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rootlocus8

rootlocus8 - Root Locus QUESTION 8 For the system shown in...

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Root Locus Q UESTION 8 For the system shown in Figure 8 with ( 29 2 C G s s = + , ( 29 2 6 25 s G s s s β + = + + , and ( 29 10 10 H s s = + sketch the Root Locus Diagram by hand and using Matlab. Note: the free parameter is β . 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) G C (s) R(s) + - Y(s) H(s) Figure 8 The closed–loop transfer function is ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 3 3 2 3 2 2 3 2 10 2 6 10 2 6 20 105 370 10 1 20 105 370 10 1 20 105 370 C C s s G s G s H s s s s s s T s s s G s G s H s s s s s s s s s β β + + + + + + + = = = + + + + + + + + + + + . The effective open–loop transfer function with β as the free variable is ( 29 2 3 2 10 20 105 370 eff s s G s s s s + = + + + There are m = 2 zeros located at 0 and –10.

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Root Locus There are n = 3 poles located at –14.52 and –2.738 ± 4.240
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