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

**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**

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**

KP: |
Proportional gain |
No unit |

KI: |
Integral rate |
(1/milliseconds) |

KD: |
Differentiation rate |
(milliseconds) |

** Fischer
& Porter DCU 3200 CON Ideal with KP = 1**

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**

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**

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) |

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) |