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Unformatted text preview: K ( s + z )] is . Therefore, K = 2.8 and z = 5.71 for Î¶ = 0.35 and Ï‰ n = 4 rad/s. The closedâ€“loop 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 closedâ€“loop system is stable for K > 0. Compensators The closedâ€“loop 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 âˆž. 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.-25-20-15-10-5 5-6-4-2 2 4 6 Real Axis Imaginary Axis Compensators 2 4 6 5 10 time (s) r y 2 4 6-5 5 time (s) e(t) 2 4 6 50 100 time (s) r y 2 4 6-2 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