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 - How to find dominant poles *without* MATLAB?

  1. Feb 14, 2017 #1
    1. The problem statement, all variables and given/known data
    Design a lag-lead compensator for the system of Figure 9.37 so that the system will operate with 20% overshoot and a twofold reduction in settling time. Further, the compensated system will exhibit a tenfold improvement in steady-state error for a ramp input.

    2. Relevant equations

    3. The attempt at a solution
    Using the equation and 20% overshoot, ##\zeta = 0.456##. How do I find the dominant poles by hand, WITHOUT matlab? Every single example in my book and the ones I've tried looking for online ALL use Matlab...
  2. jcsd
  3. Feb 14, 2017 #2


    User Avatar

    Can you solve a quadratic equation?
    You have nothing to do than to find the closed-loop function and set the denominator equal to zero. This gives you the pole distribution.
  4. Feb 14, 2017 #3
    Is it simply:
    Gol = ##\frac{K}{(s)(s+6)(s+10)}##
    Gcl = ##\frac{Gol}{1+Gol}=\frac{K}{s^3+16s^2+60s+k}##
    s^3+16s^2+60s+k = 0

    What do I do from here?
  5. Feb 14, 2017 #4
    Leave the denominator in factored form and find the 3 solutions for s(s+6)(s+10) = 0

    It should be pretty straightforward.
  6. Feb 21, 2017 #5
    The problem asks for a 20% overshoot, and the damping ratio corresponding to that is 0.456. The book says we have to drag the poles in matlab until we get our desired damping ratio shown at the bottom, and then the poles are there (-1.79+-3.5j)

    Is there a way to do this completely by hand without the use of the Root locus plot or matlab?
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted