(b) An open-loop transfer function with K = 1 is given as, G(s) = = K s(s + 1) The bode plot of the open-loop transfer function is shown in Figures Q.5b. (i) Based on the margin values obtained from the plot provided, what can you say about the stability of the system? (ii) Using the frequency domain technique, design a compensator Ge(s)so that the system will have the static velocity error constant K₁ = 50 sec¹, phase margin 50° and gain margin GM about 8 dB. Design the compensator on the given bode plot (submit it together with your answer script). (Hint: Make the necessary adjustment on the Bode plot so that the new K, is achieved) (iii) Find the new compensated gain, K and give the complete transfer function of the compensated open loop system. (iv) Sketch the plot of the compensator Ge(s) that you proposed. Phase (degree) Magnitude (dB) 60 50 40 30 20 -10 -20 -30 11 SEEE/SKEE 3143- FINAL EXAMINATION -40 -50 -60 -70 -80 0.01 0.1 1 10 100 Frequency (rad/s) -80 -90 -100 -110 -120 -130 -140 -150 -160 -170 -180 0.01 0.1 1 Frequency (rad/s) Figure Q.5b: Open Loop Bode Plot for Q.4(b) 10 100
(b) An open-loop transfer function with K = 1 is given as, G(s) = = K s(s + 1) The bode plot of the open-loop transfer function is shown in Figures Q.5b. (i) Based on the margin values obtained from the plot provided, what can you say about the stability of the system? (ii) Using the frequency domain technique, design a compensator Ge(s)so that the system will have the static velocity error constant K₁ = 50 sec¹, phase margin 50° and gain margin GM about 8 dB. Design the compensator on the given bode plot (submit it together with your answer script). (Hint: Make the necessary adjustment on the Bode plot so that the new K, is achieved) (iii) Find the new compensated gain, K and give the complete transfer function of the compensated open loop system. (iv) Sketch the plot of the compensator Ge(s) that you proposed. Phase (degree) Magnitude (dB) 60 50 40 30 20 -10 -20 -30 11 SEEE/SKEE 3143- FINAL EXAMINATION -40 -50 -60 -70 -80 0.01 0.1 1 10 100 Frequency (rad/s) -80 -90 -100 -110 -120 -130 -140 -150 -160 -170 -180 0.01 0.1 1 Frequency (rad/s) Figure Q.5b: Open Loop Bode Plot for Q.4(b) 10 100
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Please solve the following problem.
Transcribed Image Text:(b) An open-loop transfer function with K = 1 is given as,
G(s) = =
K
s(s + 1)
The bode plot of the open-loop transfer function is shown in Figures Q.5b.
(i) Based on the margin values obtained from the plot provided, what can you
say about the stability of the system?
(ii) Using the frequency domain technique, design a compensator Ge(s)so that
the system will have the static velocity error constant K₁ = 50 sec¹,
phase margin 50° and gain margin GM about 8 dB.
Design the compensator on the given bode plot (submit it together with
your answer script). (Hint: Make the necessary adjustment on the Bode
plot so that the new K, is achieved)
(iii) Find the new compensated gain, K and give the complete transfer function
of the compensated open loop system.
(iv) Sketch the plot of the compensator Ge(s) that you proposed.
Transcribed Image Text:Phase (degree)
Magnitude (dB)
60
50
40
30
20
-10
-20
-30
11
SEEE/SKEE 3143- FINAL EXAMINATION
-40
-50
-60
-70
-80
0.01
0.1
1
10
100
Frequency (rad/s)
-80
-90
-100
-110
-120
-130
-140
-150
-160
-170
-180
0.01
0.1
1
Frequency (rad/s)
Figure Q.5b: Open Loop Bode Plot for Q.4(b)
10
100
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