1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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

    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

    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook