A negative unity-feedback LTI system has a forward element consisting of an amplifier with adjustable real-valued gain K in cascade with a transfer function G(s), the transfer function G(s) known to generate the polar plot sketched in Figure 3. Use the sketch to answer each of the following questions. Im 0₂ 0 (a) Evaluate: |C(0)| (b) Evaluate: G(jw₂)| = | (c) Evaluate: limu+G(jw)| = @=0₂ @=0 Figure 3: Polar Plot of G(jw) for w=0 to x Re 30=0 (e) System Type of G(s):. (f) # of (finite) open-loop zeros (g) # of open-loop poles in right-half s-plane (h) # of closed-loop poles in right-half s-plane = (i) Phase Crossover Frequency LC(0) LG(jw₂) lim-+ LG(jw) = (d) What is the filter characteristic of the open-loop frequency response? Circle one: low-pass band-pass high-pass DC Gain of G(s): = # of open-loop poles Gain Margin Ga
A negative unity-feedback LTI system has a forward element consisting of an amplifier with adjustable real-valued gain K in cascade with a transfer function G(s), the transfer function G(s) known to generate the polar plot sketched in Figure 3. Use the sketch to answer each of the following questions. Im 0₂ 0 (a) Evaluate: |C(0)| (b) Evaluate: G(jw₂)| = | (c) Evaluate: limu+G(jw)| = @=0₂ @=0 Figure 3: Polar Plot of G(jw) for w=0 to x Re 30=0 (e) System Type of G(s):. (f) # of (finite) open-loop zeros (g) # of open-loop poles in right-half s-plane (h) # of closed-loop poles in right-half s-plane = (i) Phase Crossover Frequency LC(0) LG(jw₂) lim-+ LG(jw) = (d) What is the filter characteristic of the open-loop frequency response? Circle one: low-pass band-pass high-pass DC Gain of G(s): = # of open-loop poles Gain Margin Ga
Introductory Circuit Analysis (13th Edition)
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Publisher:Robert L. Boylestad
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
Transcribed Image Text:A negative unity-feedback LTI system has a forward element consisting of an amplifier with adjustable
real-valued gain K in cascade with a transfer function G(s), the transfer function G(s) known to generate
the polar plot sketched in Figure 3. Use the sketch to answer each of the following questions.
Im
(a) Evaluate:
(b) Evaluate:
:00-0₂
|C(0)|-
G(jw₂) =
0
Figure 3: Polar Plot of G(jw) for w=0 to ∞
(c) Evaluate: lim |G(jw)| =
lim
(d) What is the filter characteristic of the open-loop frequency response?
Circle one:
(e) System Type of G(s):.
(f) # of (finite) open-loop zeros a
(g) # of open-loop poles in right-half s-plane =
(h) # of closed-loop poles in right-half s-plane =
(i) Phase Crossover Frequency WGM
(j) Gain Crossover Frequency w =
Re
30=0
LC(0)
LG(jw₂) =
LG(jw)
low-pass band-pass high-pass
DC Gain of G(s):
# of open-loop poles
=
Gain Margin GM
Phase Margin =
(k) Determine the values of gain parameter K>0 that result in closed-loop stability.
Stable range of K > 0:
(1) Assume K satisfies the conditions of part (k). Determine the closed-loop steady-state error given a
unit-step reference input.
e(x) =
(m) Repeat part (1) but given a unit-ramp reference input.
c(∞0)
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