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Control Systems Question. Need to convert a plant from G(s) to G(z) (discrete).

  1. Oct 24, 2011 #1

    xiN

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    1. The problem statement, all variables and given/known data
    The system is given by:

    G(s) = 1/((s+0.1)(s+3))

    I need to convert it to G(z), it's discrete form.

    The sample time T is 0.1 seconds.

    2. Relevant equations

    To convert it they give

    G(z) = (1-z^(-1))*Z-transform[G(s)/s]

    3. The attempt at a solution

    Obviously I started with G(s)/s. That gives you another s term at the bottom.

    I then broke it up into partial fractions so that I had.

    (10/(3s)) + (0.1145/(s+3)) + (3.45/(s+0.1))

    Then I used the table in my book to convert all the s to z values using the following two formulas.

    1/s = z/(z-1)

    1/(s+a) = z/(z-e^(-aT))

    I then multiplied by the (1-z^(-1)) term for my G(z) answer.

    When I was done I had a second order polynomial at the top and at the bottom. And all my coefficients were wrong. I did this same question using the c2d (continuous to discrete) function in matlab, and it gave a different answer.

    Matlab and my textbook both have the same answer, which is:

    0.00452z +0.004076
    ---------------------
    z^2 -1.731z + 0.7334
     
  2. jcsd
  3. Oct 25, 2011 #2

    xiN

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    I don't know if bumps are allowed, but any help with this problem would be much appreciated. I'm really stumped.
     
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