# transfer function sampling frequency?

#### suzuki

Joined Aug 10, 2011
119
Hi all,

Apologies for the wall of text, but I wanted to be as clear as I could in describing my problem.

As some background, I am designing a controller and using a transfer function to model the feedback component. The following image has some equations that I implemented for my system.

http://imgur.com/MC7t6

However, in my case, I manipulated the H(z) tf by multiplying by (z^2/z^2) such that the degree of the equation is equal to 2.

So through some simulation, i found that the coefficients that would give me a proper regulated output as the following:

@ 530 kHz sampling frequency
b0 = -1.561
b1 = -0.05
b2 = 1
a0 = -1
a1 = 1.001
a2 = -0.05

I noted that the output of this transfer function went to infinity after x amount of time but, my output voltage plot still looked like it reached a steady state value, so I thought it was fine.

The problem I am having is that, I would like to change my sampling frequency to 140kHz. From the equations above, i thought this would be a relatively simple task, and I would just have to scale my coefficients accordingly.

My steps were to take the above values, and then solve for the ωp0, ωp2 and ωz1. I found the values to be -17660, -3177882 and -6.04e-7 respectively. With these values and the new sampling frequency, I tried to do some reverse engineering and solved for b0, b1, b2 etc.

However, when i used this values in my model, my simulation no longer was regulated and no longer functioned properly. I'm not really sure what went wrong here, so if anyone could provide some insight, please post here.