Root Locus Design Extra Credit Problem Due Tomorrow!

Discussion in 'Homework Help' started by Ncircuit, Dec 17, 2013.

  1. Ncircuit

    Thread Starter New Member

    Dec 17, 2013
    5
    0
    My professor gave the class an extra credit problem to try and make up for the low test average (less than 50%) from our first exam.

    The problem is a root locus design. The Gp(s) = 1/s(s^2+4s+5). He gave an example using a PI compensator, in which he used a K value of 3, resulting in:

    Overshoot:38.36%
    Tp=4.55
    Ts= 9.04

    He wants us to get a settling time, Ts, less than 5 seconds. However, this seems to be impossible. The only thing that I thought might work is using PID instead of PI. However, we were not taught this in class, nor r we going to be tested on it. I have tryed but failed, getting my best result of Ts=5.37 seconds using a k value of 4.9.

    Please Help!
     
  2. tshuck

    Well-Known Member

    Oct 18, 2012
    3,531
    675
    Extra credit usually implies something above and beyond that which you are expected to know - I'd say go for the PID...
     
  3. Papabravo

    Expert

    Feb 24, 2006
    10,136
    1,786
    So you know that one of the roots is at the origin and the other two roots of the original transfer function are a complex conjugate pair or they lie on the real axis. To get the entire system to behave the way you want you must either move the poles, by varying a parameter, or add additional features (poles or zeros).

    A couple of questions:
    1. What does the contour of 5 seconds settling time look like?
    2. What region has settling time less than 5 seconds?
    3. What region has settling time greater than 5 seconds?
    4. What is the minimum number of features you need to add?
    5. What one thing can you add near the pole at the origin to improve the settling time?

    While you're working on all of this remember the following:
    The positive real part of any pole must disappear or the system WILL!
     
    Last edited: Dec 18, 2013
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