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PID question

Discussion in 'Electronic Design' started by [email protected], Nov 22, 2006.

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  1. Guest

    I'm working on a linear bench power supply using a microcontroller. My
    plan is to have a DAC set the output voltage, which will be regulated
    by a simple op-amp circuit.
    An analog input on the micro will monitor load current. I plan on
    using this value to provide current limiting, via a PID algorithm
    controlling the set voltage. Some general PID tuning advice in a
    Microchip PDF says to first set Kp (with Ki and Kd set to 0) so the
    system is as stable as possible.

    With only Kp set, the voltage output just follows the error. Not too
    helpful. Things got better when I added Ki. I'm not sure if I need
    Kd. This seems like a somewhat difficult problem because anything can
    be connected as a load.

    I've searched the Internet, but nobody seems to be using PID in this
    way. I'm sure it is being done, however. What is some general advice
    on tuning this PID system? So much information out there seems to be
    related to motors and heaters.
     
  2. In general, I think a current control loop has to react much
    faster than a voltage control loop. One way to accomplish
    this is to have two PID controls, a fast one that controls
    current, and a slow one than controls voltage, by modifying
    the setpoint for the current loop. This is called a cascade
    controller (a single output controlled by two measured
    variables, one slaved to the other. You implement current
    limit by having a low selector at the current controller
    setpoint. In other words, the actual current controller
    setpoint is the lower of, the current limit value, or the
    output of the voltage controller. Both the setpoint for the
    voltage controller, and the current limit value can come
    from your DAC.

    As to tuning the controllers, a visual method is quite
    effective, if you have a load stepper that provides the
    loops with clean, repeatable steps that you can sync a scope
    to. If you need help with the tuning concepts based on
    observing the time response of a PID control loop, I wrote a
    tutorial (focused on industrial process control, but
    applicable to any PIC controller) available at:
    http://www.tcnj.edu/~rgraham/PID/popelish.html

    You would tune the current controller, first, with only the
    limit setpoint in effect, then tune the voltage controller
    supplying the setpoint for the current controller.
     
  3. Genome

    Genome Guest

    Seriously...... PID is for shitboys. Proportional, Integral,
    Derivative....... these are terms that relate to the response of various
    things in your loop. Since you are dealing with a loop you should analyse it
    to determine its control to output behaviour. Then you can decide what sort
    of sums your microprocessor should do so you can achieve a stable loop with
    'optimum' performance.

    Fiddling about with Kp, Ki and Kd is like an old fat bloke fiddling with his
    knob. He can't see what he is doing, it's a source of frustration and
    nothing good happens.

    Let's say the input to the power section of your supply is effectively a
    source follower. That means that whatever voltage you put on the input
    appears at its output.

    The control to output response of your power stage, dVpout/dVpin, is 1V/V.

    Now things get a little tricky but not too much. The chances are, and if you
    haven't then you will, that the output of your supply has some filtering
    capacitance on it. Let's be nice and assume it is a pure capacitance.

    Let's be nicer and assume that you are going to cross over your loop at a
    frequency where that capacitor is effectively a short circuit. It also
    dominates whatever the load might be.

    You sense the current at its output with a sense resistor. (perhaps using
    one of those nasty analog differential amplifier things). The voltage across
    the sense resistor works out to be dVrsns/Rsns. Because your capacitor is
    shorting things then dVrsns is the output of your power stage so that makes
    things dVpout/Rsns.

    Multiply things together and you get an output from the sense resistor in
    response to an input to your power stage of dVrsns/dVpin = 1/Rsns. If you
    have a differential amplifier in there then you can include its gain to get
    dVcdiff/dVpin = Gcdiff/Rsns.

    If your 'pass' device was not a follower...... then you might write
    dVcdiff/dVpin = GpowGcdiff/Rsns but then you would have to start worrying,
    and you do have to, about just what Gpow really is.... You also get to worry
    about whether your differential amplifier plays silly games as well.

    Anyway..... surprisingly you have managed to define the control to output
    response of the stuff external to your microprocessor as dVcdiff/dVpin =
    Gcdiff. In this 'ideal world there are no frequency dependent terms so it is
    flat from DC to light (or even gamma).

    That means that if you set Kp in your software to some value and your
    digibollocks stuff was also ideal then the system would never cross over.
    Gauranteed to be stable but unfortunately something in the real world is
    likely to bugger things up. I'm not a ditigal jock but I am sure there are
    some nasties about.

    So setting Kp to some value that seems to work and then fiddling with Ki and
    Kd is like pissing in the dark with a deaf freind holding your knob.... At
    best you'll get wet trousers. What you want to do is force the loop to cross
    over at a frequency that you define that might also take care of other
    problems that might be lieing about the place.

    In this case you don't want to be fiddling about with Kp. You should be
    messing about with Ki....... Don't forget all of those K things are crap
    because they are simpleton mong for 'I'm a digital Johnny and I don't know
    what I am doing'. They do relate to the 'real' analog world but only if you
    express them proper like.

    Having said that it's not as if you don't get analog Johnnys wibbling about
    in the same way!

    Ki is an integrator which means its response falls at 20dB/decade and it has
    a constant 90 degree phase lag. This is cool because if you add one of those
    then your loop will cross over at some frequency and its phase margin will
    be 90 degrees so it will be funky and stable......

    So, all you have to do is pick your crossover frequency.

    Having taken the piss a bit that leads me into the digital domain so I will
    now flap about the place. You are that bloke with the 100Ksps in a DSP
    thing.

    I'll be a bastard and assume that it is also doing other stuff so, in fact,
    you can only service stuff at 20KHz and then, because I'm not too hot at
    digital sampling that is going to make your cross over frequency 5KHz. Of
    course, if you know better you can adjust the numbers.

    Putting in some hypothetical bits. Let's say your current sense resistor is
    100mR and your differential amplifier has a gain of 10. Surprisingly that
    works out as a control to output response of 1V/V or 0dB. So, if you want
    your loop to cross over at 5KHz, you need the gain of your integrator to be
    1 at 5KHz as well.

    I got ahead of myself. Part of your digital stuff will be the A/D convertor
    that looks at what Vcdiff is doing and the D/A converter which is going to
    generate dVpin. I suppose this is why they use 2.56V references. Let's say
    the numbers that come in and go out are the same as the voltages they
    represent.

    If they were not then you would have to add Kad and Kda as gain terms for
    your converters. Shit!, I have just started making up K terms. However these
    are defined K terms and mean something...... I know.... I shall call them
    Gad and Gda. Problem solved.

    Now, on to the stuff that will hurt my head. Ki is an integrator so what
    you'll be doing in your microprocessor is adding up the difference between
    the output of your D/A and the set point... integrators sum things.

    Now I get the chance to look stupid.

    In analog terms I would have an inverting op-amp configuration with an input
    resistor, RIN, and a feedback capacitor, CF. I can pick RIN as 10K and then
    work out what CF needs to be to give me unity gain at 5KHz..... That's when
    its impedance is 10K which gets me a value for CF as C=1/2pifR or 3.18nF.

    If I put 1V on the end of RIN then the current through it is 1/10K or 100uA.
    In one second CF will integrate that charge up to It/CF or 314V, give or
    take a bit.

    OK, so the A/D doesn't do exactly what I said before. Let's say that 1V
    works out to be 100. You get to sample that 100 20 thousand times in one
    second and the answer is 2 million.

    Frightening stuff but hopefully the loop will sort things out so things
    don't get too big and you can probably do something else in software to take
    care of the blorks.

    Strange to say, linear loops have the same sort of problems.

    Ho-Hum.... so in order to make my digital integrator behave like my analog
    integrator I have to divide its answer by 6369 before I shunt the answer out
    to the D/A converter.

    At this point my head blows up....... It seems right and I think it is but
    there has got to be some hard thinking about how the numbers play the game
    as the loop is controlled.

    There you go, quite simple really.

    PID...... shit more like

    DNA
     
  4. Joerg

    Joerg Guest

    The task at hands is going to be similar to motors and heaters, just in
    different timing ranges. One of the engineers here in the NG (Tim
    Wescott) has written a nice article about it:

    http://www.embedded.com/2000/0010/0010feat3.htm
     
  5. Guest

    Wow, that's a lot of stuff. I hate to say it, but I don't even
    understand what a "pole" is. PID wasn't all that interesting to me in
    college. Now I might look at it a little differently.
     
  6. Jim Thompson

    Jim Thompson Guest

    A "pole" is someone native to Poland ;-)

    ...Jim Thompson
     
  7. Guest

    Keep in mind the DAC provides a reference for a regulator, so I'm not
    digitally regulating voltage. I'll be able to set the voltage via a
    user interface (as well as current), but the PID controller will have
    the capability of forcing the voltage lower to meet a current setpoint.

    Does your response still apply? I'm a bit confused about how to apply
    a cascade configuration to this. Also, I've been thinking about the
    maximum value the accumulating error can reach, the "I" part.
    Digitally, the output voltage can be set 0 - 2500. Right now, the
    accumulating error is limited in software from exceeding +/- 28 000;
    kind of a random value I chose. Is there a methodology to setting this
    limit? It seems to me now that +/- 28K is a little high and will cause
    sluggish response after settling into a "maximum error" condition for
    long enough to hit this max.
     
  8. Joerg

    Joerg Guest

    Hello Jim,


    [ ... ]
    There are actually two poles. The one in the north is used to mail your
    Christmas wishes to ;-)
     
  9. If you picture the 2 dimensional (one dimension is
    sinusoidal frequency, one is exponential) frequency response
    of a system as a surface, a pole is a point on this surface
    that has infinite response. If you think of the response
    surface as an elastic tent canvas, the point of infinite
    response can be imagined as being propped up by a pole of
    infinite height. Hence, a pole.
     
  10. Understood. In PID controller terminology, the DAC produces
    a setpoint for the voltage regulator. The regulator acts as
    a follower to copy the reference as the voltage output
    (possibly with a scaling factor).
    Read again what I said about the low selector.
    I'm not sure what you are talking about, here, but it sounds
    a lot like preventing integral wind up in the master control
    of a cascade control strategy (the voltage control, in this
    case) when it loses control of the slave (the current
    controller). In effect, you need some way to limit the
    error at the input of the error amplifier, once the output
    ceases to have an effect (the moment the current limit
    process takes over), so that voltage control resumes
    smoothly and quickly, once the current falls below the limit
    value. Limiting the integral windup causes the voltage
    controller output to match the current limit setpoint at the
    moment that the current falls below the current limit value.
     
  11. Genome

    Genome Guest

    No worries, I haven't explained too well.... especially when it got to the
    digital stuff. You probably didn't pay much attention to PID at college
    because it wasn't related to the real world. Certainly when you get people
    suggesting that you fiddle bout with things and look at the response you
    have to guess that they are guessing.

    However you'll probably find the systems they are dealing with are extremely
    complex and any answer will do. That's not to say that you should not try
    and analyse your system.... You most certainly should. If you can you'll get
    the 'right' answer and be confident about it.

    I'll try to slap together a web page.

    Ultimately it is sort of simple stuff if you have a method and it gets
    easier if you have the tools to visualise it. Get hold of LTspice

    http://www.linear.com/designtools/softwareRegistration.jsp

    And don't be ashamed to use it as a tool to model the system you are dealing
    with.
    Many systems can be broken down into and analysed as electrical/electronic
    models.

    Back in the bad old days hard men wrote big equations that don't make much
    sense without a lot of experience. If you are just beginning then it is a
    great help to see what is going on. Once you are over the initial hurdle you
    will be able to do it in your head or on a bit of paper. You just need to
    get over the first hurdles.

    DNA
     
  12. Guest

    Yes, integrator windup, I just read about that after I wrote the email.
    That part I now understand. But I'm unclear about a couple things in
    the topology. Here's a drawing of how I understand it:
    http://www.yourfilehost.com/media.php?cat=image&file=Drawing1.jpg

    I wasn't sure about where the feedback goes. One problem, if the
    feedback path is correct as I have it, is that my current range is
    0-2500 and the current range is 0-4000. Maybe it just has to be scaled.
     
  13. The block you call Voltage setpoint would be one DAC output.

    The block you call Current setpoint would be the second DAC
    output.

    The PID current control drives the pass element that
    actually controls load current.

    The measure of load current is the feedback to the PIC
    current controller.

    The measure of voltage across the load is the feedback to
    the PID voltage controller.

    Does that make more sense?
     
  14. Guest

    Well, not really. I was going to have only one DAC that provides the
    ref voltage for the regulator, then use that, along with the current
    sense value, to limit current. Remember the PID is being done in a
    micro, and the only analog I/O is one DAC out and one A/D measuring
    load current.
     
  15. Tim Wescott

    Tim Wescott Guest

    Joerg beat me to it. That article will, indeed, tell you how to tune a
    PID loop.

    In this case I would seriously consider either:

    (a) Use the DAC to drive a transistor amplifier, probably a gain stage
    followed by an emitter-follower, and use dual PID loops for current and
    voltage control. This has the advantage that you can do a lot to smooth
    out the transition from current to voltage control and back, but the
    disadvantage that you'll want to sample _fast_ to make it work well.
    Its accuracy depends on the DAC and its voltage reference, of course.

    (b) Use the DAC to drive a command to a 723 regulator, and use the 723's
    current limit. This will (potentially) give you faster response and
    immunity from software glitches, at the expense of a non-adjustable
    current limit.

    If you want to take Genome's advise and learn more about control systems
    check out my book (see below). I think you'd do fine with that article
    for starters, but if you really want to make something that's production
    quality you'll want to understand the material in the book.

    --

    Tim Wescott
    Wescott Design Services
    http://www.wescottdesign.com

    Posting from Google? See http://cfaj.freeshell.org/google/

    "Applied Control Theory for Embedded Systems" came out in April.
    See details at http://www.wescottdesign.com/actfes/actfes.html
     
  16. Tim Wescott

    Tim Wescott Guest

    That's just what Kp is supposed to do. By itself it reduces the error
    but doesn't eliminate it. The point of increasing Kp by itself is to
    find out just how high you can push it before the system starts
    misbehaving. Once you've found that level, then you start increasing Ki.
    Almost every regulated power supply on the planet uses a PI or PID loop.
    It's just so firmly buried that you don't find it in a search, just by
    looking at the details.

    --

    Tim Wescott
    Wescott Design Services
    http://www.wescottdesign.com

    Posting from Google? See http://cfaj.freeshell.org/google/

    "Applied Control Theory for Embedded Systems" came out in April.
    See details at http://www.wescottdesign.com/actfes/actfes.html
     

  17. I lost some of those details.

    So the DAC provides the analog signal representing the
    output of low selector, (the setpoint for the analog PID
    current controller), and the ADC provides the load voltage
    measurement into the software PID voltage controller.
    You will still need an analog current measurement to provide
    feedback for the analog PID current controller.

    The only question left in my mind is whether or not the
    micro has the bandwidth to perform the PID voltage
    controller and low selector with adequate response.
     
  18. Guest

    Actually, I have an ADC that reads the load current. I also have one
    that reads load voltage, which is a little redundant. The micro is 16
    bit, with a 100ksps A/D and a some DSP type functionality. It seems to
    handle it ok; it's just that some loads causes the voltage output to
    jump all over the place. For example, pure resistive loads are fine.
    If I put a small motor on as a load with some current limiting, it has
    problems. The voltage output jumps all over.
     
  19. The one that reads current cannot be involved in the analog
    current regulation, without slowing it down, though it is
    fine to use it for monitoring the average current for other
    purposes. You will have to use the analog signal it
    digitizes as the feedback for the analog PID current regulator.
    Every regulator has an upper frequency limit. You have to
    decide what is fast enough. If you add capacitance across
    the output, it can help stabilize the voltage for
    frequencies higher than the regulator can keep up with, but
    then you lose the high frequency response with the current
    limit. This is a trade off.
     
  20. And some "poles" are EEs, as well. A friend of mine that dies a few
    years ago was Polish, and served as a Merchant Marine Radio Operator
    during WWII. he was aboard one of the first ships to arrive at the ports
    of Japan after the two nuclear warheads were dropped.


    --
    Service to my country? Been there, Done that, and I've got my DD214 to
    prove it.
    Member of DAV #85.

    Michael A. Terrell
    Central Florida
     
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