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: Control Systems - Root Locus

  1. Apr 13, 2013 #1
    1. The problem statement, all variables and given/known data

    Given the transfer function:
    [tex] R(s)=\frac{K}{s(s+2)(s^2+4s+5)}[/tex]

    Find the following (needed to sketch the root locus:
    a) Number of branches
    b) Symmetry
    c) Starting and ending points
    d) behavior at infinity (asymptotes)
    e) Real axis breakaway and break-in points.
    f) calculation of jw-axis crossings

    2. Relevant equations

    3. The attempt at a solution
    a)number of branches
    The number of branches of the root locus equals the number of closed loop poles.
    -poles cause the denominator to go to 0.
    Therefore there is a pole at 0, -2,, and by quadratic eqns -2 (plus minus) j.
    so, if im not mistaken there are 4 poles at 0,-2,-2+j and -2-j. This means that there will be four branches????
    Yet, when I plot the root locus in matlab I seem to have three branches?????

    My text book just says "the root locus is symmetrical about the real axis". This is true from the image but how can I show this mathematically?

    c)Starting and ending points
    again my textbook is vague/ maybe i just dont understand it very well. "The root locus begins at the finite and infinite poles of G(s)H(s) and ends at the infinite zeroes of G(s)H(s)"
    To me this means that the branches begin at the poles from part a), which is seen in the picture - but there are no zeroes so how can there be an end point?

    d) Behavior at infinity

    e)Real axis breakaway and break-in points
    breaks away at a point where the gain (K) is max
    Breaks in where the gain is min.

    I dont understand this as teh gain should very between 0 and infinity????

    f) jw axis crossings
    I'm thinking that a routh table may be necessary here, thoughts???

    Thanks, I am fairly stuck here - so any advice will be helpful.
    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted