root locus practice 1

root locus practice 1 - 29 29 29 29 29 29 29 29 2 2 2 1 1 7...

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Root Locus Q UESTION 2 For the system shown in Figure 2 with ( 29 1 C G s = and ( 29 ( 29 ( 29 2 2 3 4 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 2 There are m = 2 zeros located at –1.414 j and 1.414 j . There are n = 2 poles located at –3 and –4. There are n = 2 branches and n m = 0 branches go to infinity. The Root Locus is on the real axis between –3 and –4. The closed–loop transfer function is
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Unformatted text preview: ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 2 2 2 1 1 7 12 2 C C K s KG s G s T s KG s G s K s s K + = = + + + + + . The closed–loop characteristic polynomial is (1+ K ) s 2 + 7 s + (12+2 K ). Since the closed–loop characteristic polynomial is second order, the closed–loop system is stable if all of the Root Locus coefficients are the same sign. Therefore, the closed–loop system is stable for all positive values of K and the Root Locus does not cross the imaginary axis. The Matlab code for producing the Root Locus Diagram is sys = zpk([-sqrt(-2) sqrt(-2)],[-3 -4],1); figure; rlocus(sys), title('G_C(s)G(s) = (s^2+2)/[(s+3)(s+4)]'); The Root Locus Diagram is shown below.-4-3-2-1-2-1 1 2 G C (s)G(s) = (s 2 +2)/[(s+3)(s+4)] Real Axis Imaginary Axis 2...
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root locus practice 1 - 29 29 29 29 29 29 29 29 2 2 2 1 1 7...

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