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Unformatted text preview: K 2 + 61 K + 96 = 0, which has solutions K = –2.485 and –4.293. Since only positive values for K are considered, the closed–loop system is stable for K > 0. The closed–loop system is overdamped for small values of K , underdamped for intermediate values of K after the two branches break out of the real axis, and becomes overdamped again Compensators when the two branches break back into the real axis. The 2% settling time decreases as K increases and approaches 4/4 s as K approaches ∞. For r ( t ) = 5, The steady state output is 5. The 2% bounds for the output are 4.9 and 5.1. The output reaches 5.1 and stays within the bounds at 1.23 s. Therefore, the graphically determined 2% settling time is 1.23 s. The percent overshoot is . The Root Locus Diagram and simulation plots are given below. 2 4 6 5 10 time (s) r y 2 4 6-5 5 time (s) e(t) 2 4 6 10 15 20 25 time (s) u(t)-8-6-4-2-2 2...
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- Spring '11
- Complex number, real axis, Root Locus Diagram, closed–loop characteristic equation