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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.
- Spring '11