This preview has intentionally blurred sections. Sign up to view the full version.View Full Document
Unformatted text preview: Setting the real and imaginary parts equal to zero and solving simultaneously, 425 K 2 + 405 K + 120 = 0, which has solutions K = –0.477 ± 0.235 j . Since only real, 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 4/7 s as K approaches ∞. For r ( t ) = 0.8 t , The Root Locus Diagram and simulation plots are given below.-40-30-20-10-15-10-5 5 10 15 Real Axis Imaginary Axis 5 0.5 1 time (s) r y 5 2 4 time (s) r y 5-0.5 0.5 1 time (s) e(t) 5 0.005 0.01 0.015...
View Full Document
- Spring '11
- Complex number, 2%, real axis, Root Locus Diagram, 0.235j, 405K