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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

CO = Controller Output, also called control variable, manipulated variable, etc.
PV = Process Variable, also called controlled variable, measured variable, etc.
SP = Set Point, also called desired value, reference signal, command, etc.
e = SP-PV

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)