Control Systems - Root Locus with proportional control

AI Thread Summary
The discussion focuses on solving a root locus problem in control systems, specifically with proportional control. The user initially solved the coordinates for the root locus diagram using a quadratic equation but struggled with determining the gain for a specified rise time. They were reminded that MATLAB can generate root locus plots, which can be used to verify their work, though manual calculations are encouraged for understanding. Ultimately, the user discovered that creating a transfer function from G and C allows for matching to the characteristic equation of second-order systems, confirming their solution with MATLAB. Understanding the material is emphasized as crucial for test preparation.
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Homework Statement



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Homework Equations



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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 is 1 second. With previous sample questions, we would use s^2 + 2zWs + W^2 for the 2nd order denominator to finish the question based on given parameters (ie dampening ratio, percentage overshoot etc). How do i deal with the numerator?
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I cannot remember root locus at all. sorry

that being said MATLAB will do a root locus plot for you
you can use that to check your work. I haven't done root locus by hand since I was required too in school.

note: Make sure you understand the material for your tests. for now only use MATLAB as a tool to help you check your answer. Do not just copy the graph to a piece of paper.

http://www.mathworks.com/help/control/ref/rlocus.html
 
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.
 
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