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,

　

　

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.

　

　

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Standard Independent PID Controller

 

There are three types of independent PID control equations:

 

 

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

 

 

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:

 

 

We strongly recommend type C, i.e.,

 

 

where

　

　

Allen Bradley Logix5550 Independent PID

where

 

Allen Bradley Logix5550 Dependent PID

where

 

Allen Bradley PLC5 Independent PID - Using Integer Blocks

where

 

Allen Bradley PLC5 Independent PID - Using PD Blocks

where

 

Allen Bradley PLC5 ISA PID - Using Integer Blocks

where

 

Allen Bradley PLC5 ISA PID - Using PD Blocks

 

where

 

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

where

 

Bailey Function Code FC19 with K=1

where

 

Bailey Function Code FC156 Independent Form with K=1

where

 

Concept PID1 - PID Controller

 

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

where

Concept PID1P - PID Controller with parallel structure

 

where

 

Fischer & Porter DCU 3200 CON Ideal with KP = 1

 

If Kp = 1, the above equation reduces to:

 

where

 

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

 

If KC=1, the above equation reduces to:

 

where

 

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

where

 

Hartmann & Braun Freelance 2000 PID

 

 

where

 

 

Honeywell TDC 3000 APM Non - Interactive PID

where

Modicon 984 PLC PID2 Equation

 

where

 

Siemens S7 PB41 CONT_C PID

where

 

Yokogawa Field Control Station (FCS) PID

where