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Unformatted text preview: There are n – m = 2 distinct asymptotes with angles The closed–loop characteristic equation is Substituting s = jω into the closed–loop characteristic equation and rearranging Compensators Setting the real and imaginary parts equal to zero and solving simultaneously, K = –12.89. Since only positive values for K are considered, the closed–loop system is stable for K > 0. The closed–loop system is always underdamped. As K approaches ∞, ζ approaches 0. The 2% settling time decreases as K increases and approaches 4/4.5 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 time constant of the pole at s = –6.265 is The Root Locus Diagram and simulation plots are given below. 5 10 0.5 1 1.5 time (s) r y 5 10-0.5 0.5 1 time (s) e(t) 5 10-10 10 20 time (s) u(t)-15-10-5 5-40-20 20 40...
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- Spring '11
- Complex number, Root Locus Diagram, closed–loop characteristic equation