 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 where

 Kp: Proportional gain No unit Ki: Integral gain (1/second) Kd: Derivative gain (seconds) 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)