HW 3 Assignment

# HW 3 Assignment - 2(10 points Is the following...

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EML 4312 Spring 2011 Root Locus and Continued Fraction Expansion The due date for this assignment is Wednesday 2/9/11. Show ALL your work. 1. Determine the root locus for the following problems. You must show the hand drawn plot, and all calculations such as centroid, relative degree, asymptote angles (at least draw the asymptotes), etc. a. (10 points) G p ( s )= s ( s +2) 3 b. (10 points) G p ( s )= ( s 1) s 2 c. (10 points) G p ( s )= ( s +1) ( s 2 +1)( s +3)( s +5)( s +10) d. (10 points) G p ( s )= 15 ( s +10)( s +20) ( s 2 +1)( s +3) e. (10 points) G p ( s )= s ( s +1) ( s +10)( s 2 +9) f. (10 points) G p ( s )= 2( s +2) s ( s 2 +2 s +4)( s +1)( s +3) g. (10 points) G p ( s )= 2( s +3)( s +2) s ( s +1)
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Unformatted text preview: 2. (10 points) Is the following characteristic equation stable? Do not use a root f nder, show your work. ∆ = s 3 + 16 s 2 + 65 s + 53 . 3. (10 points) Given the following open-loop transfer function, for what values of k is the closed-loop system stable? G p ( s ) = 1 ( s + 4) 4 ( s + 5) . 4. (10 points) Given the following open-loop transfer function, for what values of k is the closed-loop system stable? (Check your root locus plot with matlab for more insight). G p ( s ) = 15 ( s + 10) ( s + 20) ( s − 1) 2 ( s + 3) 1...
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