rootlocus12

# rootlocus12 - Root Locus QUESTION 12 1 For the system shown...

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Root Locus Q UESTION 12 For the system shown in Figure 12 with ( 29 ( 29 ( 29 1 1 4 C G s s s = + + and ( 29 ( 29 ( 29 1 2 3 G s 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) Figure 12 There are no zeros. There are n = 4 poles located at –1, –2, –3, and –4. There are n = 4 branches and n m = 4 branches go to infinity. The Root Locus is on the real axis between –1 and –2, and between –3 and –4. The asymptote real axis intercept is [ ] [ ] 1 2 3 4 0 2.5 4 0 a σ - - - - - = = - - . The asymptote angles are [ ] 0 2 1 180 0, 1, 2, a i i n m θ + = = ± ± - K . There are n m = 4 distinct asymptotes with angles 0 0 0 0 45 , 45 ,135 , 135 a θ = - - .

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Root Locus The closed–loop transfer function is ( 29 ( 29 ( 29 ( 29 (
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