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Root loci

  1. Oct 23, 2007 #1
    1. The problem statement, all variables and given/known data
    For the double integrator described with transfer function

    [tex]G(s) = \frac{1}{s^2}[/tex]

    the initial condition is zero. The double integrator is subjected to a unit‐feedback system where the controller is chosen as

    1) a PI-controller with [tex]C(s) = k_p \left( 1 + \frac{1}{s} \right)[/tex], or

    2) a PD-controller with [tex]C(s) = k_p \left( 1 + \frac{2}{3} s \right)[/tex].

    Sketch root loci of the closed‐loop systems as k_p varies from 0 to +∞. Give the breakaway and break‐in points, the points where root loci cross the imaginary axis, and the relevant values of k_p at all these points.


    2. Relevant equations
    None


    3. The attempt at a solution
    I really have no idea where to start.
     
    Last edited: Oct 23, 2007
  2. jcsd
  3. Oct 26, 2007 #2
    Hi,

    I see no particular challenge in the problem specified. Are you familiar with the root-locus concept? I guess you'd better first develop some primary insight on the subject through available resources. Do you have any access to the book "Modern Control Engineering" (Author: Ogata) or any other introductory control engineering book? It gives a procedure to draw root-locus. All you need to do is to apply the procedure to your system.
     
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