I actually just figured it out!. If you create a transfer function using G and C, you can easily match it up to the characteristic equation for 2nd order systems and solve accordingly. I double checked this on matlab so i know its the correct approach.
Here's the best part... i can't seem to verify this on matlab. Either the code is wrong or i'm wrong. I tried using my prof's example on matlab and its still inconclusive...
I've figured it out...
I don't exactly know what the explanation is but I'm dividing the characteristic equation with a 2nd order characteristic equation based off the condition ts = 10,20. After you crunch the numbers, you'll find the range of K from 10 - 20 seconds.
Homework Statement
Homework Equations
See below
The Attempt at a Solution
Root Locus? Easy Peasy right? Based on provided equation G(s), i solved the coordinates of the root locus diagram using quadratic equation.
For the 2nd part of the question, i have to find gain at which rise time...
Thanks rudeman,
Now that you mention it, i do vaguely remember my professor mentioning this. Any idea where I can find some material to read as a refresher?
I think i've figured out the limit of stability portion.
http://imgur.com/MOSEEqG
(please note there are 2 pictures)
Any ideas on how to find the range of k within the settling time?
Homework Statement
Given G(s) = 1/[(s^2+s+4)(s+6)] and C(s) = k, find the limit of stability of k. Also, what is the range of k such that the settling time is between 10 and 20 seconds.
Homework Equations
Provided above
The Attempt at a Solution
I have attempted to set this...