rootlocus1 - ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 2...

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Root Locus Q UESTION 1 For the system shown in Figure 1 with ( 29 1 5 C s G s s + = + and ( 29 2 6 s G 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 1 There are m = 2 zeros located at –1 and –2. There are n = 2 poles located at –5 and –6. 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, and between –5 and –6. The closed–loop transfer function is
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Unformatted text preview: ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 2 2 3 2 1 1 11 3 30 2 C C K s s KG s G s T s KG s G s K s K s K + + = = + + + + + + . The closedloop characteristic polynomial is (1+ K ) s 2 + (11+3 K ) s + (30+2 K ). Since the closedloop characteristic polynomial is second order, the closedloop system is stable if all of the coefficients are the same sign. Root Locus Therefore, the closedloop 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([-1 -2],[-5 -6],1); figure; rlocus(sys), title('G_C(s)G(s) = [(s+1)(s+2)]/[(s+5)(s+6)]'); The Root Locus Diagram is shown below.-7-6-5-4-3-2-1 1-2-1 1 2 G C (s)G(s) = [(s+1)(s+2)]/[(s+5)(s+6)] Real Axis Imaginary Axis 2...
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This note was uploaded on 02/01/2012 for the course MECH ENG 279 taught by Professor Landers during the Spring '11 term at Missouri S&T.

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rootlocus1 - ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 2...

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