The unity feedback system in Fig. 1 has a plant transfer function of G(s) = s(s+1)(2s+1) R(s) o K G(s) Y(s) Fig. 1 (a). Obtain the expression of the real part of G(jm). (b). The Polar plot of G(j@) is given in Fig. 2. Estimate the value of K above which the system becomes unstable. (c). What is the damping coefficient of the closed loop system for K = 1?

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The unity feedback system in Fig. 1 has a plant transfer function of
1
G(s) =
s(s+1)(2s+1)
R(s)
K H G(s)
Y(s)
Fig. 1
(a). Obtain the expression of the real part of G(jm).
(b). The Polar plot of G(j@) is given in Fig. 2. Estimate the value of K above which the system becomes
unstable.
(c). What is the damping coefficient of the closed loop system for K = 1?
(d). What is the damping coefficient of the closed loop system for K = 0.5?
-0.5
요후0.4.
-j
-2j
Fig. 2
Transcribed Image Text:The unity feedback system in Fig. 1 has a plant transfer function of 1 G(s) = s(s+1)(2s+1) R(s) K H G(s) Y(s) Fig. 1 (a). Obtain the expression of the real part of G(jm). (b). The Polar plot of G(j@) is given in Fig. 2. Estimate the value of K above which the system becomes unstable. (c). What is the damping coefficient of the closed loop system for K = 1? (d). What is the damping coefficient of the closed loop system for K = 0.5? -0.5 요후0.4. -j -2j Fig. 2
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