Rearranging Equations: Understanding C(z) and Proportionality

[Kayne]

Hi there,

In the attachment I have an equation, I have worked though to solve for C(z) which is is highlighted in green. The highlighted yellow equation is what is supposed to look like but I am unsure if I am correct or not. I have tried to used my answer to make a graph for a Proportional controller but it doesn't work out, which makes me believe i have rearranged it wrong

If someone can tell me if the answer i have found is correct or not that would be great.

Thanks for your time

 

[Mark44]

Your attached image is too small for me to read, which might be why no one has responded.

 

[Kayne]

Thanks Mark44 for let me know, it seemed to work on my computer but I have now changed it to a work document so you should be able to see it and the answer I have come up with.

 

[Mark44]

Everything looks fine down to your last unshaded equation for C(z). After that, the transition to c(k) is so abrupt, that I'm not able to decipher what's going on. I have no idea what the relationship is between c(k) and C(z).

In the last (shaded yellow) equation for C(z) it appears that you are replacing the terms involving R(z) with a finite power series in z^-1, z^-2, ..., z^-m, and something similar with the terms involving C(z).

The complex analysis class I had was so long ago that I'm not able to follow what you're doing in the last two lines.

One thing that bothers me is the e^-5x terms mixed in with powers of z, which I assume are complex numbers.

 

[Kayne]

Hi Mark44,

This attachment is the question, it has to do with porportional controllers. In this attachment I have put in the tutorial that I have been following. maybe this will help with the changing from C(z) to C(k)

 

[Mark44]

It took me awhile, but it looks like you're working with the Z-transform. I don't have any experience with that transform, so I don't think I can be much help.

Here's a link to the Wikipedia article - http://en.wikipedia.org/wiki/Z_transform.

Here's another link to an introductory tutorial than might be more helpful - http://math.fullerton.edu/mathews/c2003/ZTransformIntroMod.html

 

[Kayne]

Hi Mark44,

Thanks for the information it was a little better to understand than what i had in the textbooks. I was able to transform it into the z domain

thank