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# Basics of PI controller and transfer function

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## Basics of PI controller and transfer function

(OP)
I do not have background in system controllers. As part of a project, I am forced to learn the very basics how a PI or PID controller and transfer function derivation are made. As example to my understanding, I would like to control the volumetric flow rate at the outlet of a tank. I have the following simple functional relationships:

Q = c*(ho - h); Q as flow rate, ho and h as initial and current heads in the tank
Q = A*dh/dt; A is the surface area of the tank, dh/dt time variability of head in the tank

a generic PI controller description has the following blocks:
-data source with outlet node
-difference blocks (difference of current value and sensed value from the transfer function)
-gain blocks (multiplication of difference by a constant KP) then to another gain block ...
-integrator (integrating what is coming out of gain blocks)
-summation (adding values from gains and integrator)
-transfer function (receive values from summation and sends that value back to the difference block)

That is the maximum I understood. Now, how can I use the above flow and head relationship to establish a PI controller?

Any help and guide on this would be a great help.

### RE: Basics of PI controller and transfer function

I'm not sure from your question if this is a homework problem...a math exercise, or a real-world problem.

If it is a real world problem then you can set up a PID in a controller (DCS or PLC) without modeling very much.

Your math might be useful to calculate process time constant and deadtime and thereby derive a starting point for your tuning parameters...the controller gains. But most of the time this is done in the field empirically, with the real process and loop in action...that is to say, you tune the real loop.

The modeling and math has its place but for a loop like this it may be overkill.

### RE: Basics of PI controller and transfer function

Basically, your system is representable by a differential equation, where the flow rate is equal to the surface area times the rate of change of water level in the tank. Notice I highlighted "rate" variables as these are represented by derivatives, which can in turn be solved through integration. Solving systems in this manner is in the realm of analog computing and system model "programming". This link should help clarify some of the concepts for you and get you on the right path: http://courses.engr.illinois.edu/ece486/labs/lab1/...

You might also be interested in a simulation program like Scicos, which will allow you to generate function block systems and analyze them.

### RE: Basics of PI controller and transfer function

(OP)
Thank you for your comments. I am on a mathematical modeling task, which is intended to be used in a real world problem.

Noway2, thank you for the link to a PDF. I am not good in electricity but that material looks interesting, which I will read it carefully.

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