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rootlocus14 - Root Locus QUESTION 14 For the system shown...

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Root Locus Q UESTION 14 For the system shown in Figure 14 with ( 29 1 2 C G s s = + , ( 29 ( 29 ( 29 2 2 2 4 5 s s G s s s - + = + + , and ( 29 1 6 H s s = + , sketch the Root Locus Diagram by hand and using Matlab. How many zeros does the system contain and what are their values? How many poles does the system contain and what are their values? What are the total number of branches and how many branches will go to infinity? Where is the Root Locus on the real axis? If necessary, calculate the asymptote angles and real axis intercept, imaginary axis crossing, and the value of K at the imaginary axis crossing. G(s) KG C (s) R(s) + - Y(s) H(s) Figure 14 There are m = 2 zeros located at 1 j ± . There are n = 4 poles located at –2, –4, –5, and –6. There are n = 4 branches and n m = 2 branches go to infinity. The Root Locus is on the real axis between –2 and –4, and between –5 and –6. The asymptote real axis intercept is [ ] [ ] 2 4 5 6 1 1 9.5 4 2 a j j σ - - - - - + + - = = - - .
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Root Locus The asymptote angles are [ ] 0 2 1 180 0, 1, 2, a i i n m θ + = = ± ± - K . There are n m = 2 distinct
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