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Unformatted text preview: 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 = –4/3. 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 4/1 s as K approaches ∞. For r ( t ) = t , For K = 6.67, the closed–loop poles are located at The damping ratio and natural frequency, respectively, of the poles located at –1.53±5.756 j are and . The time constant of the pole located at –0.9401 is . The Root Locus Diagram and simulation plots are given below. 5 10 5 10 time (s) r y 5 10 0.1 0.2 time (s) e(t) 5 10 5 10 15 time (s) u(t)-3-2-1 1-10 10...
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- Spring '11
- Complex number, Root Locus Diagram, closed–loop characteristic equation