Re: PID controller: dummy questions

From	DJ Delorie <dj@delorie.com>
Newsgroups	comp.arch.embedded
Subject	Re: PID controller: dummy questions
References	<rd2odq$oiv$1@dont-email.me>
Date	2020-06-25 15:29 -0400
Message-ID	<xnlfkbc5ah.fsf@delorie.com> (permalink)

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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.

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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