# HW3 - following systems by hand. Perform all steps...

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Third Homework Eric Feron Feb 18, 2004 1. Prove that the root-locus resulting from the combination of two poles and one zero to the left of both of them on the real axis is a circle centered at the zero with radius given by p | ( p 1 - z ) || p 2 - z ) | . 2. Consider the root-locus for the equation 1 + K s ( s + 10)( s + 50) = 0 . (a) Show the real-axis segments clearly. (b) Sketch the asymptotes for K → ∞ . (c) For what values of K are the roots on the imaginary axis? 3. Sketch the complete root-locus (positive and negative gains) for the

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Unformatted text preview: following systems by hand. Perform all steps indicated in the handout and detail your computations. (a) KG ( s ) = K ( s + 4) s ( s-4)( s 2 + 2 s + 1) (b) KG ( s ) = K ( s + 2) s ( s + 1)( s 2 + 2 s + 20) (c) KG ( s ) = 2 K s ( s 2 + 5 s + 10) 1 (d) KG ( s ) = 2 K ( s 2 + s + 1) s ( s 2 + 2 s + 9)( s 2 + s + 2) (e) KG ( s ) = K ( s + 0 . 1)( s + 0 . 5) s ( s 2 + 2 s + 1)( s + 3)( s + 12) (f) KG ( s ) = K ( s + 1)( s-. 4) s ( s + 3)( s + 4)( s 2 + 6) 2...
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## This note was uploaded on 02/03/2012 for the course AERO 16.30 taught by Professor Ericferon during the Spring '04 term at MIT.

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HW3 - following systems by hand. Perform all steps...

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