11 ms·

PID Without a PhD (2016) [pdf]

301 points by darshanrai 9y ago

senatorobama 9y ago
This reminds me of my Achilles heel during undergrad. Kalman filters. No matter how much I read about the topic, I just could not grok it. The whole "state update" algorithm and sheer amount of different variables threw me off. Does anyone else feel the same way?
- roevhat 9y ago
  Yes, indeed! What worked for me in the end, was to first understand state observers (e.g. Luenberger observers) and then consider a Kalman filter as an optimal observer, where the observer gain is the steady-state Kalman gain. The whole duality between state-feedback design and observer design -- and LQR and Kalman filters. Then it made sense :-)
- blt 9y ago
  The book "Probabilistic Robotics" explains the Kalman filter really well by putting it in the larger context as a Bayesian filter. I understood it only after reading that book
  - carlmr 9y ago
    I haven't read that book, but seeing it as a Bayesian filter made it click for me. All the control theory guys who just handwaved with "it's basically a stochastic Luenberger observer" didn't capture the essence of the filter for me. With a strong statistics background it was much better to go from Bayesian first principles to the Kalman filter.
- etaioinshrdlu 9y ago
  You may enjoy this tutorial: http://www.bzarg.com/p/how-a-kalman-filter-works-in-pictures/ http://www.bzarg.com/p/how-a-kalman-filter-works-in-pictures...
- msadowski 9y ago
  You are not alone! From what I've seen many people struggle with Kalman filters. If you want to build in depth understanding of them I heard lots of good things about this online book: https://github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python https://github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Pyt...
- deleted 9y ago
  [deleted]
- a_imho 9y ago
  The whole "state update" algorithm and sheer amount of different variables threw me off. Imo it starts with the name, it tells nothing and probably implies something different. It is the dynamic programming of control theory.
  - senatorobama 9y ago
    So true. Filters should be reserved for something like low pass filters.
- syntaxing 9y ago
  I totally understand where you are coming from. I read multiple tutorials and even implemented Kalman filters in Python, Matlab, and C++ for a balancing robot project. I never really understood what was happening even though I knew what the Kalman filter is used for and when I need it. The thing that "clicked" for me is that multiple measurements are always more accurate than a single measurement. That's why there is the feedback loop that derives the predicted value and the uncertainty that is associated with it. By combining the predicted value and the measured value (and their uncertainties), you get a more accurate measurement. Then you can use this more accurate measurement to "correct" your predictions so that the next prediction has even less uncertainty. This perpetuality is why Kalman filters lead to the "true" state.
metaphor 9y ago
Fortunately, basic PID analysis, including linear state-space representation and practical tuning methods (e.g. Ziegler-Nichols[1]), is taught in pretty much any first EE control theory course at the undergraduate level. [1] https://en.wikipedia.org/wiki/Ziegler%E2%80%93Nichols_method https://en.wikipedia.org/wiki/Ziegler%E2%80%93Nichols_method
- beambot 9y ago
  Not only that... Classic controls (including PID, Routh-Hurwitz, root-locus, etc) are NOT taught in many graduate PhD controls programs!
  - budadre75 9y ago
    Are those topics no longer relevant to today's state of the art research?
    - Sean1708 9y ago
      It's possible that you're just expected to know them at that point.
      - donquichotte 9y ago
        Agreed. Many state of the art control strategies nowadays are based on optimization techniques (e.g. Model Predictive Control, MPC, optimizes a convex cost function of the state, setpoint and input to your system over a certain time horizon). This has become a viable control strategy for fast (>1kHz) processes only in the past 15 years, since the optimization can be computationally intensive.
      - regularfry 9y ago
        Or be able to derive them. PID was never explicitly taught on my course, but all the theory behind it was.
    - tnecniv 9y ago
matthberg 9y ago
Wish my highschool FRC robotics team had this when we naively attempted to control elevator levels with a PID.
- msoucy 9y ago
  The team that I mentor is about to start tuning their PID controllers... this is very timely.
- dokem 9y ago
  I also remember tuning PID values on the old Jaguar motor controllers. It was not a pleasant or particularly fruitful experience.
wnoise 9y ago
He stresses regularly spaced sampling. I don't see why high-precision timestamps wouldn't work just as well, though that would complicate the computation of the I and D signals. Actually, throughout he doesn't seem to acknowledge the different units between the P, the I, and the D, instead implicitly treating the whole system as discrete time for many purposes, in e.g. the recommendations for 100:1 ratios between P, and I; and D and P.
- ebrewste 9y ago
  Regarding equal spacing: the sample rate determines a part of the system latency, and therefore performance and stability limitations. Eliminatating the stability of sample rate eliminates the decades of work basic controls analysis relies on. Or said another way, slow your sample rate and pay with your phase margin. Not to say it’s impossible to deal with (small) changes in sample rate, but in a text where he is already wildly simplifying things, this sounds like the wrong place to innovate.
darshanrai 9y ago
There's also this[1] series of blog posts by Brett Beauregard that speaks of a few improvements for real-world implementations. [1]: http://brettbeauregard.com/blog/2011/04/improving-the-beginners-pid-introduction/ http://brettbeauregard.com/blog/2011/04/improving-the-beginn...
- carlmr 9y ago
  That gets you through 90% of real world control problems. Filtering the derivative input gives you another 5% for some noisy processes. The other 5% require somebody who knows a bit more.
the-dude 9y ago
I have been doing a (integer) PID without a PhD over the last years as well : meCoffee ( https://mecoffee.nl https://mecoffee.nl ) for espresso machines.
- jmiserez 9y ago
  I just bought an espresso machine, and it’s crazy that something as simple as a PID controller justifies a several hundred dollar markup on some models. The processing power needed is miniscule...!
  - the-dude 9y ago
    True. And if your machine does not have a pressostat, it makes a huge difference.
    - jmiserez 9y ago
      Does the optional dimming of the boiler make a difference in your design? Mine just fully turns on and off all the time, and I reckon dimming would probably be easier on the power grid. 2000W on/off vs ~80W average (I measured) is quite the difference.
      - the-dude 9y ago
        Your measurement seems to match up. It makes a difference in the fact the meCoffee PID can adjust its P response 100 times a second, it can react much faster. Dimming such heavy loads is not within spec in all jurisdictions though. It also includes normal interval behaviour.
      - lmilcin 9y ago
        I am using SSR with zero crossing and it makes much difference. First, I am dithering the boiler power (the power is applied to the boiler on only some AC cycles), I am basically deciding per cycle whether I want my boiler turned on for the next 1/100th or 1/120th of the second. I am already running my model about 50 times per second (not using PID) so that's ok. Being able to apply fractional power to the boiler means it is quiet and much less scale deposits. Also due to the zero-crossing control I have much less electrical noise. Turning the boiler fully-on blindly causes electrical noise which is not nice for other devices (my Baratza Sette grinder turns on spontaneusly when this happens).
dosshell 9y ago
I am a little suprised that the author does not use a low-pass filter for the D part, for example 1/(1+s Tf) and instead tells you to modify the hardware. Sure, you need cut off the noise with hardware in respect to your Nyquist frequence but you can still have a lot of high frequency noise. And it is not always possible to use hardware filters to get rid of the noise, for example if your are tracking an object with a camera and the x,y is your input to the pid. Ofcourse you can skip the D part. What am I missing here? I also find it more easy to use a reset based integrator anti-windup, where you specify your limits on your control signal instead of limiting the integrator. Here is an diagram of what I usally do: +--------+ +------+ -y | 1 | | | -------->+ ------ +---------->+ Kd*s +----+ | 1+s*Tf | | | | | | +------+ v +--------+ +----+ +-+-+ +-------+ e=r-y | | | | | __ | u --------+------------>+ Kp +----------->+ ∑ +---+-->+ __/ +---+---> | | | | | | | | | | +----+ +-+-+ | +-------+ | | ^ | | | +----+ +---+ +-----+ | | +---+ | | | | | | | 1 | | | - | | + | +-->+ Ki +-->+ ∑ +--->+ - +-----+ +---->+ ∑ +<----+ | | | | | s | | | +----+ +-+-+ +-----+ +-+-+ ^ | | | | +----+ | | | | | +------+ kt +<-------------------+ | | +----+ The kt gain will reduce the integrator when we have saturated output. Does some one knows the pros and coins with the different anti-windup solutions?
- balda 9y ago
  yeah
- jgable 9y ago
  I always do integrator wind-up similar to how you do it -- apply limits to the overall controller output (which are typically necessary for the system anyway), and use that to limit the integrator. Just putting limits on the integrator is too crude, and it's not like it's any easier to program. Maybe the author introduced that because it's easier for a beginner to understand. However, I typically do not change the state of the integrator the way you are doing here. I just hold the integrator state (i.e. don't update it) if the controller is limited. That way, noise on the P or D signals doesn't cause my integrator state to hop around. I may do it your way if the controller limits are changing over time for some reason. I also always low-pass filter the D term, as you mentioned. Otherwise, the D term is just too noisy. I often find that my P and D terms are limited by how much sensor noise I'm willing to let thru to my controller output.
budadre75 9y ago
what I have been searching for years is not theories or tutorials about PID, but a detailed explanation on how to tune a digital controller(instead of a continuous one) in a easy-to-setup environment, whether it be simulation or a cheap hardware. I know examples can include inverted pendulum(IP), double IP, mountain cart, heater with thermometer feedback, line-follower, etc, but where can I easily play around with these examples?
- cellularmitosis 9y ago
  I found this video useful: https://youtu.be/uXnDwojRb1g https://youtu.be/uXnDwojRb1g
xchip 9y ago
Or you can use my PID simulator, where you can play with the constants in a simulated car to reach different speeds, it updates the output graph instantly http://codinglab.blogspot.be/2016/04/online-pdi-trainer.html http://codinglab.blogspot.be/2016/04/online-pdi-trainer.html
- Tepix 9y ago
  Great, thanks!
xchip 9y ago
My sousvide controller uses a PID to regulate the temperature super precisely. https://github.com/aguaviva/SousVide https://github.com/aguaviva/SousVide
Double_a_92 9y ago
It's so sad. I studies this stuff in depth for almost 1 year in college... And now after 2 years of working as a software dev I forgot almost everything.
- rrmm 9y ago
  I wouldn't worry about it. In your career, you're going to forget a ton of stuff (if you're not repeating the same project over and over again). That's just how it works. The win is that someday you will end up needing either the stuff you learned or the math that you used, and you'll find out it's way easier (and more illuminating) learning it the second time around.
roel_v 9y ago
So here's an awfully uninformed question that will probably get me laughed at by actual engineers (as in, not 'software engineers' like myself - and yes Canadians please bite your tongues, I've heard your shpiel by now): when you have a more powerful computer to work with, isn't it much easier to just derive some regression parameters and call it a day? My use case: I have this home-build growhouse that I use to start my seedlings in at the end of winter (and as a fermentation chamber for wine). It's controlled by a Raspberry Pi and as inputs I have 4 groups of LED grow lights, a 30w heating element, a fan that draws warm air out of the box and thus brings the temperature within the box towards ambient temperature, and DHT22 sensors that measure temperature and humidity inside and outside the box. The goal is to keep temperature as close to a certain target temperature as possible, keeping in mind that I want the lights to be on for a certain nr of hours per day and the lights give off so much heat that they will pretty much always make the temperature go over the target (so the fan then needs to bring it down again). It's easy to get this working the naive way with an hysteresis of say +/- 2 degrees (which is fine for my purposes), but the nerd inside me sees it as a game to make that band smaller. So I've been reading up on PID controllers and dear baby jesus I can't even work out how I'd get started. So the pragmatic part of my brain goes 'just run it for a few weeks with incremental inputs between 15 and 35 degrees (C, of course), measure the responses, toss all measurements into R and derive some regression parameters'. Does anyone do this in industry? Probably not because everywhere I've asked, everybody's who's ever done real work on this uses PID controllers - but is that because they're easier to build on microprocessors (i.e., need less number crunching)?
- deleted 9y ago
  [deleted]
- Tepix 9y ago
  There will almost always be external influences that change the behaviour over time. If you have a vehicle, going up the hill will require more energy to keep the speed constant. For your growhouse, if it's hot outside of the box it may requires less heating, etc. Or the LEDs that you use get less efficient over time. You really want to have a dynamic algorithm such as PID that can deal with these changes in a near optimal fashion.
- 9y ago
fest 9y ago
There was an "aha" moment for me when I realized that PID loop only works well for linear systems (and sometimes it's not obvious if a system is linear or not). Real world example: imagine you have a single-axis motion stage driven by electric motor and you want to control position of a carriage. Usually your control output is motor voltage. Motor voltage approximately translates to current through motor windings, which in turn approximately translates to torque exerted by motor. Torque exerts a force (T = F * r) on carriage. Applying force to the carriage makes it accelerate (F = m * a). Acceleration linearly increases the carriage velocity (v = v0 + a * t). Carriage having some velocity finally causes the position change (s = v0 * t + a * t^2). In the essence, the system turns out to be non-linear with the respect to parameter you are controlling. To improve this system, one solution is to add velocity sensor (or differentiate the position sensor, if it's resolution is high enough) and introduce a cascading PID loop topology- the outer loop takes position error and outputs velocity error, which is fed to inner loop (input = velocity error, output = acceleration). The coefficients for the loops have to be tuned starting from innermost loop. Another solution is to use different control algorithm which is suited for non-linear systems (e.g. LQR).
- lmilcin 9y ago
  PID will also work for non-linear systems provided they are not too non-linear. Even simple steam boiler is already non-linear but PID will work fine if you are just interested in practical results.
  - fest 9y ago
    Sure, but for such systems even a simple on-off controller works fine, if the sensor is close enough to heating element (and if it's too much decoupled, PID won't help either). The biggest issue for me was spending a lot of time trying to achieve a better system response (fast settling time with minimal overshoot) for system that was just designed badly.
    - lmilcin 9y ago
      I was able to achieve optimal control and no overshoot with my espresso machine by using Model Predictive Control (https://en.wikipedia.org/wiki/Model_predictive_control https://en.wikipedia.org/wiki/Model_predictive_control) aided by Moving Horizon Estimation (https://en.wikipedia.org/wiki/Moving_horizon_estimation https://en.wikipedia.org/wiki/Moving_horizon_estimation) to continually update model parameters. Additionally, the set value for the boiler temperature is calculated using separate model that takes the group head temperature into the account. The end result is that the controller is able to stabilize immediately, with maximum power of the heater and with no overshoots or undershoots to a temperature that takes into the account the state of group head to provide the ideal water when brewing. While PID is able to control the temperature very accurately I found even in best case it took additional 50% of the time to stabilize and also it was difficult to optimally use 100% power of the heater until last possible moment. Being able to achieve stability almost immediately means I can keep lower water temperature in the boiler and bring it to temperature at the last possible moment. End result being that it is now much faster to get it ready.
Tepix 9y ago
Is a machine learning algorithm capable of getting better results than a PID? Is the extra effort worth it?
- dosshell 9y ago
  How do you mean with "better result"? For a non-linear system, machine learning can perform much better and solve more complex tasks. Like walking for a humanoid robot. A linearzied PID solution can not beat that. For linear systems: Depends of what you mean with better I guess. My understanding is that you can place some of the poles of a system with a PID pretty much where you want. So for a simple linear system: no. There exist also other controllers where a LQR can be used in linear systems to get a perfect theoritical controller based upon to minimize the cost of control outputs. (yes, several outputs). However maybe a ML can be used to choose and tune the controllers better than humans? EDIT: Also, the discretication is not always perfect (backward or forward euler is common estimates). So maybe ML can help in that too?
  - tnecniv 9y ago
    > For a non-linear system, machine learning can perform much better and solve more complex tasks. Like walking for a humanoid robot. A linearzied PID solution can not beat that. Right but you are comparing a nonlinear regression model with a linear control scheme, which isn't really fair. Plenty of nonlinear control strategies exist and are used in practice for things like humanoid walking. Moreover, many people prefer these controllers due to the theoretical guarantees they provide over a learned control policy. That said, ML does have a place in control theory, and you can find papers going back to at last the 90s (I never looked earlier but they probably exist) that combine the two, and not just in a reinforcement learning context. > However maybe a ML can be used to choose and tune the controllers better than humans? Probably not, assuming you are discussing linear systems. You would need to come up with some cost function for your ML algorithm to determine the performance of a particular control policy, but then why not just use that as the objective function for your optimal control algorithm?
- wenc 9y ago
  > Is a machine learning algorithm capable of getting better results than a PID? Is the extra effort worth it? Potentially yes, but by it being a component of a completely different control paradigm (MPC). ML itself will probably not improve on PID while still keeping it PID. So, there are two parts to a control system: 1) The predictive model (prediction) 2) The feedback control law (action) ML primarily concerns itself with function approximation from data, y = f(x, p), where p are parameters -- in the parametric model case. ML practitioners create predictive models but don't really consider feedback loops. That is more the domain of control theory, which is concerned with system behavior when exogenous inputs (actions) act on the system. The math is different. ML can be used to fulfill the role of (1). It has nothing to say about (2). In the PID case, (1) is extremely simple -- it is simply an error function (difference). (2) is where the magic happens... based on the error, the controller computes the right action. The beauty of PID control is that it is technically "model-free" (if you don't consider an error function a model). You can apply it to systems where you have very little data, and still be able to do fairly good job. You could replace (1) in PID with an ML model, but then you would defeating one of the some of attractive qualities of PID control: effectiveness under uncertainty without a model. You can use ML to guide the tuning of PIDs, but that's about it. That said, ML models have a place. In advanced controllers like MPC, (1) is typically a dynamic (state-space, FIR/FSR, physics equations-based) causal model of the system under control. (2) is an optimization algorithm. You could conceivably replace (1) with an ML model. This is done in many cases -- in many plants, there is a predictive model that infer states based on images and sound (for instance, using Near Infra Red sensors to inferentially predict certain chemical properties). But that's no longer PID.
leafario2 9y ago
What's the reason he insists on using double precision math? (If not using fixed point)
- davepage 9y ago
  Keeping things simple, if the input data SNR is, say, 16 bits, and the PID coefficients are 16 bits, then there is 32 bits of significand at the output of the control gain multipliers. For single precision float, this is truncated to 23 bits. So, the system may settle when the transducer input is near zero (and the exponent can scale down to maintain sufficient precision), but then fail to settle well at the ends of the transducer range (where the transducer input is near +/-2^15 and the exponent in the single needs to stay high to avoid saturation). Also, consider the numerical integrator is running an infinite series of adds, so therein lies a trap for error growth, as well. I have made this mistake before, and the sometimes strange control behavior can be frustrating. Considering the small performance penalty for using doubles on modern hardware, it is excellent advice.
  - leafario2 9y ago
    Thanks for the explanation! I have only hardware with no FPU (teensy 3.2) or single precision FPU(teensy 3.5)... I suppose in that case it would be better to write a fixed point implementation?
    - ebrewste 9y ago
      Fixed point often works better, as it has better resolution because it doesn't need the exponent. The flip side is that the range of a fixed point is very limited (because it doesn't have the exponent). Practically, that means you need to do some analysis to make sure don't overflow or saturate, and use the bulk of your fixed point range to get the resolution benefits. If you do that, fixed point is great. If you don't have time or knowledge to do that, floating point works better because you can be more ham-fisted with your scaling and still not overflow or saturate.
      - 9y ago
RhysU 9y ago
'Feedback systems: an introduction for scientists and engineers' is another nice reference [1]. I used it and another Wescott text to put together effectively a somewhat extended version of the OP's code [2]. [1] http://www.cds.caltech.edu/~murray/amwiki/index.php/Main_Page http://www.cds.caltech.edu/~murray/amwiki/index.php/Main_Pag... [2] https://github.com/RhysU/helm https://github.com/RhysU/helm
midjji 9y ago
The matlab system identification toolbox is nice to get a casual feel for the systems. Note that pid controllers are mostly used due to their computational rather than control performance. They are math equivalent for linear systems, but thats like saying x=inv(A)b is just as good... The powerful idea is the linear system model or the stochastic linear system model. Understand them and the properties of recursive filters and pid will come naturally.
throwawaybbqed 9y ago
My SW eng program did not even hint at these. Is there a good edX or coursera course that goes through more extensive material than the pdf? I'm also curious what tools are used by professionals? Matlab, simulink???
- wustangdan 9y ago
  Not sure if this is allowed but I created a Udemy course on PID control where I go through the theory and then in the assignments you write Python code to create a PID controller for an elevator (with the goal of moving the elevator to the desired height). A PID controller can be written in less than 10 lines of code but understanding the different components is very important for tuning it and getting it to work. If your interested just go to Udemy and search PID Control, you'll find it. If you'd like a discount code (not worth the full price if your a SW eng) DM me on Twitter as I'm not sure I'm allowed to post it here. When I did my MSc I did all my PID controllers in MATLAB/Simulink but since the actual code for a PID controller is very simple, it's easy to implement in Python or C++.
  - throwawaybbqed 9y ago
    Looks interesting .. as a SW Eng, I find Udemy very useful for these hw courses. Thanks for the pointer!
- tnecniv 9y ago
  Google for a class in (classical) control theory. This is a standard topic for electrical, mechanical, and chemical engineering programs. For implementing a PID loop, you can do it in pretty much any language you want -- it's relatively straightforward once you know the math. You can even do it in hardware via an analog circuit if you desire. However MATLAB / Simulink are commonly used when experimenting with system parameters due to the presence of straightforward plotting tools and numerical ODE solvers.
- ninly 9y ago
  The Control Lectures series by Brian Douglas on YouTube is a fantastic resource (https://www.youtube.com/user/ControlLectures https://www.youtube.com/user/ControlLectures). Also U. Mich. has a great set of control tutorials put together with a focus on implementations in MATLAB/Simulink (http://ctms.engin.umich.edu/CTMS http://ctms.engin.umich.edu/CTMS). All of my own experience in controls (both as a student and professional) uses MATLAB/Simulink to model and generate controller code. Other tools are out there, but I don't know much about them.
cr0sh 9y ago
Just going to throw my 2-cents in - I should note that my knowledge of PID is very limited. The first time I encountered an explanation of how PID worked that made sense to me, was via the Udacity CS373 course that I took in 2012 (Thrun also had a great explanation on how a Kalman filter worked as well). This explanation of PID was repeated when I took the Udacity Self-Driving Car Engineer Nanodegree (starting in 2016). In the CS373 course, Thrun detailed a few different ways to tune a PID controller - but one way he covered was rather curious in how it worked. It wasn't perfect, but it got you "close enough". I'm not sure if it would work well for a "real system" but for the purpose of learning it seemed to work well enough. He called it "twiddle" - I don't know if he was the original author of it, or what - but here's a video that describes how it is implemented and how it works: https://www.youtube.com/watch?v=2uQ2BSzDvXs https://www.youtube.com/watch?v=2uQ2BSzDvXs It's actually pretty neat - and the concept can be applied to virtually any algorithm in which you are trying to minimize an error amount.
- gh02t 9y ago
  Twiddle, AKA coordinate ascent, definitely works in practice. It's basically the same process a human uses to tune PID parameters, cyclically tune one parameter at a time until you're performance is good enough. It's closely related to gradient ascent and suffers from the same problems, namely that it can get trapped in a local minimum, but it's easy to implement and does a good job if you start with an ok guess at the parameters.
fixermark 9y ago
This is a great short overview, and timely for the First Robotics Competition season. I took a course on this in college, and while that course mentioned the notion of sampling the D signal directly from feedback instead of from error, it never laid out why. This guide's practical explanation of why one might want to do that is great.
davidblair 9y ago
Mirror: https://web.archive.org/web/20170721121215/http://www.wescottdesign.com:80/articles/pid/pidWithoutAPhd.pdf https://web.archive.org/web/20170721121215/http://www.wescot...
beagle3 9y ago
Does anyone here have experience with Fliess iPID controllers?[0] The papers indicate they are superior, Fliess is a generally respected academic, but the math seems the same with slightly different terminology.... [0] https://hal-polytechnique.archives-ouvertes.fr/inria-00372325/document https://hal-polytechnique.archives-ouvertes.fr/inria-0037232...
clebio 9y ago
509'd. Does anyone have the PDF for it? Google cache seems to just render the document, not give me the PDF (I like to download and read offline, from time to time).

301 points by darshanrai 9y ago

This reminds me of my Achilles heel during undergrad. Kalman filters. No matter how much I read about the topic, I just could not grok it. The whole "state update" algorithm and sheer amount of different variables threw me off. Does anyone else feel the same way?

roevhat 9y ago
Yes, indeed! What worked for me in the end, was to first understand state observers (e.g. Luenberger observers) and then consider a Kalman filter as an optimal observer, where the observer gain is the steady-state Kalman gain. The whole duality between state-feedback design and observer design -- and LQR and Kalman filters. Then it made sense :-)
blt 9y ago
The book "Probabilistic Robotics" explains the Kalman filter really well by putting it in the larger context as a Bayesian filter. I understood it only after reading that book
- carlmr 9y ago
  I haven't read that book, but seeing it as a Bayesian filter made it click for me. All the control theory guys who just handwaved with "it's basically a stochastic Luenberger observer" didn't capture the essence of the filter for me. With a strong statistics background it was much better to go from Bayesian first principles to the Kalman filter.
etaioinshrdlu 9y ago
You may enjoy this tutorial: http://www.bzarg.com/p/how-a-kalman-filter-works-in-pictures/ http://www.bzarg.com/p/how-a-kalman-filter-works-in-pictures...
msadowski 9y ago
You are not alone! From what I've seen many people struggle with Kalman filters. If you want to build in depth understanding of them I heard lots of good things about this online book: https://github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python https://github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Pyt...
deleted 9y ago
[deleted]
a_imho 9y ago
The whole "state update" algorithm and sheer amount of different variables threw me off. Imo it starts with the name, it tells nothing and probably implies something different. It is the dynamic programming of control theory.
- senatorobama 9y ago
  So true. Filters should be reserved for something like low pass filters.
syntaxing 9y ago
I totally understand where you are coming from. I read multiple tutorials and even implemented Kalman filters in Python, Matlab, and C++ for a balancing robot project. I never really understood what was happening even though I knew what the Kalman filter is used for and when I need it. The thing that "clicked" for me is that multiple measurements are always more accurate than a single measurement. That's why there is the feedback loop that derives the predicted value and the uncertainty that is associated with it. By combining the predicted value and the measured value (and their uncertainties), you get a more accurate measurement. Then you can use this more accurate measurement to "correct" your predictions so that the next prediction has even less uncertainty. This perpetuality is why Kalman filters lead to the "true" state.

metaphor 9y ago

Fortunately, basic PID analysis, including linear state-space representation and practical tuning methods (e.g. Ziegler-Nichols[1]), is taught in pretty much any first EE control theory course at the undergraduate level. [1] https://en.wikipedia.org/wiki/Ziegler%E2%80%93Nichols_method https://en.wikipedia.org/wiki/Ziegler%E2%80%93Nichols_method

beambot 9y ago
Not only that... Classic controls (including PID, Routh-Hurwitz, root-locus, etc) are NOT taught in many graduate PhD controls programs!
- budadre75 9y ago
  Are those topics no longer relevant to today's state of the art research?
  - Sean1708 9y ago
    It's possible that you're just expected to know them at that point.
    - donquichotte 9y ago
      Agreed. Many state of the art control strategies nowadays are based on optimization techniques (e.g. Model Predictive Control, MPC, optimizes a convex cost function of the state, setpoint and input to your system over a certain time horizon). This has become a viable control strategy for fast (>1kHz) processes only in the past 15 years, since the optimization can be computationally intensive.
    - regularfry 9y ago
      Or be able to derive them. PID was never explicitly taught on my course, but all the theory behind it was.
  - tnecniv 9y ago

matthberg 9y ago

Wish my highschool FRC robotics team had this when we naively attempted to control elevator levels with a PID.

msoucy 9y ago
The team that I mentor is about to start tuning their PID controllers... this is very timely.
dokem 9y ago
I also remember tuning PID values on the old Jaguar motor controllers. It was not a pleasant or particularly fruitful experience.

wnoise 9y ago

He stresses regularly spaced sampling. I don't see why high-precision timestamps wouldn't work just as well, though that would complicate the computation of the I and D signals. Actually, throughout he doesn't seem to acknowledge the different units between the P, the I, and the D, instead implicitly treating the whole system as discrete time for many purposes, in e.g. the recommendations for 100:1 ratios between P, and I; and D and P.

ebrewste 9y ago
Regarding equal spacing: the sample rate determines a part of the system latency, and therefore performance and stability limitations. Eliminatating the stability of sample rate eliminates the decades of work basic controls analysis relies on. Or said another way, slow your sample rate and pay with your phase margin. Not to say it’s impossible to deal with (small) changes in sample rate, but in a text where he is already wildly simplifying things, this sounds like the wrong place to innovate.

darshanrai 9y ago

There's also this[1] series of blog posts by Brett Beauregard that speaks of a few improvements for real-world implementations. [1]: http://brettbeauregard.com/blog/2011/04/improving-the-beginners-pid-introduction/ http://brettbeauregard.com/blog/2011/04/improving-the-beginn...

carlmr 9y ago
That gets you through 90% of real world control problems. Filtering the derivative input gives you another 5% for some noisy processes. The other 5% require somebody who knows a bit more.

the-dude 9y ago

I have been doing a (integer) PID without a PhD over the last years as well : meCoffee ( https://mecoffee.nl https://mecoffee.nl ) for espresso machines.

jmiserez 9y ago
I just bought an espresso machine, and it’s crazy that something as simple as a PID controller justifies a several hundred dollar markup on some models. The processing power needed is miniscule...!
- the-dude 9y ago
  True. And if your machine does not have a pressostat, it makes a huge difference.
  - jmiserez 9y ago
    Does the optional dimming of the boiler make a difference in your design? Mine just fully turns on and off all the time, and I reckon dimming would probably be easier on the power grid. 2000W on/off vs ~80W average (I measured) is quite the difference.
    - the-dude 9y ago
      Your measurement seems to match up. It makes a difference in the fact the meCoffee PID can adjust its P response 100 times a second, it can react much faster. Dimming such heavy loads is not within spec in all jurisdictions though. It also includes normal interval behaviour.
    - lmilcin 9y ago
      I am using SSR with zero crossing and it makes much difference. First, I am dithering the boiler power (the power is applied to the boiler on only some AC cycles), I am basically deciding per cycle whether I want my boiler turned on for the next 1/100th or 1/120th of the second. I am already running my model about 50 times per second (not using PID) so that's ok. Being able to apply fractional power to the boiler means it is quiet and much less scale deposits. Also due to the zero-crossing control I have much less electrical noise. Turning the boiler fully-on blindly causes electrical noise which is not nice for other devices (my Baratza Sette grinder turns on spontaneusly when this happens).

dosshell 9y ago

I am a little suprised that the author does not use a low-pass filter for the D part, for example 1/(1+s Tf) and instead tells you to modify the hardware. Sure, you need cut off the noise with hardware in respect to your Nyquist frequence but you can still have a lot of high frequency noise. And it is not always possible to use hardware filters to get rid of the noise, for example if your are tracking an object with a camera and the x,y is your input to the pid. Ofcourse you can skip the D part. What am I missing here? I also find it more easy to use a reset based integrator anti-windup, where you specify your limits on your control signal instead of limiting the integrator. Here is an diagram of what I usally do: +--------+ +------+ -y | 1 | | | -------->+ ------ +---------->+ Kd*s +----+ | 1+s*Tf | | | | | | +------+ v +--------+ +----+ +-+-+ +-------+ e=r-y | | | | | __ | u --------+------------>+ Kp +----------->+ ∑ +---+-->+ __/ +---+---> | | | | | | | | | | +----+ +-+-+ | +-------+ | | ^ | | | +----+ +---+ +-----+ | | +---+ | | | | | | | 1 | | | - | | + | +-->+ Ki +-->+ ∑ +--->+ - +-----+ +---->+ ∑ +<----+ | | | | | s | | | +----+ +-+-+ +-----+ +-+-+ ^ | | | | +----+ | | | | | +------+ kt +<-------------------+ | | +----+ The kt gain will reduce the integrator when we have saturated output. Does some one knows the pros and coins with the different anti-windup solutions?

balda 9y ago
yeah
jgable 9y ago
I always do integrator wind-up similar to how you do it -- apply limits to the overall controller output (which are typically necessary for the system anyway), and use that to limit the integrator. Just putting limits on the integrator is too crude, and it's not like it's any easier to program. Maybe the author introduced that because it's easier for a beginner to understand. However, I typically do not change the state of the integrator the way you are doing here. I just hold the integrator state (i.e. don't update it) if the controller is limited. That way, noise on the P or D signals doesn't cause my integrator state to hop around. I may do it your way if the controller limits are changing over time for some reason. I also always low-pass filter the D term, as you mentioned. Otherwise, the D term is just too noisy. I often find that my P and D terms are limited by how much sensor noise I'm willing to let thru to my controller output.

budadre75 9y ago

what I have been searching for years is not theories or tutorials about PID, but a detailed explanation on how to tune a digital controller(instead of a continuous one) in a easy-to-setup environment, whether it be simulation or a cheap hardware. I know examples can include inverted pendulum(IP), double IP, mountain cart, heater with thermometer feedback, line-follower, etc, but where can I easily play around with these examples?

cellularmitosis 9y ago
I found this video useful: https://youtu.be/uXnDwojRb1g https://youtu.be/uXnDwojRb1g

xchip 9y ago

Or you can use my PID simulator, where you can play with the constants in a simulated car to reach different speeds, it updates the output graph instantly http://codinglab.blogspot.be/2016/04/online-pdi-trainer.html http://codinglab.blogspot.be/2016/04/online-pdi-trainer.html

Tepix 9y ago
Great, thanks!

xchip 9y ago

My sousvide controller uses a PID to regulate the temperature super precisely. https://github.com/aguaviva/SousVide https://github.com/aguaviva/SousVide

Double_a_92 9y ago

It's so sad. I studies this stuff in depth for almost 1 year in college... And now after 2 years of working as a software dev I forgot almost everything.

rrmm 9y ago
I wouldn't worry about it. In your career, you're going to forget a ton of stuff (if you're not repeating the same project over and over again). That's just how it works. The win is that someday you will end up needing either the stuff you learned or the math that you used, and you'll find out it's way easier (and more illuminating) learning it the second time around.

roel_v 9y ago

So here's an awfully uninformed question that will probably get me laughed at by actual engineers (as in, not 'software engineers' like myself - and yes Canadians please bite your tongues, I've heard your shpiel by now): when you have a more powerful computer to work with, isn't it much easier to just derive some regression parameters and call it a day? My use case: I have this home-build growhouse that I use to start my seedlings in at the end of winter (and as a fermentation chamber for wine). It's controlled by a Raspberry Pi and as inputs I have 4 groups of LED grow lights, a 30w heating element, a fan that draws warm air out of the box and thus brings the temperature within the box towards ambient temperature, and DHT22 sensors that measure temperature and humidity inside and outside the box. The goal is to keep temperature as close to a certain target temperature as possible, keeping in mind that I want the lights to be on for a certain nr of hours per day and the lights give off so much heat that they will pretty much always make the temperature go over the target (so the fan then needs to bring it down again). It's easy to get this working the naive way with an hysteresis of say +/- 2 degrees (which is fine for my purposes), but the nerd inside me sees it as a game to make that band smaller. So I've been reading up on PID controllers and dear baby jesus I can't even work out how I'd get started. So the pragmatic part of my brain goes 'just run it for a few weeks with incremental inputs between 15 and 35 degrees (C, of course), measure the responses, toss all measurements into R and derive some regression parameters'. Does anyone do this in industry? Probably not because everywhere I've asked, everybody's who's ever done real work on this uses PID controllers - but is that because they're easier to build on microprocessors (i.e., need less number crunching)?

deleted 9y ago
[deleted]
Tepix 9y ago
There will almost always be external influences that change the behaviour over time. If you have a vehicle, going up the hill will require more energy to keep the speed constant. For your growhouse, if it's hot outside of the box it may requires less heating, etc. Or the LEDs that you use get less efficient over time. You really want to have a dynamic algorithm such as PID that can deal with these changes in a near optimal fashion.
9y ago

fest 9y ago

There was an "aha" moment for me when I realized that PID loop only works well for linear systems (and sometimes it's not obvious if a system is linear or not). Real world example: imagine you have a single-axis motion stage driven by electric motor and you want to control position of a carriage. Usually your control output is motor voltage. Motor voltage approximately translates to current through motor windings, which in turn approximately translates to torque exerted by motor. Torque exerts a force (T = F * r) on carriage. Applying force to the carriage makes it accelerate (F = m * a). Acceleration linearly increases the carriage velocity (v = v0 + a * t). Carriage having some velocity finally causes the position change (s = v0 * t + a * t^2). In the essence, the system turns out to be non-linear with the respect to parameter you are controlling. To improve this system, one solution is to add velocity sensor (or differentiate the position sensor, if it's resolution is high enough) and introduce a cascading PID loop topology- the outer loop takes position error and outputs velocity error, which is fed to inner loop (input = velocity error, output = acceleration). The coefficients for the loops have to be tuned starting from innermost loop. Another solution is to use different control algorithm which is suited for non-linear systems (e.g. LQR).

lmilcin 9y ago
PID will also work for non-linear systems provided they are not too non-linear. Even simple steam boiler is already non-linear but PID will work fine if you are just interested in practical results.
- fest 9y ago
  Sure, but for such systems even a simple on-off controller works fine, if the sensor is close enough to heating element (and if it's too much decoupled, PID won't help either). The biggest issue for me was spending a lot of time trying to achieve a better system response (fast settling time with minimal overshoot) for system that was just designed badly.
  - lmilcin 9y ago
    I was able to achieve optimal control and no overshoot with my espresso machine by using Model Predictive Control (https://en.wikipedia.org/wiki/Model_predictive_control https://en.wikipedia.org/wiki/Model_predictive_control) aided by Moving Horizon Estimation (https://en.wikipedia.org/wiki/Moving_horizon_estimation https://en.wikipedia.org/wiki/Moving_horizon_estimation) to continually update model parameters. Additionally, the set value for the boiler temperature is calculated using separate model that takes the group head temperature into the account. The end result is that the controller is able to stabilize immediately, with maximum power of the heater and with no overshoots or undershoots to a temperature that takes into the account the state of group head to provide the ideal water when brewing. While PID is able to control the temperature very accurately I found even in best case it took additional 50% of the time to stabilize and also it was difficult to optimally use 100% power of the heater until last possible moment. Being able to achieve stability almost immediately means I can keep lower water temperature in the boiler and bring it to temperature at the last possible moment. End result being that it is now much faster to get it ready.

Tepix 9y ago

Is a machine learning algorithm capable of getting better results than a PID? Is the extra effort worth it?

dosshell 9y ago
How do you mean with "better result"? For a non-linear system, machine learning can perform much better and solve more complex tasks. Like walking for a humanoid robot. A linearzied PID solution can not beat that. For linear systems: Depends of what you mean with better I guess. My understanding is that you can place some of the poles of a system with a PID pretty much where you want. So for a simple linear system: no. There exist also other controllers where a LQR can be used in linear systems to get a perfect theoritical controller based upon to minimize the cost of control outputs. (yes, several outputs). However maybe a ML can be used to choose and tune the controllers better than humans? EDIT: Also, the discretication is not always perfect (backward or forward euler is common estimates). So maybe ML can help in that too?
- tnecniv 9y ago
  > For a non-linear system, machine learning can perform much better and solve more complex tasks. Like walking for a humanoid robot. A linearzied PID solution can not beat that. Right but you are comparing a nonlinear regression model with a linear control scheme, which isn't really fair. Plenty of nonlinear control strategies exist and are used in practice for things like humanoid walking. Moreover, many people prefer these controllers due to the theoretical guarantees they provide over a learned control policy. That said, ML does have a place in control theory, and you can find papers going back to at last the 90s (I never looked earlier but they probably exist) that combine the two, and not just in a reinforcement learning context. > However maybe a ML can be used to choose and tune the controllers better than humans? Probably not, assuming you are discussing linear systems. You would need to come up with some cost function for your ML algorithm to determine the performance of a particular control policy, but then why not just use that as the objective function for your optimal control algorithm?
wenc 9y ago
> Is a machine learning algorithm capable of getting better results than a PID? Is the extra effort worth it? Potentially yes, but by it being a component of a completely different control paradigm (MPC). ML itself will probably not improve on PID while still keeping it PID. So, there are two parts to a control system: 1) The predictive model (prediction) 2) The feedback control law (action) ML primarily concerns itself with function approximation from data, y = f(x, p), where p are parameters -- in the parametric model case. ML practitioners create predictive models but don't really consider feedback loops. That is more the domain of control theory, which is concerned with system behavior when exogenous inputs (actions) act on the system. The math is different. ML can be used to fulfill the role of (1). It has nothing to say about (2). In the PID case, (1) is extremely simple -- it is simply an error function (difference). (2) is where the magic happens... based on the error, the controller computes the right action. The beauty of PID control is that it is technically "model-free" (if you don't consider an error function a model). You can apply it to systems where you have very little data, and still be able to do fairly good job. You could replace (1) in PID with an ML model, but then you would defeating one of the some of attractive qualities of PID control: effectiveness under uncertainty without a model. You can use ML to guide the tuning of PIDs, but that's about it. That said, ML models have a place. In advanced controllers like MPC, (1) is typically a dynamic (state-space, FIR/FSR, physics equations-based) causal model of the system under control. (2) is an optimization algorithm. You could conceivably replace (1) with an ML model. This is done in many cases -- in many plants, there is a predictive model that infer states based on images and sound (for instance, using Near Infra Red sensors to inferentially predict certain chemical properties). But that's no longer PID.

leafario2 9y ago

What's the reason he insists on using double precision math? (If not using fixed point)

davepage 9y ago
Keeping things simple, if the input data SNR is, say, 16 bits, and the PID coefficients are 16 bits, then there is 32 bits of significand at the output of the control gain multipliers. For single precision float, this is truncated to 23 bits. So, the system may settle when the transducer input is near zero (and the exponent can scale down to maintain sufficient precision), but then fail to settle well at the ends of the transducer range (where the transducer input is near +/-2^15 and the exponent in the single needs to stay high to avoid saturation). Also, consider the numerical integrator is running an infinite series of adds, so therein lies a trap for error growth, as well. I have made this mistake before, and the sometimes strange control behavior can be frustrating. Considering the small performance penalty for using doubles on modern hardware, it is excellent advice.
- leafario2 9y ago
  Thanks for the explanation! I have only hardware with no FPU (teensy 3.2) or single precision FPU(teensy 3.5)... I suppose in that case it would be better to write a fixed point implementation?
  - ebrewste 9y ago
    Fixed point often works better, as it has better resolution because it doesn't need the exponent. The flip side is that the range of a fixed point is very limited (because it doesn't have the exponent). Practically, that means you need to do some analysis to make sure don't overflow or saturate, and use the bulk of your fixed point range to get the resolution benefits. If you do that, fixed point is great. If you don't have time or knowledge to do that, floating point works better because you can be more ham-fisted with your scaling and still not overflow or saturate.
    - 9y ago

RhysU 9y ago

'Feedback systems: an introduction for scientists and engineers' is another nice reference [1]. I used it and another Wescott text to put together effectively a somewhat extended version of the OP's code [2]. [1] http://www.cds.caltech.edu/~murray/amwiki/index.php/Main_Page http://www.cds.caltech.edu/~murray/amwiki/index.php/Main_Pag... [2] https://github.com/RhysU/helm https://github.com/RhysU/helm

midjji 9y ago

The matlab system identification toolbox is nice to get a casual feel for the systems. Note that pid controllers are mostly used due to their computational rather than control performance. They are math equivalent for linear systems, but thats like saying x=inv(A)b is just as good... The powerful idea is the linear system model or the stochastic linear system model. Understand them and the properties of recursive filters and pid will come naturally.

throwawaybbqed 9y ago

My SW eng program did not even hint at these. Is there a good edX or coursera course that goes through more extensive material than the pdf? I'm also curious what tools are used by professionals? Matlab, simulink???

wustangdan 9y ago
Not sure if this is allowed but I created a Udemy course on PID control where I go through the theory and then in the assignments you write Python code to create a PID controller for an elevator (with the goal of moving the elevator to the desired height). A PID controller can be written in less than 10 lines of code but understanding the different components is very important for tuning it and getting it to work. If your interested just go to Udemy and search PID Control, you'll find it. If you'd like a discount code (not worth the full price if your a SW eng) DM me on Twitter as I'm not sure I'm allowed to post it here. When I did my MSc I did all my PID controllers in MATLAB/Simulink but since the actual code for a PID controller is very simple, it's easy to implement in Python or C++.
- throwawaybbqed 9y ago
  Looks interesting .. as a SW Eng, I find Udemy very useful for these hw courses. Thanks for the pointer!
tnecniv 9y ago
Google for a class in (classical) control theory. This is a standard topic for electrical, mechanical, and chemical engineering programs. For implementing a PID loop, you can do it in pretty much any language you want -- it's relatively straightforward once you know the math. You can even do it in hardware via an analog circuit if you desire. However MATLAB / Simulink are commonly used when experimenting with system parameters due to the presence of straightforward plotting tools and numerical ODE solvers.
ninly 9y ago
The Control Lectures series by Brian Douglas on YouTube is a fantastic resource (https://www.youtube.com/user/ControlLectures https://www.youtube.com/user/ControlLectures). Also U. Mich. has a great set of control tutorials put together with a focus on implementations in MATLAB/Simulink (http://ctms.engin.umich.edu/CTMS http://ctms.engin.umich.edu/CTMS). All of my own experience in controls (both as a student and professional) uses MATLAB/Simulink to model and generate controller code. Other tools are out there, but I don't know much about them.

cr0sh 9y ago

Just going to throw my 2-cents in - I should note that my knowledge of PID is very limited. The first time I encountered an explanation of how PID worked that made sense to me, was via the Udacity CS373 course that I took in 2012 (Thrun also had a great explanation on how a Kalman filter worked as well). This explanation of PID was repeated when I took the Udacity Self-Driving Car Engineer Nanodegree (starting in 2016). In the CS373 course, Thrun detailed a few different ways to tune a PID controller - but one way he covered was rather curious in how it worked. It wasn't perfect, but it got you "close enough". I'm not sure if it would work well for a "real system" but for the purpose of learning it seemed to work well enough. He called it "twiddle" - I don't know if he was the original author of it, or what - but here's a video that describes how it is implemented and how it works: https://www.youtube.com/watch?v=2uQ2BSzDvXs https://www.youtube.com/watch?v=2uQ2BSzDvXs It's actually pretty neat - and the concept can be applied to virtually any algorithm in which you are trying to minimize an error amount.

gh02t 9y ago
Twiddle, AKA coordinate ascent, definitely works in practice. It's basically the same process a human uses to tune PID parameters, cyclically tune one parameter at a time until you're performance is good enough. It's closely related to gradient ascent and suffers from the same problems, namely that it can get trapped in a local minimum, but it's easy to implement and does a good job if you start with an ok guess at the parameters.

fixermark 9y ago

This is a great short overview, and timely for the First Robotics Competition season. I took a course on this in college, and while that course mentioned the notion of sampling the D signal directly from feedback instead of from error, it never laid out why. This guide's practical explanation of why one might want to do that is great.

davidblair 9y ago

Mirror: https://web.archive.org/web/20170721121215/http://www.wescottdesign.com:80/articles/pid/pidWithoutAPhd.pdf https://web.archive.org/web/20170721121215/http://www.wescot...

beagle3 9y ago

Does anyone here have experience with Fliess iPID controllers?[0] The papers indicate they are superior, Fliess is a generally respected academic, but the math seems the same with slightly different terminology.... [0] https://hal-polytechnique.archives-ouvertes.fr/inria-00372325/document https://hal-polytechnique.archives-ouvertes.fr/inria-0037232...

clebio 9y ago

509'd. Does anyone have the PDF for it? Google cache seems to just render the document, not give me the PDF (I like to download and read offline, from time to time).