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Help with root locus

  1. Mar 7, 2006 #1
    I had to use state-variable feedback to design a position control system for a motor. I have to design the controller using root locus methods.
    The gain that is varied is located in the feedback loop as shown in the picture.
    I am completely lost as to how to generate a root locus with the gain in the feedback loop.
    Can anybody give me a general form to get into so I can draw the root locus?
     

    Attached Files:

  2. jcsd
  3. Mar 7, 2006 #2
    Let the output of the summer going into G(s) be called E(s). Y(s) is then E(s)G(s). But E(s) = V(s)-K(s+1)Y(s). So

    [tex]Y(s) = E(s)G(s) = [V(s) - K(s+1)Y(s)] G(s) [/tex]
    [tex]Y(s) = \frac {E(s)G(s)}{1 + K(s+1)G(s)}[/tex]

    Then you draw the root locus plot of G(s) (s+1).
     
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