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Rearranging Equations

  1. Apr 10, 2010 #1
    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

    Attached Files:

    Last edited: Apr 10, 2010
  2. jcsd
  3. Apr 10, 2010 #2


    Staff: Mentor

    Your attached image is too small for me to read, which might be why no one has responded.
  4. Apr 10, 2010 #3
    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.

    Attached Files:

  5. Apr 10, 2010 #4


    Staff: Mentor

    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.
  6. Apr 10, 2010 #5
    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)

    Attached Files:

  7. Apr 11, 2010 #6


    Staff: Mentor

    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 [Broken]
    Last edited by a moderator: May 4, 2017
  8. Apr 12, 2010 #7
    Hi Mark44,

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

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