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root locus practice 4 - Root Locus QUESTION 15 For the...

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Root Locus Q UESTION 15 For the system shown in Figure 15 with ( 29 1 C G s = and ( 29 ( 29 ( 29 2 2 2 1 2 s s 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 15 There are m = 2 zeros located at 1 j ± . There are n = 2 poles located at –1 and –2. There are n = 2 branches and n m = 0 branches go to infinity. The Root Locus is on the real axis between –1 and –2. The closed–loop transfer function is ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 2 2 2 2 1 1 3 2 2 2 C C K s s KG s G s T s KG s G s K s K s K - + = = + + + - + + . The closed–loop characteristic
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