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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 closedloop system is stable for K > 0. Compensators The closedloop 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 closedloop 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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- Spring '11