Homework Answers
DC gain is the magnitude of the transfer fucntion at frequency = 0 i.e 10^0
From the plot the gain at that point is definately below the halfway point of 0 and 20dB and approximatel 1/4th of the way up from 0dB, so around 5dB
Crossover frequency is the frequency where gain drops by 3dB i.e. gain -3dB compared to DC
5-3 = 2dB, that point is somewhere between 2 and 4 on the log scaled plot (between 10^0 = 0 and 10^1 = 10)
So best approximation is answer (C)
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Determine DC gain and crossover frequency from the following Bode plots. Magnitude (dB) Phase (deg) -180...
a. For the following Bode diagram, determine: Bode Diagram (7 marks Magnitude (dB) Phase (deg! Frequency...
a. For the following Bode diagram, determine: Bode Diagram (7 marks Magnitude (dB) Phase (deg! Frequency (rad/s! 1. The gain margin. 2. The phase margin. 3. Gain crossover frequency. 4. Phase crossover frequency. 5. Comment on the stability of this system.
752) See Figure 752. D-4. The Bode gain and phase plots for a RC circuit are phase (deg), and frequency B. Also find the other shown in the fig. Determine gain (dB), (rad/sec) for the points la...
752) See Figure 752. D-4. The Bode gain and phase plots for a RC circuit are phase (deg), and frequency B. Also find the other shown in the fig. Determine gain (dB), (rad/sec) for the points labeled A and exponents. Answers: GdBA, phA, wA, GdBB, phB,wB,C, E,F. ans:9 Bode Gain and Phase Plots Gain in dB 6 -10 12.64 10 Frequency in rad/sec 10 10 Phase in deg 765 40 10 F 4764 Frequency in rad/sec Figure 752 10 10...
The Bode plots for a plant, G(s), used in a unity feedback system are shown in Figure P10.7. Do the following: Find the gain margin, phase margin, zero dB frequency, 180° frequency, and the closed-l...
The Bode plots for a plant, G(s), used in a unity feedback
system are shown in Figure P10.7. Do the following:
Find the gain margin, phase margin, zero dB frequency, 180°
frequency, and the closed-loop bandwidth.
Use your results in Part a to estimate the damping ratio,
percent overshoot, settling time, and peak time.
ANSWERS GIVEN BY PROFESSOR
1. Gain margin = 20dB, Phase margin = 55 deg, Zero dB frequency
= 1rad/s, 180deg frequency = 4.5rad/s, bandwidth (-7dB) closed-loop...
Q2. Fill in the following table based on the magnitude and phase plots shown below. Freq...
Q2. Fill in the following table based on the magnitude and phase plots shown below. Freq (rad/s) Mag (dB) Mag Phase 40 20 0 -20 -40 .1 Magnitude (dB) 1 2 100 10 Frequency w rad/s) 5 90 10 45 0 Phase (deg) 40 -45 -90 -135 -180 100 10 100 Frequency w rad/s)
Consider the system given below where K is a constant gain, Gp is the plant, and Ge is a compensator. The Bode Plots of a Gp is given below. Problem 1: Bode Diagram 20 2 40 -60 80 -100 90 135 180 a 2...
Consider the system given below where K is a constant gain, Gp is the plant, and Ge is a compensator. The Bode Plots of a Gp is given below. Problem 1: Bode Diagram 20 2 40 -60 80 -100 90 135 180 a 225 270 101 10 Frequency (rad/s) 102 a. Looking at the low frequency behavior, determine its number of poles at origin. Explain. b. Looking at the high frequency behavior, determine the number of excess poles. Explain. C....
5. Consider the feedback system in Figure 4 where! G(s) = 26+10% Figure 4 The Bode...
5. Consider the feedback system in Figure 4 where! G(s) = 26+10% Figure 4 The Bode plot of G is shown in Figure 5. Boda Diagram Magnitude (dB) -100- -156 -135 -root -225 10 Frequency radici Figure 5: Bode plot of G (a) [2 marks] Find the phase margin, gain margin and gain crossover frequency (approximate as needed) for the case when C(s) = 1. PM = GM = wc = You are asked to design a feedback controller C(s)...
Consider the following magnitude and phase plot of a minimum phase system. Please answer the following and explain. Consider the following magnitude and phase plot of a minimum phase system. Is this...
Consider the following magnitude and phase plot of a minimum
phase system. Please answer the following and explain.
Consider the following magnitude and phase plot of a minimum phase system. Is this system stable or unstable? Explain your answer. Bode Diagram: Minimum-Phase Systenm 100 Gain Crossover 40 -60 80 100 90 135 -180 225 -270 -360 Phase Crossover Op Og Frequency (rad/sec)
Consider the following magnitude and phase plot of a minimum phase system. Is this system stable or unstable?...
Sketch the Bode plots for a stable three-pole amplifier with dc gain 10^5 whose poles have magnit...
Sketch the Bode plots for a stable three-pole amplifier with dc
gain 10^5 whose poles have magnitudes 0.1 MHz, 1 MHz and 10 MHz.
Find the gain margin and phase margin of the amplifier if it is
connected in a feedback loop with (a) unity feedback factor; (b)
feedback factor 5.623 x 10^-5; (c) closed-loop dc gain 50 dB. In
each case indicate whether the closed-loop amplifier is stable or
unstable. What is the minimum stable closed-loop dc gain of...
Low frequency DC gain is db 0 10 O 100 none of these Question 2 Low...
Low frequency DC gain is db 0 10 O 100 none of these Question 2 Low frequency DC phase lag is __ degrees OO O-90 O-180 O -270 O-360 none of these Question 3 Asymptotic magnitude slope at 5 rad/sec is __db/decade O 0 -20 O-40 O -60 O -80 - 100 none of these Question 4 Asymptotic magnitude slope at 50 rad/sec is _ db/decade -20 -40 -60 -80 O - 100 none of these
For the following closed-loop transfer functions, sketch the bode plots (magnitude and phase), id...
For the following closed-loop transfer functions, sketch the bode plots (magnitude and phase), iden- tifying the zero gain, the slopes (in Decibels) and the high-frequency cutt-off rate. Then verify with Matlab C()101 100) s 0.1) (s 10) 100 s(s +10)2 G(s) = (56) G(s) = s+10(s+100)
For the following closed-loop transfer functions, sketch the bode plots (magnitude and phase), iden- tifying the zero gain, the slopes (in Decibels) and the high-frequency cutt-off rate. Then verify with Matlab C()101 100) s...
a. For the following Bode diagram, determine: Bode Diagram (7 marks Magnitude (dB) Phase (deg! Frequency (rad/s! 1. The gain margin. 2. The phase margin. 3. Gain crossover frequency. 4. Phase crossover frequency. 5. Comment on the stability of this system.
752) See Figure 752. D-4. The Bode gain and phase plots for a RC circuit are phase (deg), and frequency B. Also find the other shown in the fig. Determine gain (dB), (rad/sec) for the points labeled A and exponents. Answers: GdBA, phA, wA, GdBB, phB,wB,C, E,F. ans:9 Bode Gain and Phase Plots Gain in dB 6 -10 12.64 10 Frequency in rad/sec 10 10 Phase in deg 765 40 10 F 4764 Frequency in rad/sec Figure 752 10 10...
The Bode plots for a plant, G(s), used in a unity feedback
system are shown in Figure P10.7. Do the following:
Find the gain margin, phase margin, zero dB frequency, 180°
frequency, and the closed-loop bandwidth.
Use your results in Part a to estimate the damping ratio,
percent overshoot, settling time, and peak time.
ANSWERS GIVEN BY PROFESSOR
1. Gain margin = 20dB, Phase margin = 55 deg, Zero dB frequency
= 1rad/s, 180deg frequency = 4.5rad/s, bandwidth (-7dB) closed-loop...
Q2. Fill in the following table based on the magnitude and phase plots shown below. Freq (rad/s) Mag (dB) Mag Phase 40 20 0 -20 -40 .1 Magnitude (dB) 1 2 100 10 Frequency w rad/s) 5 90 10 45 0 Phase (deg) 40 -45 -90 -135 -180 100 10 100 Frequency w rad/s)
Consider the system given below where K is a constant gain, Gp is the plant, and Ge is a compensator. The Bode Plots of a Gp is given below. Problem 1: Bode Diagram 20 2 40 -60 80 -100 90 135 180 a 225 270 101 10 Frequency (rad/s) 102 a. Looking at the low frequency behavior, determine its number of poles at origin. Explain. b. Looking at the high frequency behavior, determine the number of excess poles. Explain. C....
5. Consider the feedback system in Figure 4 where! G(s) = 26+10% Figure 4 The Bode plot of G is shown in Figure 5. Boda Diagram Magnitude (dB) -100- -156 -135 -root -225 10 Frequency radici Figure 5: Bode plot of G (a) [2 marks] Find the phase margin, gain margin and gain crossover frequency (approximate as needed) for the case when C(s) = 1. PM = GM = wc = You are asked to design a feedback controller C(s)...
Consider the following magnitude and phase plot of a minimum
phase system. Please answer the following and explain.
Consider the following magnitude and phase plot of a minimum phase system. Is this system stable or unstable? Explain your answer. Bode Diagram: Minimum-Phase Systenm 100 Gain Crossover 40 -60 80 100 90 135 -180 225 -270 -360 Phase Crossover Op Og Frequency (rad/sec)
Consider the following magnitude and phase plot of a minimum phase system. Is this system stable or unstable?...
Sketch the Bode plots for a stable three-pole amplifier with dc
gain 10^5 whose poles have magnitudes 0.1 MHz, 1 MHz and 10 MHz.
Find the gain margin and phase margin of the amplifier if it is
connected in a feedback loop with (a) unity feedback factor; (b)
feedback factor 5.623 x 10^-5; (c) closed-loop dc gain 50 dB. In
each case indicate whether the closed-loop amplifier is stable or
unstable. What is the minimum stable closed-loop dc gain of...
Low frequency DC gain is db 0 10 O 100 none of these Question 2 Low frequency DC phase lag is __ degrees OO O-90 O-180 O -270 O-360 none of these Question 3 Asymptotic magnitude slope at 5 rad/sec is __db/decade O 0 -20 O-40 O -60 O -80 - 100 none of these Question 4 Asymptotic magnitude slope at 50 rad/sec is _ db/decade -20 -40 -60 -80 O - 100 none of these
For the following closed-loop transfer functions, sketch the bode plots (magnitude and phase), iden- tifying the zero gain, the slopes (in Decibels) and the high-frequency cutt-off rate. Then verify with Matlab C()101 100) s 0.1) (s 10) 100 s(s +10)2 G(s) = (56) G(s) = s+10(s+100)
For the following closed-loop transfer functions, sketch the bode plots (magnitude and phase), iden- tifying the zero gain, the slopes (in Decibels) and the high-frequency cutt-off rate. Then verify with Matlab C()101 100) s...
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