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Re: PID controller: dummy questions

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On 25/06/2020 21:29, DJ Delorie wrote:
> 
> I'm not an expert, but I've gone through this puzzle in the past, so...
> 
> pozz <pozzugno@gmail.com> writes:
>> For the proportional term, we have an output from PID controller that is
>>
>>   P = Kp*err
> 
> Yup!
> 
>> FIRST STEP
>> T = 20°C. Error = 60°C. P = 6V.
>> Should I set the power supply output voltage to 6V? I think so.
> 
> Yup!
> 
>> SECOND STEP
>> T = 30°C. Error = 50°C. P = 5V.
>> Should I set Vout=5V or increase Vout by 5V so setting it to 11V?
> 
> 5V.
> 
> 
>> The mathematics say the output of PID controller *is* Kp*err,
> 
> As a first step, yes.  You're not done though.  Even with a pure P
> controller, you can just set Kp high enough that the error is small.
> I.e. if your Kp was 10V/V, you'd get a 10V swing from 79C to 81C, which
> may be enough.  If you set Kp REALLY high, you effectively get an on-off
> control like a mechanical thermostat.
> 
> Ideally, you'd set Kp as high as you can get away with, but not so high
> that you get runaway oscillations in the output.
> 
>> but I'm not sure. With the increase of temperature, the errore
>> decreases to a minimum, so the Vout. At the steady state the error
>> should be zero, but the voltage from the power supply can't be zero.
> 
>   P = Kp * err   (note = not += )
> 
>   Vout = P
> 
> So far you've done the "P" part of PID.  Next you need to do the "I"
> part of PID.
> 
> The P portion quickly (hopefully) gets you close to the goal, with some
> steady-state error.  The next step is to integrate the remaining error
> over time, which undoes any "offset" in the system.
> 
>   I += Ki * err   (note += not = )
> 
>   Vout = P + I
> 
> So now, if the Kp isn't enough to get you to goal, the system will
> slowly boost the output to remove the offset.  This is a PI controller.
> Note that the accumulated I value is often limited in magnitude to
> prevent runaway.
> 
> Now for the "D" term.  The D term is designed to prevent overshoot by
> "putting on the brakes" if you're approaching the goal too quickly.
> 
>   D = Kd * (err[t] - err[t-1])
>   (i.e. how fast is the error changing)
> 
>   Vout = P + I + D;
> 
> Now you have a PID controller :-)
> 
> There's one more term that's often used to optimize the system - a "feed
> forward" term.
> 
>   F = Kf * Tgoal
> 
> I.e. if your system is of the type where (approximately) input voltage =
> output temperature, you can estimate this with an F term, and use the
> PID control just for precision.
> 

There's a few clarifications I'd like to add to this.

Sometimes in examples or literature you'll see a different form of the
integral term.  Instead of writing:

	I += Ki * err

you write:

	S += err

	I = Ki * S

This makes more sense to me, and many people - you integrate the error
over time, and then apply a scale factor when you use it.  It also means
your windup limits are consistent while you play with different Ki
factors to get a nice regulation.

It's worth noting that Kd here is negative, while Kp and Ki are positive.

And sometimes the scaling is written with a single K and time factors
for the I and D parts.  Ultimately this is all the same in the end, but
it can be useful for the OP to understand when he reads about it online.

Finally, the F term you have here can be a function, not just a simple
scale.  You might base it on a table, or from a linear function (scale
and offset).

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Thread

PID controller: dummy questions pozz <pozzugno@gmail.com> - 2020-06-25 19:55 +0200
  Re: PID controller: dummy questions Hans-Bernhard Bröker <HBBroeker@t-online.de> - 2020-06-25 21:14 +0200
  Re: PID controller: dummy questions DJ Delorie <dj@delorie.com> - 2020-06-25 15:29 -0400
    Re: PID controller: dummy questions David Brown <david.brown@hesbynett.no> - 2020-06-26 08:43 +0200
  Re: PID controller: dummy questions Richard Damon <Richard@Damon-Family.org> - 2020-06-25 22:21 -0400
  Re: PID controller: dummy questions pozz <pozzugno@gmail.com> - 2020-06-26 10:59 +0200
    Re: PID controller: dummy questions David Brown <david.brown@hesbynett.no> - 2020-06-26 11:07 +0200
    Re: PID controller: dummy questions Rick C <gnuarm.deletethisbit@gmail.com> - 2020-06-26 09:10 -0700
    Re: PID controller: dummy questions Richard Damon <Richard@Damon-Family.org> - 2020-06-26 12:29 -0400
      Re: PID controller: dummy questions Rick C <gnuarm.deletethisbit@gmail.com> - 2020-06-26 12:00 -0700
        Re: PID controller: dummy questions Richard Damon <Richard@Damon-Family.org> - 2020-06-26 22:24 -0400
          Re: PID controller: dummy questions Paul Rubin <no.email@nospam.invalid> - 2020-06-26 21:41 -0700
            Re: PID controller: dummy questions DJ Delorie <dj@delorie.com> - 2020-06-27 01:15 -0400
              Re: PID controller: dummy questions Paul Rubin <no.email@nospam.invalid> - 2020-06-26 23:12 -0700
                Re: PID controller: dummy questions Rick C <gnuarm.deletethisbit@gmail.com> - 2020-06-27 00:07 -0700
                Re: PID controller: dummy questions pozz <pozzugno@gmail.com> - 2020-06-27 16:53 +0200
                Re: PID controller: dummy questions David Brown <david.brown@hesbynett.no> - 2020-06-27 17:31 +0200
                Re: PID controller: dummy questions Rick C <gnuarm.deletethisbit@gmail.com> - 2020-06-27 10:09 -0700
                Re: PID controller: dummy questions Rick C <gnuarm.deletethisbit@gmail.com> - 2020-06-27 15:44 -0700
                Re: PID controller: dummy questions Richard Damon <Richard@Damon-Family.org> - 2020-06-27 12:34 -0400
                Re: PID controller: dummy questions DJ Delorie <dj@delorie.com> - 2020-06-27 11:51 -0400
            Re: PID controller: dummy questions Rick C <gnuarm.deletethisbit@gmail.com> - 2020-06-26 23:06 -0700
              Re: PID controller: dummy questions Paul Rubin <no.email@nospam.invalid> - 2020-06-26 23:18 -0700
                Re: PID controller: dummy questions Rick C <gnuarm.deletethisbit@gmail.com> - 2020-06-27 00:23 -0700
            Re: PID controller: dummy questions Tauno Voipio <tauno.voipio@notused.fi.invalid> - 2020-06-27 10:28 +0300
            Re: PID controller: dummy questions Richard Damon <Richard@Damon-Family.org> - 2020-06-27 18:13 -0400
    Re: PID controller: dummy questions Hans-Bernhard Bröker <HBBroeker@t-online.de> - 2020-06-26 22:30 +0200
      Re: PID controller: dummy questions Phil Martel <pomartel@comcast.net> - 2020-06-28 13:10 -0400

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