Friday's PID controller design quiz

[Peter Nachtwey]

Another closed loop solution without over shoot.

ftp://ftp.deltacompsys.com/public/NG/Mathcad%20-%20t1p1%20IMC%20Pandiani.pdf

I used the Internal Model Control method to calculate the controller. This is the method use on the www.controlguru.com site. Basicially it is a zero cancelation method.

One doesn't have much control over what the controller will look like. In this case the controller turns out to be a simple PD controller. Notice that the PD controller has a much faster response. Much of this is due to the fact that the derivative gain speeds up the response whereas the integrator gain slows it down.

 

[tacm]

I'm spending my Friday night emptying beer cans

X2

 

[kamenges]

Originally posted by Peter Nachtwey:

Basicially it is a zero cancelation method.

I thought pole/zero cancellation was an iffy proposition since, in practical systems, you can't guarantee that the poles and zeros will stay exactly where you put them. If they move just slightly you will have a significant change in gain over a small change in frequency. Or is this just an issue if the poles and zeros are on the imaginary axis?

Originally posted by Peter Nachtwey:

In this case the controller turns out to be a simple PD controller.

I would have thought a PD controller would be the preferred controller in the first place. Since the process was type 1 it had an integrator already. Granted, in real life you probably need an integrator. But from a purely academic standpoint an integrator in this systems doesn't seem to bring a benefit.

Keith

 

[Peter Nachtwey]

I thought pole/zero cancellation was an iffy proposition since, in practical systems, you can't guarantee that the poles and zeros will stay exactly where you put them. If they move just slightly you will have a significant change in gain over a small change in frequency. Or is this just an issue if the poles and zeros are on the imaginary axis?

You are right. If the zero drift closer to the origin than the poles the gain will go above 1 in the region inbetweeen. I should add a random number generator to the model after calculating the gains just to see what happens. I have done that on many of my worksheets but for the most part they just confuse the issue...........more.

[quote[
I would have thought a PD controller would be the preferred controller in the first place. Since the process was type 1 it had an integrator already. Granted, in real life you probably need an integrator. But from a purely academic standpoint an integrator in this systems doesn't seem to bring a benefit.
[/QUOTE]
Yes, but Pandiani was insistant that the problem be solved exactly as it is. That is why it is academic toruture. In reality I would have a few solutions for the problem. Trying to make one work that can't work is futile. For Pandiani's problem the thing to do is to prove the zero will always be closer to the origin than the pole. Since I have symbolic formulas for these I can find if this is possible. The zero is at -Tp or -1/9*Tm. The pole is at -1/(3*Tm). Therefore the zero will always be closer to the origin than the poles.