# 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.

In the following PID equations,

 CO: Controller Output (also called OutPut and denoted by OP) PV: Process Variable SP: SetPoint e=SP-PV

There are three types of PID controllers: Type A, Type B, and Type C. It is strongly recommended that type C be used. For more about this, please take a look at http://bestune.50megs.com/typeABC.htm. A method of desinging type C PID is given at http://bestune.50megs.com/piddesign.htm. For a quick look at a type C PID loop, take a look at this picture.

BESTune.Com

Email: bestune@netzero.net

Standard Independent PID Controller

There are three types of independent PID control equations:

 Type A: Type B: Type C:

We strongly recommend type C (Unfortunately, most industrial PID controllers use either type A or type B equations). Differentiating both sides of type C equation gives:

Discretization of the above equation with sampling period Ts gives the following form that can be implemented in a digital computer:

where

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

The last important thing that is often ignored but can never be ignored is to bring CO back to the upper or lower limit values whenever it is outside these limits, i.e., whenever CO(k)>CO’s upper limit value, we must set CO(k)=CO’s upper limit value; and whenever CO(k)<CO’s lower limit value, we must set CO(k)=CO’s lower limit value.

For example, if CO(k)=100 means the control valve is 100% open and CO=10 means the control valve is just closed, then whenever the value of CO(k) calculated by the above PID equation is larger than 100, we must set CO(k)=100 and whenever the value of CO(k) calculated by the above PID equation is less than 10, we must set CO(k)=10.

Standard Dependent PID Controller

Similarly, there are also three types of dependent PID equations:

 Type A: Type B: Type C:

We strongly recommend type C, i.e.,

where

 Kc: Proportional gain No unit Ti: Reset time (min/rep) Td: Rate time (min)

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

The equivalent continuous time equation the Concept PID1 PID algorithm implements is:

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)