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Unformatted text preview: From the necessary and sufficient conditions for second order systems, all of the coefficients must be positive, which is true for K > –0.2. Since only positive values for K are considered, the closed–loop system is stable for K > 0. Compensators The closed–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 until the branches break into the real axis, and then increases and approaches 4/5 s as K approaches ∞. For r ( t ) = 1, The closed–loop poles are located at The damping ratio and natural frequency, respectively, of the poles at are and The Root Locus Diagram and simulation plots are given below. 5 10 0.5 1 time (s) r y 5 10 5 10 time (s) r y 5 10 0.5 1 time (s) e(t) 5 10 1 2 Compensators-15-10-5-4-3-2-1 1 2 3 4 Real Axis Imaginary Axis...
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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