Homework Answers
ANSWER PART-A) - When time delay increase then phase margin decreases as due to time delay e^-t times a factor is introduced which is equals to 57.32 omega times of t when delay increases this causes a decrease in phase margin which also decreases stability.
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System dynamics and control
4. A Controller K is used to control the angle y, of...
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...
The Bode diagram of the forward-nath transfer function of a unity-feedback control system is obtained experimentally when the forward gain Kis set at its nominal valuc. (a) Find the gain and phase ma...
The Bode diagram of the forward-nath transfer function of a unity-feedback control system is obtained experimentally when the forward gain Kis set at its nominal valuc. (a) Find the gain and phase margins of the system from the diagram as best you can read them. Find the gain- and phase-crossover frequencies. (b) Repeat part (a) if the gain is doubled from its nominal value. (c) Repeat part (a) if the gain is 10 times its nominal value. (d) Find out...
Determine the proportioanl gain constant Kp and T such that the bandwidth of the closed-loop system...
Determine the proportioanl gain constant Kp and T such that the
bandwidth of the closed-loop system is around 0.55 rad/sec and an
overshoot of around 9%. Note that the closed-loop bandwidth is
close to the gain crossover (cut-off) frequency. Check your design
in both frequency and time domain and comment. Determine the
maximum overshoot and settling time. Determine as well, using a
Bode diagram, the expression of the stead state closed loop output
for a sinusodial input with 0 deg...
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)...
6) The open loop transfer function of a control system is 10-011. Ata frequency of 1...
6) The open loop transfer function of a control system is 10-011. Ata frequency of 1 Hz, the system phase shift is: (1) 0.9 kg (2) 5.7" tag (3) 18 (6) 36"lag (5) none of the above h) The open-loop transfer function of control system is 10 At high frequencies, the gain will: (1) be constant (2) roll off at -20 d/decade (3) roll off at -40 dB/decade (6) roll off at 60 dB/decade The open-loop transfer function of a...
Note: Course Name: Automatic Control Systems. Please help me to solve this problem step-by-step. And thank...
Note: Course Name: Automatic Control Systems. Please help me to
solve this problem step-by-step. And thank very much for your great
support and time.
3. (10 points) Suppose the feedback system from problem #2 has a delay of Td seconds in reporting sensor data so that the feedback system is R(s + Y (s) G(s) Delay of Ts The frequency response of G(s) is repeated for convenience. If Td - 0, find the phase and gain margins. What is the...
A1 A water heating system is represented by the block diagram shown in figure A1. The valve mixes hot and cold water to obtain the desired water temperature using an integral controller of gain K. Th...
A1 A water heating system is represented by the block diagram shown in figure A1. The valve mixes hot and cold water to obtain the desired water temperature using an integral controller of gain K. The water temperature is controlled by sensing the output temperature 0o and comparing with the desired temperature 0d. Write down an expression, in Bode form, for the open-loop frequency response function in terms of K and frequency o. Hence draw the open-loop Bode plot for...
8) A three-phase thyristor controlled converter is used to drive a motor system. What is the...
8) A three-phase thyristor controlled converter is used to drive a motor system. What is the required trigger delay angle a if the required average output DC voltage is 0.5Vm [2 points) a) 90 degrees. b) 45 degrees. c) 58.43 degrees. d) O degrees. 9) A 3-point motor starter arrangement is shown in the diagram below (1 point). Starting Resistence No volt col OFF Soft ron piece Starter handie Spring Over load release Lever Trangular iron Three Point Starter As...
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...
G) r(t) Figure 1: Feedback control system A pulley and belt transmission has a linearized relationship between the driven pulley angle θ(t) in degrees and the input torque u(t) in Newton meters given...
G) r(t) Figure 1: Feedback control system A pulley and belt transmission has a linearized relationship between the driven pulley angle θ(t) in degrees and the input torque u(t) in Newton meters given by the following differential equation du(t) A feedback control system (illustrated in Figure 1) needs to be designed such that the closed-loop system is asymptotically stable and such that the following design criteria are met: 1. the gain crossover frequency a should be between and a 2....
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...
The Bode diagram of the forward-nath transfer function of a unity-feedback control system is obtained experimentally when the forward gain Kis set at its nominal valuc. (a) Find the gain and phase margins of the system from the diagram as best you can read them. Find the gain- and phase-crossover frequencies. (b) Repeat part (a) if the gain is doubled from its nominal value. (c) Repeat part (a) if the gain is 10 times its nominal value. (d) Find out...
Determine the proportioanl gain constant Kp and T such that the
bandwidth of the closed-loop system is around 0.55 rad/sec and an
overshoot of around 9%. Note that the closed-loop bandwidth is
close to the gain crossover (cut-off) frequency. Check your design
in both frequency and time domain and comment. Determine the
maximum overshoot and settling time. Determine as well, using a
Bode diagram, the expression of the stead state closed loop output
for a sinusodial input with 0 deg...
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)...
6) The open loop transfer function of a control system is 10-011. Ata frequency of 1 Hz, the system phase shift is: (1) 0.9 kg (2) 5.7" tag (3) 18 (6) 36"lag (5) none of the above h) The open-loop transfer function of control system is 10 At high frequencies, the gain will: (1) be constant (2) roll off at -20 d/decade (3) roll off at -40 dB/decade (6) roll off at 60 dB/decade The open-loop transfer function of a...
Note: Course Name: Automatic Control Systems. Please help me to
solve this problem step-by-step. And thank very much for your great
support and time.
3. (10 points) Suppose the feedback system from problem #2 has a delay of Td seconds in reporting sensor data so that the feedback system is R(s + Y (s) G(s) Delay of Ts The frequency response of G(s) is repeated for convenience. If Td - 0, find the phase and gain margins. What is the...
A1 A water heating system is represented by the block diagram shown in figure A1. The valve mixes hot and cold water to obtain the desired water temperature using an integral controller of gain K. The water temperature is controlled by sensing the output temperature 0o and comparing with the desired temperature 0d. Write down an expression, in Bode form, for the open-loop frequency response function in terms of K and frequency o. Hence draw the open-loop Bode plot for...
8) A three-phase thyristor controlled converter is used to drive a motor system. What is the required trigger delay angle a if the required average output DC voltage is 0.5Vm [2 points) a) 90 degrees. b) 45 degrees. c) 58.43 degrees. d) O degrees. 9) A 3-point motor starter arrangement is shown in the diagram below (1 point). Starting Resistence No volt col OFF Soft ron piece Starter handie Spring Over load release Lever Trangular iron Three Point Starter As...
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...
G) r(t) Figure 1: Feedback control system A pulley and belt transmission has a linearized relationship between the driven pulley angle θ(t) in degrees and the input torque u(t) in Newton meters given by the following differential equation du(t) A feedback control system (illustrated in Figure 1) needs to be designed such that the closed-loop system is asymptotically stable and such that the following design criteria are met: 1. the gain crossover frequency a should be between and a 2....
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