# Re: [foxboro] PID Equations

• From: "Stapper, Hub" <Hub.Stapper@xxxxxxxxxxxx>
• To: "foxboro@xxxxxxxxxxxxx" <foxboro@xxxxxxxxxxxxx>
• Date: Thu, 17 Mar 2011 09:53:16 -0400
```May the below description, part of my PIDA manual could bring some light in the
darkness:
Unfortunately the drawings do no copy into the email, see therefore the
attachment

Regards, Hub Stapper (Invensys Operations management, The Netherlands.

8- Old and New structures for PI(D) controllers

Figure 8- 1 shows the evolution that has taken place in the algorithms
used for PI(D) controllers.

Figure 8- 1: Old and new PID controller structures

In the Old PID structure the error (SP-M) was calculated and the
controller proportional, integral and derivative actions were calculated
without interaction:
P action was =  (SP-M)*k,             where k   = controller GAIN
I action was =   (SP-M)*(1/Tr*s)   where Tr = the reset (or integral)
time
D action was =  (SP-M)*Td*s        where Td = the derivative time
In these controllers the proportional, integral and derivative actions
were non-interactive; this means that when changing the controller gain, only
the proportional action was influenced. So when controller  gain k is increased
with a factor 2, the proportional action would increase with  factor 2, while
the slope of the integral action would stay as it was before. Therefore, the
term repeat time for integral action, can not be used for these non-interacting
controllers.

Under new PID structures there are two new schemes:
The first scheme (a) shows that the proportional tuning parameter (PB)
will have an effect on all three actions, the proportional, the integral and
the derivative, as the error (SP_M) is multiplied by 100/PB; this result is
being used to calculate the proportional, integral and derivative actions
P action was =  (SP-M)*(100/PB),                 where PB = controller
Prop. Band
I action was  =   (SP-M)*(100/PB)*(1/Tr*s)   where Tr = the reset (or
integral) time
D action was =  (SP-M)*(100/PB)*Td*s        where Td = the derivative
time
This structure can be found in old Foxboro controller, like SPEC 200

For these controllers the proportional, integral and derivative actions
do interact. When PB is decreased with factor two, the integral action will be
increased with factor 2 (slope will be twice as steep) and the differential
action will also be twice as big. For the integral action it means that the
repeat time (this is the time it takes for the integral action to become as big
as the proportional action is constant = Tr.

The structure under new PID structure b shows yet another difference:
here the derivative action (Td*s) is only active in the term with the
Measurement (M). The Setpoint (SP) only has proportional and integral action.
This means that there will be no derivative action when the setpoint of the
controller is changed. Derivative action will only be seen on changes in the
measurement. This has great advantages, as setpoint changes usually are step
changes, giving a big "bump" to the derivative component of the output of the
controller.

This structure can be found in Foxboro Spectrum and I/A controllers.

-----Original Message-----
From: foxboro-bounce@xxxxxxxxxxxxx [mailto:foxboro-bounce@xxxxxxxxxxxxx] On
Behalf Of Gregory A Hurwitt
Sent: Thursday, March 17, 2011 2:26 PM
To: foxboro@xxxxxxxxxxxxx
Subject: Re: [foxboro] PID Equations

[Sorry about the previous attempt.  Let's try one more time.]
You should have a look at "Integrated Control Block Descriptions",
document number B0193AX.  Per the documentation, the available modes on
the PIDA block are:

Proportional (P)
Integral (I)
Proportional-plus-Derivative (PD)
Proportional-plus-Integral (PI)
Proportional-plus-Integral-plus-Derivative (PID)
Non-Interactive PID (NIPID)
Proportional, integral, deadtime (interacting if derivative not 0) (PITAU)
Non-interacting proportional, integral, derivative, deadtime (PIDTAU)

The documentation also has a (very limited) writeup of when you might want
to use some of these.  See the section headed "PIDA is Recommended Over
Other PID Algorithms" under the writeup for the PIDA block.  (Section
94.1.1, at least in Rev. S of the document.)

Perhaps some of the list members with more experience on the topic can
expand on typical uses for some of the different modes.

Greg Hurwitt
BASF - Freeport, TX

foxboro-bounce@xxxxxxxxxxxxx wrote on 03/17/2011 03:09:13 AM:

> From:
>
> "Ravindrakumar Ratnakumara \(PLM/MLNG\)" <ravindrakumar@xxxxxxxxxxxxxxx>
>
> Hey List,
>
> Noob here. What are the available PID equations on Foxboro? I've heard > of P
> on Error and P on PV, does this refer to these equations? Why do we
> need each of these different equations and on what circumstances do we >
> choose to use them?
>
> Thank you and best regards. J
>
> TES/5 - Making Automation Work!
>
> RAVINDRAKUMAR RATNAKUMARA
>

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