Q5. Consider the Nyquist plot of the frequency response of the open-loop system 10000 G.(s) = (s + 1)(s+10)(s + 50) which is shown in Figure Q5 below. Imaginary Axis 0.5 Real Axis -08 0.5 -0.5 Figure Q5
Q5. Consider the Nyquist plot of the frequency response of the open-loop system 10000 G.(s) = (s + 1)(s+10)(s + 50) which is shown in Figure Q5 below. Imaginary Axis 0.5 Real Axis -08 0.5 -0.5 Figure Q5
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![Q5. Consider the Nyquist plot of the frequency response of the open-loop system
10000
G.(s)
(s+ 1)(s+10)(s + 50)
which is shown in Figure Q5 below.
Imaginary Axis
0.5
Real Axis
-08
-0.5
-0.5
Figure Q5
2
Tutorial 2: Frequency Response Analysis
(a) Write down the expression of the frequency response for this system, clearly
showing the overall gain.
(b) Is the corresponding closed-loop system with unity feedback gain stable or not?
Explain why.
(c) Determine the approximate value of the gain margin from Figure Q5. What is
the maximum value of an additional gain K for which the closed loop would still
be stable?
(d) Determine the approximate value of the phase margin from Figure Q5. Assuming
that the corresponding point on the plot occurs at 12rad/s, what is the maximum
delay which can be added to the system before the closed loop would become
unstable?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0d77d484-a887-469d-aaae-779d8340e1ea%2Ff34daca4-fc56-4c1d-a2ce-ee09c669301b%2Fbkx91co_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Q5. Consider the Nyquist plot of the frequency response of the open-loop system
10000
G.(s)
(s+ 1)(s+10)(s + 50)
which is shown in Figure Q5 below.
Imaginary Axis
0.5
Real Axis
-08
-0.5
-0.5
Figure Q5
2
Tutorial 2: Frequency Response Analysis
(a) Write down the expression of the frequency response for this system, clearly
showing the overall gain.
(b) Is the corresponding closed-loop system with unity feedback gain stable or not?
Explain why.
(c) Determine the approximate value of the gain margin from Figure Q5. What is
the maximum value of an additional gain K for which the closed loop would still
be stable?
(d) Determine the approximate value of the phase margin from Figure Q5. Assuming
that the corresponding point on the plot occurs at 12rad/s, what is the maximum
delay which can be added to the system before the closed loop would become
unstable?
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