PID Equations

PID Controllers in BESTune

The following PID controllers can be optimized by using the excellent PID auto-tuning software BESTune (see http://bestune.50megs.com for details). Theoretically, BESTune is able to optimize any PID controllers, as long as the PID equations implemented in them are known. In order to include more PID controllers in BESTune, I am asking you to give me more information about other well-known brands of industrial PID controllers (brand names, PID equations implemented, units of the three PID constants, etc). Your help will be very much appreciated.

The actual PID equations that are implemented inside these PLCs are all in discrete time or digital form. One example of the discrete time form of "Allen Bradley Logix5550 Independent PID" can be found on the web page http://bestune.50megs.com/typeABC.htm.

Variable Definition

Allen Bradley Logix5550 Independent PID

where

Kp:

Proportional gain

No unit

Ki:

Integral gain

(1/second)

Kd:

Derivative gain

(seconds)

Allen Bradley Logix5550 Dependent PID

where

Kc:

Proportional gain

No unit

Ti:

Reset time

(min/rep)

Td:

Rate time

(min)

 Allen Bradley PLC5 Independent PID - Using Integer Blocks

where

Kp:

Proportional gain

(0.01)

Ki:

Integral gain

(0.001/ second)

Kd:

Derivative gain

(seconds)

 Allen Bradley PLC5 Independent PID - Using PD Blocks

where

Kp:

Proportional gain

No unit

Ki:

Integral gain

(1/ second)

Kd:

Derivative gain

(seconds)

 Allen Bradley PLC5 ISA PID - Using Integer Blocks

where

Kc:

Proportional gain

(0.01)

Ti:

Reset time

(0.01min/rep)

Td:

Rate time

(0.01min)

 Allen Bradley PLC5 ISA PID - Using PD Blocks

 where

Kc:

Proportional gain

No unit

Ti:

Reset time

(min/rep)

Td:

Rate time

(min)

 Allen Bradley SLC5/02,SLC5/03 and SLC5/04 ISA PID

where

Kc:

Proportional gain

(0.1)

Ti:

Reset time

(0.1min/rep)

Td:

Rate time

(0.01min)

 Bailey Function Code FC19 with K=1

where

K:

Gain multiplier

No unit

Kp:

Proportional gain

No unit

Ki:

Integral reset

1/min

Kd:

Derivative rate action

Min

 Bailey Function Code FC156 Independent Form with K=1

where

K:

Gain multiplier

No unit

Kp:

Proportional gain

No unit

Ki:

Integral reset

Resets/min

Kd:

Derivative rate action

Min

 

Concept PID1 - PID Controller

where

Gain:

Proportional gain

No unit

TI:

Reset time

(milliseconds)

TD:

Derivative Action time

(milliseconds)

Concept PID1P - PID Controller with parallel structure

 where

KP:

Proportional gain

No unit

KI:

Integral rate

(1/milliseconds)

KD:

Differentiation rate

(milliseconds)

 Fischer & Porter DCU 3200 CON Ideal with KP = 1

 If Kp = 1, the above equation reduces to:

where

KC:

Gain constant

No unit

TR:

Reset time

(min/rep)

TD:

Derivative term

(min)

 Fischer & Porter DCU 3200 CON Parallel KP variable with KC=1

 If KC=1, the above equation reduces to:

where

KP:

Proportional gain

No unit

TR:

Reset time

(min/rep)

TD:

Derivative term

(min)

 GE Fanuc Series 90-30 and 90-70 Independent Form PID

where

Kp:

Proportional gain

(0.01)

Ki:

Reset time

(0.001rep/second)

Kd:

Derivative gain

(0.01 seconds)

 Hartmann & Braun Freelance 2000 PID

 where

CP:

Proportional correction value

No unit

TR:

Reset time

(milliseconds)

TD:

Rate time

(milliseconds)

Honeywell TDC 3000 APM Non - Interactive PID

where

K:

Gain

No unit

T1:

Integral time constant

(min/rep)

T2:

Derivative time constant

(min)

Modicon 984 PLC PID2 Equation

where

PB:

Proportional band

No unit

K2:

Integral mode gain constant

(0.01min/rep)

K3:

Derivative mode gain constant

(0.01min)

 Siemens S7 PB41 CONT_C PID

where

Gain:

Proportional gain

No unit

TI:

Reset time

(seconds)

TD:

Derivative time

(seconds)

 Yokogawa Field Control Station (FCS) PID

where

PB:

Proportional band

No unit

Ti:

Integral time

(seconds)

Td:

Derivative time

(seconds)