dx(e^(iwx)) = iw*e^(iwx)...
| that is, differentiation amplifies higher frequencies more
| than lower ones.
| aidenn0 wrote:
| Right, an integral is a low-pass filter with infinite gain
| at DC and a derivative is a high-pass filter with gain of 0
| (negative infinity dB) at DC; they both have 90 degrees of
| phase shift.
| silentwanderer wrote:
| In high school we nearly always left out the I term because
| we didn't mathematically verify our controllers, couldn't
| risk breaking the systems we were controlling with windup,
| and cared more about smooth and predictable motion than
| accuracy.
| rcxdude wrote:
| It does depend on the system you're controlling, often
| there's a natural integral in there and so you effectively
| 'shift' everything down one (P acts more like I, D acts like
| P, and I is a double-integral). Like how PD is fine for the
| quadcopter control until wind is added to the simulation.
| jbay808 wrote:
| Definitely.
|
| The main price of an integrator is 90 degrees of phase lag;
| this will harm the stability of many systems but as long as
| it's kept at a low bandwidth it's usually fine.
|
| The main price of derivative gain is high frequency noise
| amplification, and so a well designed PID will have a
| limited bandwidth for the D term as well. For many systems,
| especially those that are already damped or don't need the
| extra phase margin, it's not needed or not worth the noise
| cost.
| joeberon wrote:
| Yeah I've usually heard that the derivative component is what
| gets left out, never heard of leaving out the integral
| zwieback wrote:
| If you have a system without natural dampening and can't
| tolerate overshoot or oscillation you'd use a bit of D to
| slow things down.
| [deleted]
| edge17 wrote:
| Yea, I built a ball beam balancing device that torqued the
| beam using electromagnets (instead of the standard 2nd
| order system with a motor in the center and fast response).
| The electromagnets can not 'instantly' change the angle of
| the beams, and the ball's dynamics lead to overall
| instability as it rolls around and accelerates faster than
| the system can respond.. Without a derivative term it would
| have been impossible to control the system. That being
| said, the project was deliberately contrived in a way where
| the effects of the P,I,D terms were observable.
| elteto wrote:
| This was the controls lab final project when I was back in
| college [0] (video is not mine). It was a super cool project.
|
| Our task was to tune two PID controllers (one for each motor) to
| move the "head/pickup tip" to the color balls on the screen and
| then drive back to "drop" the ball in its respective "bucket". We
| were given the forward and inverse kinematic models, as well as a
| black box piece of code to actuate the motors, so we could focus
| on just tuning the PIDs. Lots of fun!
|
| [0] https://www.youtube.com/watch?v=PLk7nn2hWN0
|
| Edit: found a video of a project from a different year, also
| really cool and about tuning PIDs:
|
| [1] https://www.youtube.com/watch?v=ohwVLDmCSns
| supernova87a wrote:
| Those are great controllable animations/simulations! Thanks for
| sharing that!
|
| I had always wanted to get a physical intuition for how PID
| changes led to different behaviors. (And for example, in
| practical life, how an autopilot doesn't wildly overshoot and
| oscillate around a VOR radial when trying to intersect it).
| LoSboccacc wrote:
| it's interesting but that not how thermostats work, sure they're
| on-off but they have hysteresis they don't keep switching
|
| also you can use bang bang demo and inertia to orbit the thing
| moving the point on the tangent at the fastest approach, which is
| awesome.
| paulgb wrote:
| The thermostat he describes is not stateless, the key phrase is
| "When the temperature is too high _by some amount_ " (emphasis
| mine) -- the thermostat will turn on outside a particular
| range.
|
| This matches my understanding of a simple thermostat, is it
| wrong?
| TeMPOraL wrote:
| The JS simulation doesn't demonstrate this, though; the bang-
| bang controller keeps oscillating in very short steps around
| the goal.
| Tade0 wrote:
| Beautiful introduction.
|
| I remember my PID lab in college - we had two plexiglass towers
| with water in them and a pump - our task was to calculate the PID
| parameters so that one of the columns reached a certain level. I
| think it was measured by a buoy, so we had a pretty noisy input
| to begin with, but that was part of the problem at hand.
|
| It was a great introduction because the lab was 2h and the pump
| rather slow, so we couldn't just half-ass it.
| moritonal wrote:
| Great explanation, we often end up writing the same rules in
| video games.
|
| Any "drone" logic to do with some kind of builder unit or even a
| literal drone in something like COD needs rules like this.
| artemonster wrote:
| every time I see such great, simple and intuitive explanations
| I always remember how these topics were presented in Uni and
| want to tear-up a little: monotone voiced prof draws some
| nonsensical formulas and crap on blackboard, explaining zero
| things, giving zero context and examples. After a lecture you'd
| go to an excercize and start applying these formulas to
| artificial isolated problems, like a symbol manipulating
| machine. I always imagined myself being a person in that famous
| "chinese room experiment", a mindless monkey, manipulating
| symbols in equations with zero underlying understandings, just
| as it was "taught". brrr.
| ilikerashers wrote:
| I second that. University education in Electronic Engineering
| tends to favour rote learning over understanding.
|
| People could be genuinely interested in this stuff if
| engineering tried to focus more on creativity than
| memorization.
| TeMPOraL wrote:
| Same here. Give some interesting, non-artificial problems
| to solve. Tune a PID on an actual (real or simulated) pole
| balancing machine. Tune a controller on a (simulated!)
| rocket chasing a target in the sky. Give problems that
| students can relate to and understand, and in context that
| allows for exploration and interactively verifying
| solutions.
| arethuza wrote:
| The CS course I did had a lot of the maths content of the
| related electrical engineering courses - admittedly with a
| focus on discrete maths for the third and fourth years.
| This did give us a lot of maths, but with no real idea as
| to what people actually _did_ with it.
|
| Fortunately, for me at least this was fixed when as a
| postgraduate I joined a research group that was largely
| control engineers!
| rcxdude wrote:
| Maybe I shouldn't be so hard on the teaching at my uni then.
| There was a pretty decent amount of attempts at getting an
| intuitive explanation of how the systems worked, and quite a
| few demos of different control schemes and how they worked
| and might fail (as well as tons of maths).
| regularfry wrote:
| My memory of learning control theory at university was
| learning some super complicated stuff that was applicable to
| 99% of control problems. PID controllers, which are good for
| probably 95% of control problems, were effectively "an
| exercise for the reader". So trivial compared to the broader
| theory we were studying that nobody even thought to mention
| them. The expectation seemed to be that when you needed them,
| they'd just drop out of the maths and they'd need no further
| explanation.
|
| We'd already done a form of proportional control with op-
| amps. It would have been _enormously_ helpful to start
| control theory with discrete PI and PID to give us a
| practical grounding and something we could actually _use_
| before leaping off into the wider theory, but that 's not how
| academia works...
| HeyLaughingBoy wrote:
| This problem persists even in applied classes. I was taking
| a set of courses in Mechatronics for engineers who were
| already working in in industry. We went deep into the
| theory of various types of controls but when one of the
| students (an engineer with probably 20+ years of
| experience) asked about PID, it was dismissed as a "special
| case" of (I think) a Phase Lead control.
|
| Happily the guy teaching the lab portion of the class was
| himself an experienced controls engineer who actually knew
| how to use the math to accomplish something useful. We
| learned far more from him than from the lecture classes.
| Filligree wrote:
| As someone who's only worked with PID controllers, do you
| have any pointers to the more complicated stuff you're
| thinking about? A wikipedia article maybe?
| nuclearnice1 wrote:
| Try Model predictive control (MPC) and linear quadratic
| regulator (LQR)
| Greek0 wrote:
| PID Without a PhD [1] is an excellent paper that gives a good
| intuition for PID controllers. In addition, it has concrete
| advice on how to go about implementing a practical control
| scheme, and how to tune the PID constants.
|
| It's really my go-to reference for any practical control theory
| application.
|
| [1]:
| https://www.wescottdesign.com/articles/pid/pidWithoutAPhd.pd...
| wrigby wrote:
| Love this! I had read another paper from Wescott about
| sampling[1] years ago and loved it, but I didn't realize
| there's a handful of other great articles[2] that they've
| published.
|
| 1: https://www.wescottdesign.com/articles/Sampling/sampling.pdf
|
| 2: https://www.wescottdesign.com/articles.html
| RealityVoid wrote:
| It kind of bugs me that I understand PID quite well and I've
| coded quite a few for of them. But trying to dive deeper into
| control systems, I always hit a wall caused by my weak mastery
| or mathematics.
|
| I've heard someone say that PID is the deepest you can get
| without in control systems without advanced mathematics and I
| think hey might be right.
| zwieback wrote:
| Very nice! I've been working as a controls engineer for 20+ years
| and this is one of the best visualizations I've come across.
| Jugurtha wrote:
| I've had the chance to have had a teacher who exposed us to the
| design of robust RST controllers and optimal control (Pontryagin,
| Lyapunov, Bellman, Hamilton, Jacobi), Evans' work. Getting into
| an ML shop and looking at what my colleagues who do DL were doing
| made me think: hmmm, this backpropagation-thingy looks really
| familiar.
|
| There was, and still _is_ , a comparatively scarcity of
| documentation on these as most of the content online only tackles
| PID when it comes to "control systems".
|
| Fascinating stuff.
| RealityVoid wrote:
| Soo, if I wanted to look deeper in the maths for these RST
| controllers, where should I be looking? As I've been confessing
| in another comment in this thread, I am quite stumped how to
| proceed to understand more complex controllers. This is all my
| fault, because of my weak grasp of advanced mathematics.
| HeyLaughingBoy wrote:
| The best book I know of is pretty old by this point, but it's
| very readable! _Modern Control Systems_ by Dorf & Bishop.
| Probably pretty expensive by now, too!
|
| There's also the Control Systems Design Guide, but that's
| more of a cookbook-style. Dorf and Bishop is a theory book,
| but a good one.
| baylessj wrote:
| Really like the visualization, this does a great job of
| explaining the concepts of PID in an easy to understand way!
|
| The visualization used here could also work as a nice foundation
| for more complex controls algorithms for 2D space like path
| planning splines and pure pursuit.
| ryanmarsh wrote:
| A great example of this is a tweet from Max Howell (creator of
| Homebrew) regarding interviewing at Google.
|
| _Google: 90% of our engineers use the software you wrote
| (Homebrew), but you can't invert a binary tree on a whiteboard so
| fuck off._
|
| https://twitter.com/mxcl/status/608682016205344768?lang=en
| lb1lf wrote:
| As others have said, this page provided more understanding than
| more than one university course I've taken.
|
| Oh, and anecdotally I'll state that while Ziegler-Nicholls was
| great for my lab exercises, it was, ahem, quickly dropped when I
| started tuning heavy lifting equipment. Increasing proportional
| gain until stable oscillation was achieved with 160 metric tons
| in the test tower outside was, ahem, not boring. Not in the
| least.
| pgt wrote:
| PID-controlled sous vide with Clojure transducers:
| https://blog.adafruit.com/2014/10/06/boiling-sous-vide-eggs-...
| seiferteric wrote:
| In lieu of my final in control systems class, the professor
| allowed anyone to make a PID controller and present it to the
| class instead. All the EEs went this route (seems unfair to the
| others in retrospect LOL) and it was a great experience. Many did
| it digitally, but I opted for purely analog with op-amps for P, I
| and D with a summing op amp circuit at the end. This was
| connected to a pair of power transistors to drive a DC motor
| (from my lego mindstorm) and some gears to move a stick on a
| board. The input was a potentiometer with a nice metal knob. Each
| of the PID also had a pot to control it's own amplification
| before going into the summing circuit so you could adjust and see
| the behavior of each element. This was one of the most rewarding
| projects I have ever done I think, so cool to see it in action.
| deadso wrote:
| Reminds me of this project from MIT students where they built
| an analog Segway:
|
| https://techtv.mit.edu/videos/687f4627e5c14a52b24c694f7eeecf...
| daxterspeed wrote:
| These visualization are very satisfying and provide some
| wonderful insight.
|
| A few minor bugs: - The gray area is always too small, so there's
| plenty of area of the canvas that never gets cleared. - Perhaps
| this is intended, or maybe it's caused by by the demo running at
| 144Hz, but the drone is always swept away by the wind for me. It
| doesn't even stand a chance to fight it.
| vardump wrote:
| Same issue at 120 Hz, the drone had no chance against the wind.
| Confused me up until reading your comment.
|
| Works fine after setting refresh rate to 60 Hz. (Btw, amazing
| how bad scrolling looks at 60 Hz after getting used to 120 Hz!
| Never noticed it before nor did I think it could matter...)
| timvdalen wrote:
| Very cool! On my device, the actual canvas is a bit bigger than
| the area you're clearing, resulting in this[1].
|
| [1]: https://i.imgur.com/orrXwZT.png
| dmarchand90 wrote:
| I think I got a better insight into PID from this one page from
| me entire control engineering course in university
| regularfry wrote:
| Yeah, that's the best explanation I think I've ever seen of the
| I and D terms.
| scrooched_moose wrote:
| I was thinking the same thing.
|
| In my class, at no point was it explained why we would want to
| do this. It was "This is the math for a P controller. Here's
| some homework. Now test. This is the math for a PID
| controller....". Things didn't click until years later.
|
| Looking back, it was a shortcoming in so many classes I took.
| Actually discussing the problem we were trying to solve adds so
| much intuition and understanding to the mathematics.
| jagged-chisel wrote:
| OT anecdote
|
| If the cruise control in my vehicle is using PID, it still needs
| some tweaks. It's super aggressive when it's lower by 2pmh and
| often overshoots.
|
| My mom's is horrid: takes forever to get up to speed, then allows
| downhill drift to drive the vehicle nearly 5mph over the set
| speed.
|
| I feel like this kind of stuff would be fun to tweak in a
| simulator to help me understand why it doesn't work better, or
| show that I'm not entirely crazy and it can indeed be improved.
| ncallaway wrote:
| What's often hard about this situation is tuning to one problem
| case (fixing that downhill drift) often makes a _different_
| scenario worse. For example, fixing the downhill drift can make
| that overshoot worse.
|
| I can imagine tuning something like this for a cruise control
| scenario would be tricky, because there's probably hundreds of
| different cases to test for.
|
| I think a simulator here could be particularly fun to toy with,
| because you could have "unit tests" with 200 different
| scenarios that you try to optimize for. You could set your
| parameters, and it could run the 200 different scenarios, and
| show you were your parameters did well and where they did
| badly.
| aidenn0 wrote:
| My wife's Kia downshifts when you go more than a certain
| amount over the set-speed, which lets it apply "negative"
| throttle with engine braking.
| jacques_chester wrote:
| There's a lot of literature spread across a bunch of fields.
| The one I first saw was "Active Nonlinear Tests"[0] from the
| systems dynamics / complex systems area. The idea is that you
| perform searches of parameter space for a simualation to find
| the places where it exhibits dramatic nonlinearities.
|
| I've since seen something similar but not identical in the
| Statistical Process Control world: robust process (or
| product) design[1]. The idea is that any given system can be
| thought of as a function that represents X = F(a, b, c, ...)
| + E, where E is some measure of error or noise that can't be
| removed. The goal is to find settings for a, b, c etc that
| _minimise the effect of E_. So that even if uncontrolled
| noise swirls around, your process remains stable. You can
| imagine flipping that to look for maxima instead.
|
| [0] https://www.santafe.edu/research/results/working-
| papers/acti...
|
| [1] Web search results are underwhelming, I refer you instead
| to Douglas Montgomery's _Introduction to Statistical Process
| Control_.
| dls2016 wrote:
| Hrm... I wonder if they use a feed-foward control taking into
| account the angle of the dangle?
| mauvehaus wrote:
| In cars with manual transmissions, stepping on the clutch turns
| off the cruise control. In one '96 Honda Civic I was driving, I
| decided to see what happens if you slip it out of gear while
| cruise control is on _without_ stepping on the clutch.
|
| Answer: it revs the engine up. I hit the clutch before I got
| the chance to find out whether the cruise control or the rev
| limiter has ultimate authority. My guess is the rev limiter,
| but I didn't want to bet on it.
|
| Still, it's surprising that a computer that clearly knows
| vehicle speed (well, wheel speed) and engine speed (presumably,
| for engine control reasons) doesn't know that the vehicle is
| out of gear (or suffering some kind of serious mechanical
| malady) and respond appropriately.
| chillingeffect wrote:
| that's an example of non-linearity. probably the car only
| applies throttle to regulate speed and not brakes.
|
| home heating systems are similar in that the usually only add
| heat.
|
| in both cases, the PID would be generating the proper output,
| but it doesn't have a means to drive the system consistent with
| its output. e.g. it can't turn on the brakes, or air
| conditioner.
| pgt wrote:
| I built a volume control system (hardware + software) using
| mainly a PID controller: https://wallfly.webflow.io/
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