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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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- Spring '11
- Root Locus, Complex number, Root Locus Diagram, imaginary axis