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Tutorial A layman's analogy guide to PIDs

Discussion in 'DIY Motion Simulator Building Q&A / FAQ' started by noorbeast, Nov 11, 2015.

  1. noorbeast

    noorbeast VR - The Next Generation Staff Member Moderator

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    Now for many of us mere mortals the math and explanation of PID just sounds like gobbledygook!

    The Wikipedia explanation will likely make your eyes glaze over, so feel free to skip over it if you want, I have included it for context only.

    Wikipedia says that a proportional-integral-derivative controller (PID controller) is a control loop feedback mechanism (controller) commonly used in industrial control systems. A PID controller continuously calculates an "error value" as the difference between a measured process variable and a desired setpoint. The controller attempts to minimize the error over time by adjustment of a control variable, such as the position of a control valve, a damper, or the power supplied to a heating element, to a new value determined by a weighted sum:

    u(t) = K_p e(t) + K_i \int_{0}^{t}e(\tau)d\tau + K_d \frac{de}{dt}

    where K_p, K_i, and K_d, all non-negative, denote the coefficients for the proportional, integral, and derivative terms, respectively (sometimes denoted P, I, and D). In this model, P accounts for present values of the error (e.g. if the error is large and positive, the control output will also be large and positive), I accounts for past values of the error (e.g. if the output is not sufficient to reduce the size of the error, error will accumulate over time, causing the controller to apply stronger output), and D accounts for predicted future values of the error, based on its current rate of change.

    For a literal introduction to PID check out Mastering PID Control Without A PHD, but it is a bit deeper swan dive into the topic than the following lay persons analogous rendition: http://www.xsimulator.net/community/marketplace/mastering-pid-control-pid-without-phd.43/

    I thought I would try giving a simplified layman's analogy guide to understand PIDs and PID setting.

    So let's start with P, proportional control. You can think of P as a bit like a car that only has an accelerator pedal. Now if you have a target like getting to 100 km per hour, that target is what is meant by the "error value".

    If the car is stopped the car needs to accelerate to 100 km per hours, so you stomp on the accelerator. The weakness of the P controller by itself becomes apparent when the car reaches 100 km per hour and you take your foot off the accelerator. Instead of stopping at exactly 100 km per hour the momentum of the car carries it past that target.

    Now being a simple P controller nothing happens until the car drops below 100 km per hour but when it does you stand on the throttle again and what you will notice at that speed is that there will be some lag before the car can reach its maximum acceleration rate and if you take your foot off the accelerator at 100 km there will still be a slight overshoot. Hence a P controller by itself will initially hover around a target value before settling and can be susceptible to disturbances, such as a change because of going up or down a hill. If 100% accuracy is not needed and there are no disturbances to complicate the situation, such as going up and down hills, then P by itself is about as simple and useful a closed loop control system as you can get.

    But if you do have complications and need more accuracy that is where 'I', the Integral comes in. What 'I' does is sum the historical error. In effect what that means is that 'I' drags something toward the intended value, so in our car analogy 'I' can be thought of as a sort of cruise control, that will drag the P oscillation toward the intended 100 km per hour, including where external disturbances come into play like going up or down a hill.

    Unfortunately our motion simulators are more like a race between traffic lights and the cruise control like effect of 'I' is not particularly helpful when you just need to accelerate as quickly as possible and then stop both quickly and as accurately as possible at the next set of traffic lights. That is where D, the Derivative comes in.

    D is a bit like adding brakes to the car and the way it works is that it builds up the closer it gets to the stop point. So 'I' looks to the past and sums the error, where D looks to the future, where you need to stop, and increases in effect so you stop as quickly and as accurately as possible at the stop lights.

    Now that we have a bit of an understanding of what a PID does, and why the go/stop PD controller is useful for motion simulator control, let's move on to approaches to manually tuning PD.

    The 'step-response' method of manually tuning PD values is captured in @bsft's basic guide to setting up JRKs: http://www.xsimulator.net/community...-set-up-simtools-jrks-and-write-profiles.112/

    The 'step-response' method starts by setting the value of P, in our analogy how well the accelerator works, and then determines D, how well the brakes work. There is nothing wrong with this approach but it has an inherent effect that many members experience but perhaps do not expect. The inherent effect is that changing the value of D, how effective the brakes are, also changes the value of P, the optimal point for acceleration. So it takes a number of steps to narrow down both P and D.

    @bsft asked if I had a better idea about PID tuning: http://www.xsimulator.net/community/threads/motion-sim-w-surge-traction-loss.5950/page-16#post-91447

    In my view 'better' is always somewhat subjective, but there are 'different' approaches to manual PID setting. The second form of manual PD setting is “zone-based tuning”: http://www.pmdcorp.com/downloads/Tuning_Servomotors.pdf

    Zone-based tuning refers to the frequency zones of the P, I, and D terms, and is adapted from George Ellis’ book 'Control System Design Guide', which you can download here: http://aussiedistiller.com.au/books/Chocaholic/control-system-design-guide-third-edition-using-your-computer-to-understand-and-diagnose-feedback-controllers.(2004).9780122374616.33181.pdf

    The Zone-based method starts by setting D first, which is like adjusting your brakes to be as fast as possible, that way all you then have to do is increase P, your acceleration, to the point where the acceleration and already set braking effect combine so the car stops on or as near as possible to the second set of traffic lights.

    In the zone-based method D is increased until the actual velocity profile closely matches the desired velocity profile, which is different from the position approach used in step-response tuning. It is about matching the desired speed of the brakes, not a position such as the traffic lights. P is then set relative to the desired position, actual position and position error in the same way as it would be for the step-response tuning approach. P is increased until the error is minimized.

    Chuck Lewin, CEO of Performance Motion Devices, advises that at some point as you increase P the motion may have high over-shoot, or become unstable, at which point you should back off this value by at least 20% for the final value.

    The stated advantages of zone-based tuning over step-response tuning is being "less iterative, because it tunes the PID terms in order of the frequency response domain. Secondly, it allows you to utilize real motion profiles with ramps, rather than unrealistic position jumps".

    In the end manual PID tuning is as much an art as it is a science and experience is key, regardless of what method is utilised. Having a basic understanding of how a PID functions hopefully takes out some of the frustrations of PID tuning, particularly if using the step-response method, as it inherently takes time to optimise PD settings.

    It also helps to know what you are looking for when using the step-response method. The aim should be to set P with a slight overshoot and then increase D to critically dampen, as in the illustration:

    DampedResponses.jpg
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    Last edited: Nov 13, 2015
  2. Archie

    Archie Eternal tinkerer

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    Excellent post @noorbeast - It's certainly lifted the cloak from the PID for me. I never understood the relationships and just blindly entered numbers until the arm moved in a way that looked OK. Love the analogy! I always revert to cars when I explain computer related issues!

    My favourite is when the powers that be don't understand why a system need to come down for maintenance... I reply with "Would you keep your car engine running while the mechanic worked on the pistons??" :D

    Thanks again @noorbeast
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  3. Archie

    Archie Eternal tinkerer

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    Actually... I was just looking at my settings and the P and D values are quite close to each other. (as per @Avenga76 'settings in his thread)

    I assume the actual numbers don't really matter that much so long as the desired graph is close to the target without a huge overshoot or over-dampen?

    @noorbeast - Would you be able to maybe make a short video where you tune a JRK from scratch to highlight the relationships? I know it's asking a lot. What can I say.. I'm a visual learner!
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  4. bsft

    bsft

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    Thats right @Archie , everyones numbers will be different. And with different controllers and motor power settings can also affect PID. Granted the information is relative and more detailed , its still a lot to grasp. Maybe for the teachers here it helps , but the document I wrote is a simple thing. Of course if people want to know more they now can read this detailed description.
    Again , as I only understand JRKS , I cannot comment much further.
  5. Avenga76

    Avenga76 Well-Known Member

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    Here is some info from when I first did my PID testing on my old motors.

    I have changed it a bit since then. I find that would my new motors I can run less D because I don't have to run as much of the "Braking" effect because the motors have less inertia.

    With my old motors I ended up going for P=0.5 I=0 D=0.8

    I found I got oscillation at P=1.3 and I halved that down to P=0.75 at first but I found that I couldn't add enough D to get it from overshooting.

    I ended up dropping the P back to 0.5 and then I could set a D of 0.8 to get it to stop nicely.

    With my bigger motors it also seems to help my over all speed having the lower P and D. With my smaller motors I can get a way with running less D so I run them about the same.

    I also find that if I run too much P then I get more motor driver errors, this is because I am overloading the JRK, again, if you have smaller motors then you can increase the P because the JRK can handle more gain.

    Here are some test I did back on my old motors.

    This was at the higher PID P=0.75 I=0 D=1.2. I could stop it on the way up but on the way down it would over shoot. This is stepping the motor from a target of 1000 to 2000 and back again

    [​IMG]

    [​IMG]

    This is what I settled on with my bigger motors at P=0.5 I=0 D=0.8

    [​IMG]

    [​IMG]
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  6. noorbeast

    noorbeast VR - The Next Generation Staff Member Moderator

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    I think most of us have been in this boat @Archie, but in many ways it is what you end up doing anyway with the 'step-response' method of manually tuning PD values, as it takes some iterations to truly tune the PD, but I am hoping the analogy understanding makes that something that is expected and the simple visual guide to what you are looking for makes it a bit quicker to get to the end result.

    I will put a video on the To Do list @Archie but am very busy with my business at the moment and fingers crossed may get far more busy as I am a finalist in the Sensis business grant awards for Technology and Innovation.

    @Avenga76 it was your experimentation with PID that got me really interested in finding out more and your posts are the most informative because you include the graphs.
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  7. GIB SimRacing

    GIB SimRacing Active Member

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    Liking the analogy @noorbeast - I have spent a bit of time reading about PID and trying to understand what exactly is going on when changing the values. But as you said, it does get quite involved and some of the terminology went straight over my head when reading some articles about PID controllers.
    Even though my setup is running pretty good atm, I'm sure there are still improvements I can make.
    Your post definitely helped me to confirm what I thought I understood.
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  8. BlazinH

    BlazinH Well-Known Member

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    An interesting analogy of a PID controller @noorbeast! But while I follow your logic, I don’t believe the comparison to a moving vehicle is the best. For example, momentum will not cause a car to accelerate past 100 when power is removed at 100 as you stated. Immediately as the power being applied is less than what is needed to overcome the resistance to the car moving forward, it will immediately start slowing down and can never start moving faster (unless maybe you’re on one hell of a downhill grade or driving off of a cliff). Also, with simple P control, it is not true that, “nothing happens until the car drops below 100”. If the car did continue past 100 when its target was 100, P would start applying a harder and harder breaking force the further past the target the car accelerates. And another thing, P control would not be applying full power all the way to 100 and then immediately stop either. As 100 is being approached, P would start reducing power so that when 100 was reached, power would already be at zero. Therefore, when using P control only, it is much more likely that you will fall slightly short of ever reaching the target as opposed to overshooting it unless there is enough inertia left in the system when at the target of 100 to do it.

    So while I follow what you are attempting to explain, I’m not sure someone without prior knowledge of PID control would. Therefore, I will attempt to further understanding with a somewhat different explanation (or add to the confusion :D).

    P, which stands for proportional, is a relationship between the amount of power being applied to the motor and the current error. As noorbeast stated, the error is the difference between the rigs current position and the position that is being called for, the target. As the error increases or decreases, P increases or decreases proportionally based on its setting. P is considered the main control perimeter in a PID system. On a rig that stays in perfect balance at all times, P is all that is really needed to get good control for the most part.

    I, which stands for integral, simply consist of a variable that stores the accumulation of all past error values, both positive and negative. It adds the values together and if there is a difference remaining then that value is added or subtracted to P in proportion to the setting for I. In essence, what I does is help P get to the target position faster than it can on its own and all the way to the target position. It should be noted however that I can’t help P get to the target any faster if P is already applying full power on its own. One other thing I can do is help get your rig back to a perfectly centered position also. When using P only, as the target position is approached, P will reduce in power and at some point will not supply enough power to push the rig all the way to the target before stalling. When this happens the error value will accumulate in I until it will push the rig the rest of the way to the target position. However, I should note that you should also set your motors minimum speed to a value just above stall point. Therefore, even if P stalls by falling below this minimum speed prior to getting to the target, the motor will still continue moving to the target until reached.

    Many types of systems run perfectly well on P and I control alone and are fairly easy to understand. But D, which stands for derivative, is quite a bit harder to comprehend. But mathematically speaking it is the average of errors recorded over a specific amount of time. These values give an indication of the current direction of control needed in the near future and in effect dampens or brakes the effects of P and I. One example of where D can really benefit a rig though is when it has a heave axis, especially a heave axis that has no counter balance. It this case, the heave motor may never need to actually reverse directions since gravity will already pull it down at 1g. Therefore, without D, P and I would attempt reversing the motor to go downward when what is really needed is to apply less power in the upward direction to go downward.

    As far a getting into the process of setting your PID controller though, I’m going to pass on that one.

    For a better understanding of D though, here is a link to a more comprehensive explanation.
    http://www.controleng.com/index.php?id=483&cHash=081010&tx_ttnews[tt_news]=18861
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  9. noorbeast

    noorbeast VR - The Next Generation Staff Member Moderator

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    While I do agree with you @BlazinH I am openly and deliberately being analogous, not literal, and while I may need to find a slightly refined analogous way of saying it I think you would agree that P alone will move around the target before settling. I think @Archie also gave a good example as to why an analogy can be useful as a way to convey meaning.

    Same with I, the cruise control analogy for summing the error gives something to hang an understanding on as most people have an idea of how a car response to disturbances. In a more literal sense cruise control is a PID system but I was looking for a simple way to convey what I does in a way that links it to why it could be, but is often not included in a simple PD model for a motion sim.

    If there are ways to simplify/refine my analogy approach then I think that is useful.

    I think it easy to get really complicated descriptions of PID and included the Wikipedia description as an accurate example. There are also far more potential tweaks that make understanding PID and manual PID setting even more complicated. And I have provided links to some substantial resources on the subject.

    However my aim in doing this tutorial was in trying to give a basic understanding of why PD is common with motion sims, but not very common in more general PID use, and having a starting point for manual tuning that is just a bit more than plugging in random numbers.

    We already do have more accurate and complex PID information available, it is a bit deeper swan dive into the topic but I have added it to the original post as a literal reference guide: http://www.xsimulator.net/community/marketplace/mastering-pid-control-pid-without-phd.43/
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    Last edited: Nov 12, 2015
  10. Avenga76

    Avenga76 Well-Known Member

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    Thanks. I tend to find that pictures and graphs help a lot. I am not too good with the maths behind it all so I just go by feel and what I see in the graphs.

    This has prompted me to have another play around with my PID and I have found a few interesting things.

    The main one I really wanted to test was with slow movements like in flight sims. I have found that the scaled feedback doesn't track the target very well with my old setup, it always lags behind on the upwards movement, it never corrects the error.

    I played around with the I and it made a massive difference.

    This is a screenshot of a steady upwards movement with no Integral. It is like it never corrects for the initial lag as the duty cycles ramp up to the point that the motor starts moving.

    [​IMG]

    Here is the same test with the Integral set to 0.02, it now corrects and follows the target perfectly

    [​IMG]

    Downhill seems to be a bit smoother also. This is with Integral turned off

    [​IMG]

    And this is it with Integral set at 0.02

    [​IMG]

    I recorded a quick video showing the difference. The video really shows the difference well.



    How do you set the motors minimum speed on a JRK12v12? I think this is part of my problem with slow speed simulation. The duty cycles need to ramp up to around 20% before it will move the rig if the lever arm are going upwards (if the lever are going downwards then it takes almost no duty cycles), any lower than that then the motors stall. This means it takes a little while for the controller to slowly ramp up the duty cycles so you get a bit of a delay. It would be great if I could set a minimum so it starts at 20% duty cycles instead of having to ramp up.

    It isn't a problem with racing games because the error is large enough that the duty cycles jump way up to to a really high duty cycle.

    Like this is a example of a fast movement. You can see it jumps straight up to my duty cycle limit, I have it limited to 85% duty cycles. (Ignore the actual curve, I am playing around with different settings)

    [​IMG]
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  11. Archie

    Archie Eternal tinkerer

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    Awesome thread!!
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  12. Archie

    Archie Eternal tinkerer

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  13. Archie

    Archie Eternal tinkerer

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  14. noorbeast

    noorbeast VR - The Next Generation Staff Member Moderator

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    @Archie I think you may want to rule out some other potential issues before messing with the PID. You can hide/compensate for some issues in how you set the PID and motor options, but often it is best to identify what actually is the cause of the issue.
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    Last edited: Nov 13, 2015
  15. Avenga76

    Avenga76 Well-Known Member

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    Hey guys.

    I have done heaps more testing.

    Here is a video that I recorded explaining the effect of PID.

    This is 30 minutes long but it is worth the watch if you have time.

    I start off by showing a few different PID settings while driving and explaining the difference, you can see my PID settings for each test in the top left corner and you will see the pots vs target graph overlayed over the game.

    After that I show the effects of each of the PID settings using the JRK tools

    Let me know what you guys think or if you have any comments

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  16. noorbeast

    noorbeast VR - The Next Generation Staff Member Moderator

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    A great contribution @Avenga76 and a really valuable resource to show what to look for.
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  17. Archie

    Archie Eternal tinkerer

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    @Avenga76 - Massive thank you for making this video.

    I finally managed to take the time to watch it in full HD and in full screen to watch the details.
    I now have a much better understanding of the relationship of P/D, and I also noticed you are using a small of of I.
    I've pretty much left that value alone until now, but after setting my P and D to it's tolerances, I set my I to about 0.049999 and it makes a massive difference to the fidelity of the sim.

    It seems to really help in violent movements like going up a rumble strip as you corner, you get a real sense of the suspension slapping back down onto the road with the "I" value in play. It certainly feels more focused. It's VERY noticeable in DIRT:Rally where hitting the ground from a large jump gives a nice (and sudden) thud. As you point out, it basically error correction so the Sim more completely follows the onscreen action.

    It's not a value that gets much attention on this forum, (I) but is certainly worth looking into. Thank you very much.

    My Shoulder mount is almost finished (aesthetics) so I will post a video of it in action soon. (Kids / Wife / Life permitting!) :D
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    Last edited: Dec 4, 2015
  18. tombo

    tombo Active Member

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    Hello,
    thanks for all the Informations and work you put in this thread and video @noorbeast, @Avenga76.
    This helps me alot understanding the whole thing better, and tune my settings for a better movement.
    All of you seem to using Jrks, which have a nice software as I can see in the Video.
    I'm using The arduino way with Smc 3, where also a nice software from @RufusDufus is avalible.
    My question is it enough to turn on the Motion function in Smc3 utilitis and set the motor to following the target position? Or is there a way to do it on the fly while ingame for Smc3?
  19. bsft

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    Ask on the SMC3 thread
  20. Avenga76

    Avenga76 Well-Known Member

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    2DOF, DC motor, JRK
    That is really awesome news @Archie

    I am really glad that my video was helpful to you. I learnt a lot myself while experimenting and recording the video so it is great to pass some of my finding on.
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