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.
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:
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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.
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.
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:
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.
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I love to cook with wine. Sometimes I even put it in the food.
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.
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.
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.
Yes.
reach, the "I" part.
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.
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
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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.
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:
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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.
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.
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
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
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.
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.
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.
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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