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Controls System Question

  1. Jun 7, 2014 #1
    I'm attempting to solve a control systems problem, however I'm stuck on the first step.

    The system is specified with a difference equation:
    [tex]y(k+2)+y(k+1)+0.16y(k)=u(k+1)+2u(k)[/tex]

    So I need to convert this back onto the usual pulse transfer function form to use one of the standard methods of deriving the matrix.

    The thing is I can't get to the transfer function. Due to the k shifts there are all of the initial condition constant terms such as z*y(0) that don't appear in the solutions at all.

    Neither the problem or the solution specify that those conditions are zero. Are the initial conditions just being ignored, or am I missing something here?

    Thanks!
     
    Last edited: Jun 7, 2014
  2. jcsd
  3. Jun 9, 2014 #2

    rude man

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    By definition, a transfer function assumes zero initial conditions.

    What matrix? Are you looking for the z transform?
     
  4. Jun 9, 2014 #3
    I need to get the whole system into some form of state space equation.

    So I was going to take the z transform of that difference equation, then take the zeros and poles of that z domain transfer function to get the G and H matrices of the state space representation.
     
  5. Jun 9, 2014 #4

    donpacino

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    Yes that is a correct method

    note: I have always referred to the state space matrices as A,B,C & D.
    I am assuming G & H are the system dynamics and input effects matrices respectivly
     
  6. Jun 9, 2014 #5
    Yes. For reference I'm using the Discrete Time Controls systems textbook by Ogata.
     
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