D R+ E K U + 1 Y + s²+2s+5 + N +
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To calculate the closed-loop transfer function, we need to use the following formula: T(s) = G(s) / (1 + G(s)H(s)) where G(s) is the open-loop transfer function and H(s) is the feedback transfer function. Let's assume that G(s) = K / (s^2 + 2s + 1) and H(s) = Show more…
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For the block diagram of a closed-loop system on the Figure, 1. Derive a closed-loop transfer function for set point and disturbance changes, Y/Ysp and Y/D. 2. For the following transfer functions, what values of Kc will result in a stable closed-loop system? Use any method you know.
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Stability - Exercise Consider the open-loop transfer function: a. Draw the Bode diagram (log-magnitude and phase plots) (assume K=1). b. Find the range of K for stability from the Bode plots. c. Evaluate the gain margin, phase margin, zero dB frequency (gain crossover frequency), and 180° frequency from the Bode plot for K = 10000. Answer for b) K = 96,270 (gives marginally stable), -> K < 96,270 for a stable system.
6.17 Determine the range of K for which each of the listed systems is stable by making a Bode plot for K = 1 and imagining the magnitude plot sliding up or down until instability results. Verify your answers by using a very rough sketch of a root-locus plot. (a) KG(s) = K(s+1) / (s(s+10)) (b) KG(s) = K(s+1) / (s^2(s+10)) (c) KG(s) = K / ((s+2)(s^2+9)) (d) KG(s) = K(s+1)^2 / (s^3(s+10))
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