Homework Answers
Derive the transfer function, vo/vi(s), in terms of G1, G2, G3, G4, G5 where Gį =...
Derive the transfer function, vo/vi(s), in terms of G1, G2, G3, G4, G5 where Gį = 1/Zį. Z2 N Via Z1 Z3 ο νο a. Derive the transfer function, vo/vi(s), if Z1 = R1, Z2 = R2,23 = R3 (i.e., resistors) and 24 = 1/sC1,25 = 1/sC2 (i.e., capacitors). b. Using Excel/Matlab/Python, etc., to draw the Bode plot of the magnitude using the following design values: R1=180k22, R2=180k12, R3=100522, C1=100nF, C2=25nF. c. What are the values of w, and Q?
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)...
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...
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?
1) Consider the directed graph below. “S” is the start state and “G1,G2,G3” are 3 goal...
1) Consider the directed graph below. “S” is the start state and “G1,G2,G3” are 3 goal states. In traversing the graph one can move only in the direction indicated by the arrows. The numbers on the edges indicate the step-cost for traversing that edge. The numbers in the nodes represent the estimated cost to the nearest goal state. In the following you will be asked to search this graph using various search strategies. When you work out your answer, please...
For the system transfer function given by: s +10 $2 x (82100.+10) 1. Identify each term in the tr...
For the system transfer function given by: s +10 $2 x (82100.+10) 1. Identify each term in the transfer function (constant, poles, zeros) (a) For any constant terms, what is the dB magnitude? What is the phase angle? (b) For any real poles not at the origin, what is the break frequency? (c) For any real zeros not at the origin, what is the break frequency? 2. Give the value of the DB magnitude and phase angle at w =...
find Consider the Transfer Function Shown Below: G(S) = (s +2) s(s + 3)(s + 5)2...
find
Consider the Transfer Function Shown Below: G(S) = (s +2) s(s + 3)(s + 5)2 a. Plot the magnitude and phase plots for each element of the above transfer function. (1 b. Plot the Bode magnitude and phase plots of the system in the given logarithmic paper. Use the plotted Bode plots to estimate the gain and phase margins of the system. (10 P d. Is the system stable or not? Explain why? (5 Pts) C.
QUESTION #2 PLEASE 1. Derive the transfer function for the circuit shown below. Plot H(s) versus...
QUESTION #2 PLEASE
1. Derive the transfer function for the circuit shown below. Plot H(s) versus frequency in Hertz, on a semilog scale. Ri 11.3 k Ri 22.6 k R R = 68.1 kN R3 C C 0.01 uF R2 Vout(s) Vin(s) C2 10 (s+5) H(s) = (s+100)(s5000) , (a) draw the magnitude Bode plot 2. For the transfer function and find the approximate maximum value of (H(jw) in dB, (b) find the value of w where 1 for w>5...
Figure 1 Problem 3 For the system shown in the above figure, where G(s) a) Draw...
Figure 1 Problem 3 For the system shown in the above figure, where G(s) a) Draw a Bode diagram of the open-loop transfer function G(s) when K 10. b) On your plot, indicate the crossover frequencies, PM, and GM. Is the closed-loop system stable with K-10? c) Determine the value of K such that the phase margin is 30°. What are the gain margin and the crossover frequencies with this K? Note: You can finish problems 2-3 with the help...
BUS 1 BUS 2 LINE 1 T1 L1 T2 G1 G2 R = 0,6 pu LINE 2 L2 T3 G3 BUS 3 a) For the above network, draw positive, negative an...
BUS 1 BUS 2 LINE 1 T1 L1 T2 G1 G2 R = 0,6 pu LINE 2 L2 T3 G3 BUS 3 a) For the above network, draw positive, negative and zero sequence networks (60 marks) b) Provide the main mathematical steps that will allow you to calculate the magnitude (in ampere) of the phase to phase fault current at BUS 1. As part of your answer you should show clearly, on a diagram, how the networks of part (a)...
Derive the transfer function, vo/vi(s), in terms of G1, G2, G3, G4, G5 where Gį = 1/Zį. Z2 N Via Z1 Z3 ο νο a. Derive the transfer function, vo/vi(s), if Z1 = R1, Z2 = R2,23 = R3 (i.e., resistors) and 24 = 1/sC1,25 = 1/sC2 (i.e., capacitors). b. Using Excel/Matlab/Python, etc., to draw the Bode plot of the magnitude using the following design values: R1=180k22, R2=180k12, R3=100522, C1=100nF, C2=25nF. c. What are the values of w, and Q?
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)...
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...
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?
For the system transfer function given by: s +10 $2 x (82100.+10) 1. Identify each term in the transfer function (constant, poles, zeros) (a) For any constant terms, what is the dB magnitude? What is the phase angle? (b) For any real poles not at the origin, what is the break frequency? (c) For any real zeros not at the origin, what is the break frequency? 2. Give the value of the DB magnitude and phase angle at w =...
find
Consider the Transfer Function Shown Below: G(S) = (s +2) s(s + 3)(s + 5)2 a. Plot the magnitude and phase plots for each element of the above transfer function. (1 b. Plot the Bode magnitude and phase plots of the system in the given logarithmic paper. Use the plotted Bode plots to estimate the gain and phase margins of the system. (10 P d. Is the system stable or not? Explain why? (5 Pts) C.
QUESTION #2 PLEASE
1. Derive the transfer function for the circuit shown below. Plot H(s) versus frequency in Hertz, on a semilog scale. Ri 11.3 k Ri 22.6 k R R = 68.1 kN R3 C C 0.01 uF R2 Vout(s) Vin(s) C2 10 (s+5) H(s) = (s+100)(s5000) , (a) draw the magnitude Bode plot 2. For the transfer function and find the approximate maximum value of (H(jw) in dB, (b) find the value of w where 1 for w>5...
Figure 1 Problem 3 For the system shown in the above figure, where G(s) a) Draw a Bode diagram of the open-loop transfer function G(s) when K 10. b) On your plot, indicate the crossover frequencies, PM, and GM. Is the closed-loop system stable with K-10? c) Determine the value of K such that the phase margin is 30°. What are the gain margin and the crossover frequencies with this K? Note: You can finish problems 2-3 with the help...
BUS 1 BUS 2 LINE 1 T1 L1 T2 G1 G2 R = 0,6 pu LINE 2 L2 T3 G3 BUS 3 a) For the above network, draw positive, negative and zero sequence networks (60 marks) b) Provide the main mathematical steps that will allow you to calculate the magnitude (in ampere) of the phase to phase fault current at BUS 1. As part of your answer you should show clearly, on a diagram, how the networks of part (a)...
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