From - Thu May  8 18:50:36 1997
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From: Klaus Moellmann <moe@berlin.snafu.de>
Newsgroups: sci.engr.control
Subject: Re: PID Algorithms
Date: Sat, 03 May 1997 07:58:16 -0100
Organization: Unlimited Surprise Systems, Berlin
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Message-ID: <336AFE28.34B4@berlin.snafu.de>
References: <5kdvf1$r27@camel1.mindspring.com>
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Brian & Amy Kuhnel wrote:
> =

> I was hoping someone may be able to provide mathematical equations or
> functions which perform PID control.  Information on books or other
> references containing such information would also be helpful.  Thanks
> in advance, Brian.

Try this PI controller. PI is enough for most purposes. It uses speed =

algorithm for several reasons. It has a sophisticated feed forward input =

Z. There is a bumbless switch-over manual to automatic. You have to =

realize a bumbless automatic-manual yourself.

----------------------------------------------------------------------
/* RESET */
if (IR)
   {
   if (errors at input) goto 'error handling';
   Y =3D YR;
   if (YR > UL)  Y =3D UL;
   if (YR < LL)  Y =3D LL;
   E_old =3D 0; =

   Z_old =3D Z; =

   goto 'error handling';
   };

/* 'No module-enable' or 'first run' */
if ('No module-enable' or 'first run')
   {
   E_old =3D E; =

   Z_old =3D Z; =

   goto End;
   };

/* manual/automatic */
if (errors at input) goto 'error handling';
if (TN =3D 0)
   {
   'error handling';
   goto End;
   };

/* manual */
if (IM)
   {
   Y =3D YM;
   E_old =3D E; =

   Z_old =3D Z; =

   goto 'error handling';
   };

/* automatic */
/* limit was active */
if (LIAC)
   {
   LIAC =3D 0;
   E_old =3D E; =

   Z_old =3D Z; =

   goto 'error handling';
   };
 =

/* upper limit */
if (Y =3D UL) und (Z_old <> UL)
   {
   Y =3D Y + KP * (E - E_old + dt / TN * (E + E_old) / 2);
   goto Algo_End;
   };

/* lower limit */
if (Y =3D LL) und (Z_old <> LL)
   {
   Y =3D Y + KP * (E - E_old + dt / TN * (E + E_old) / 2);
   goto Algo_End;
   };

Y =3D Y + KP * (E - E_old + dt / TN * (E + E_old) / 2) + Z - Z_old;

Algo_End:
E_old =3D E; =

Z_old =3D Z; =


if (Y < LL)  =

    {
    Y =3D LL;
    LIAC =3D 1;
    };
if (Y > UL)
    {
    Y =3D UL;
    LIAC =3D 1;
    };

'error handling':
if (error)  error message;
----------------------------------------------------------------------

The floating point signals are as follows:
E       errors signal (setpoint - actual value)
Z       feed forward input
YR      reset value for controller output
YM      manual value for controller output
Y       controller output
KP      controller gain
TN      reset time
dt      sample time
UL      upper limit for output
LL      lower limit for output

The binary signals:
IR      module reset
IM      switch to manual
LIAC    limit indicator

The following books were quite useful to me:
[1] Regelungstechnik; Otto F=F6llinger; 6.Aufl. 1990; ISBN 3-7785-1808-9; =

H=FCthig Buch Verlag GmbH, Heidelberg; Seite 237
[2] Grundlagen der linearen Regelungstechnik I; Irmfried Hartmann, =

Christian Landgraf; Skript zur Vorlesung Regelungstechnik 1979; =

Technische Universit=E4t Berlin; Seite 202
[3] Principles and Practice of Automatic Process Control; Carlos A. =

Smith, Armando B. Corripio; 1985; ISBN 0-471-61633-8; John Wiley & Sons, =

Inc., New York, New York 10158; page 253
[4] La r=E9gulation industrielle; Jean-Marie Flaus; 1994; ISBN =

2-86601-441-3; Herm=E8s, Paris; chapitre 1


-- =

Klaus Moellmann                    Moelli@t-online.de
Heimstr.21
10965 Berlin