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Unformatted text preview: K ( s + z )] is . Therefore, K = 2.8 and z = 5.71 for = 0.35 and n = 4 rad/s. The closedloop characteristic equation is Since the characteristic polynomial is second order, the necessary and sufficient condition for stability is that all of the coefficients must have the same sign. Since only positive values for K are considered, the closedloop system is stable for K > 0. Compensators The closedloop system is underdamped for small values of K and becomes overdamped when the two branches break into the real axis. The 2% settling time decreases as K increases and approaches 4/5.71 s as K approaches . For r ( t ) = 5 For r ( t ) = 10 t For r ( t ) = 8 t 2 , The Root Locus Diagram and simulation plots are given below.252015105 5642 2 4 6 Real Axis Imaginary Axis Compensators 2 4 6 5 10 time (s) r y 2 4 65 5 time (s) e(t) 2 4 6 50 100 time (s) r y 2 4 62 2...
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 Spring '11
 LANDERS

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