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3. (28 pts.) The unity feedback system with K(5+3) G(s) = (s + 1)(s + 4)(s...
3. (28 pts.) The unity feedback system with K(5+3) G(s) = (s + 1)(s + 4)(s + 10) is operating with 12% overshoot ({=0.56). (a) the root locus plot is below, find the settling time (b) find ko (c) using frequency response techniques, design a lead compensator that will yield a twofold improvement in K, and a twofold reduction in settling time while keeping the overshoot at 12%; the Bode plot is below using the margin command and using the...
You may prepare your answer in softcopy, print out and submit or use hardcopy approach. Put...
You may prepare your answer in softcopy, print out and submit or use hardcopy approach. Put all your MATLAB codes and Simulink Diagram under the appendix. The system below is to be compensated to achieve a phase margin of 50 degrees. s +3 x(t) 5+2s+ 2s E-KH. yệt) Design gain and phase-lead compensator to achieve the desired PM of 45 degrees. +PART A: Uncompensated system analysis % created by Fakhera 2020 Determine the uncompensated PM and GM s=tf('s'); g= (5+3)/...
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....
please show steps 5. GH(s) is a minimum-phase system which has the Bode plot shown below. It is desired to increase the phase margin by 40 degrees and also increase the closed-loop system bandwidth....
please show steps
5. GH(s) is a minimum-phase system which has the Bode plot shown below. It is desired to increase the phase margin by 40 degrees and also increase the closed-loop system bandwidth. Design a lead compensator for this purpose. Determine (1) the ratio of the pole to the zero, α , (2) the frequency where the maximum phase shift from the compensator should be placed, and then (3) the pole and zero. You need not draw the Bode...
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)...
b- Consider a unity feed- back control system has (S+1 +)(S+2) (S+1-j) 3 4S2 6S +...
b- Consider a unity feed- back control system has (S+1 +)(S+2) (S+1-j) 3 4S2 6S + 4 a-Prove that as K-8 the gain margin-7.96 db at 2.45 rad/sec. and the phase margin 44.1 degrees at 1.56 rad/sec.? b-Sketch the polar plot? c-Sketch the Bode plot? d- Sketch the Nichols plot and Show Gm and Ym on the plots? e-Write short MATLAB program to solve a, b, c and d?
Question 3 (10 +10+10+15 45 marks) E(s) C(s) R(s) Figure 3: Unity feedback control system for Question 3 For the unity...
Question 3 (10 +10+10+15 45 marks) E(s) C(s) R(s) Figure 3: Unity feedback control system for Question 3 For the unity feedback control system shown in Figure 3, 100 G(S) (s+2)(+10) Page 3 of 7 NEE3201 Examination Paper CRICOS Provider No: 00124k a) Determine the phase margin, the gain crossover frequency, the gain margin, the phase crossover frequency of the system when Gc(s)-1, 10 marks) b) Design a proportional controller Gc(s)-K so that a phase margin of 50° is achieved....
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...
Consider the following unity feedback system for Problems 2-3 R(9) —tqKAG YIS) Figure 1 Problem 2...
Consider the following unity feedback system for Problems 2-3 R(9) —tqKAG YIS) Figure 1 Problem 2 Consider the system shown in the above figure, where G(s) = s(8+1128+1) a) Draw a Bode diagram of the open-loop transfer function G(s) when K=1. b) On your plot, indicate the crossover frequencies, PM, and GM. Is the closed-loop system stable with K=1? c) Determine the range of K for which the closed-loop systems will be stable. d) Verify your answer in (c) using...
Consider the transfer function of a DC motor given by G(s) = 1 / s(s+2) 3. Consider the transfer function of a DC motor...
Consider the transfer function of a DC motor given by G(s) = 1 /
s(s+2)
3. Consider the transfer function of a DC motor given by 1 G(s) s (s2) The objective of this question is to consider the problem of control design for this DC motor, with the feedback control architecture shown in the figure below d(t r(t) e(t) e(t) C(s) G(s) Figure 4: A feedback control system (a) Find the magnitude and the phase of the frequency response...
3. (28 pts.) The unity feedback system with K(5+3) G(s) = (s + 1)(s + 4)(s + 10) is operating with 12% overshoot ({=0.56). (a) the root locus plot is below, find the settling time (b) find ko (c) using frequency response techniques, design a lead compensator that will yield a twofold improvement in K, and a twofold reduction in settling time while keeping the overshoot at 12%; the Bode plot is below using the margin command and using the...
You may prepare your answer in softcopy, print out and submit or use hardcopy approach. Put all your MATLAB codes and Simulink Diagram under the appendix. The system below is to be compensated to achieve a phase margin of 50 degrees. s +3 x(t) 5+2s+ 2s E-KH. yệt) Design gain and phase-lead compensator to achieve the desired PM of 45 degrees. +PART A: Uncompensated system analysis % created by Fakhera 2020 Determine the uncompensated PM and GM s=tf('s'); g= (5+3)/...
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....
please show steps
5. GH(s) is a minimum-phase system which has the Bode plot shown below. It is desired to increase the phase margin by 40 degrees and also increase the closed-loop system bandwidth. Design a lead compensator for this purpose. Determine (1) the ratio of the pole to the zero, α , (2) the frequency where the maximum phase shift from the compensator should be placed, and then (3) the pole and zero. You need not draw 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)...
b- Consider a unity feed- back control system has (S+1 +)(S+2) (S+1-j) 3 4S2 6S + 4 a-Prove that as K-8 the gain margin-7.96 db at 2.45 rad/sec. and the phase margin 44.1 degrees at 1.56 rad/sec.? b-Sketch the polar plot? c-Sketch the Bode plot? d- Sketch the Nichols plot and Show Gm and Ym on the plots? e-Write short MATLAB program to solve a, b, c and d?
Question 3 (10 +10+10+15 45 marks) E(s) C(s) R(s) Figure 3: Unity feedback control system for Question 3 For the unity feedback control system shown in Figure 3, 100 G(S) (s+2)(+10) Page 3 of 7 NEE3201 Examination Paper CRICOS Provider No: 00124k a) Determine the phase margin, the gain crossover frequency, the gain margin, the phase crossover frequency of the system when Gc(s)-1, 10 marks) b) Design a proportional controller Gc(s)-K so that a phase margin of 50° is achieved....
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...
Consider the following unity feedback system for Problems 2-3 R(9) —tqKAG YIS) Figure 1 Problem 2 Consider the system shown in the above figure, where G(s) = s(8+1128+1) a) Draw a Bode diagram of the open-loop transfer function G(s) when K=1. b) On your plot, indicate the crossover frequencies, PM, and GM. Is the closed-loop system stable with K=1? c) Determine the range of K for which the closed-loop systems will be stable. d) Verify your answer in (c) using...
Consider the transfer function of a DC motor given by G(s) = 1 /
s(s+2)
3. Consider the transfer function of a DC motor given by 1 G(s) s (s2) The objective of this question is to consider the problem of control design for this DC motor, with the feedback control architecture shown in the figure below d(t r(t) e(t) e(t) C(s) G(s) Figure 4: A feedback control system (a) Find the magnitude and the phase of the frequency response...
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