Homework Answers
from the given bode plot, the phase margin is 10 degrees approximately.
therefore the final phase margin requirement = 10 + 40 = 50 degrees.
the ratio of pole to zero alpha is given by alpha = (1-sin(50))/(1+sin(50)) = 0.1325.
hould locate the frequency at which the uncompensated system has a logarithmic magnitude of -20log(1/sqrt(alpha))
Select this frequency as the new gain crossover frequency since the compensator provides a gain of 20log(1/sqrt(alpha)) at ωmax.
-20log(1/sqrt(alpha)) = -8.7778 dB
Therefore wmax = 10 rad/sec approximately.
we already know,
Therefore 10 = 1/tau*sqrt(0.1325) => tau = 1/(10*sqrt(0.1325)) = 0.2747
Therefore C(s) = (0.2747s+1)/(0.2747*0.1325*s+1) = (0.2747s+1)/(0.0364s+1)
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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....
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 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?...
You are asked to design a compensator to increase the phase margin to about 45degree without...
You are asked to design a compensator to increase the phase
margin to about 45degree without affecting the steady state
behavior and with the system bandwidth at least 4 rad/s. Would you
use a lag or lead compensator? Briefly explain.
R6 18-01-2018) as In the diagram, the block C(s) represents a compensator. The frequency response of the plant G(s) is shown below. Rode Data Magnitude (c) 40L 135 Phase (deg) .180 Frequency (rad/sec) (a) Suppose a compensator C(s) = 1...
Answers are given.. Explain with calculations how to see from bode plot which compensator it is and how is the d(s) wri...
Answers are given.. Explain with calculations how to see from
bode plot which compensator it is and how is the d(s) written?
The next two questions require the following diagram -10 -15 -20 50 -50 100 Frequency (rad/sec) 10 4. The given Bode diagram is that of a lead compensator □ lag compensator lead-lag compensator D lag-lead compensator 5. Write the transfer function of the system represented by the given Bode diagram Solution The low frequency region indicates a lag...
Consider the system shown as below. Draw a Bode diagram of the open-loop transfer function G(s).
1 Consider the system shown as below. Draw a Bode diagram of the open-loop transfer function G(s). Determine the phase margin, gain-crossover frequency, gain margin and phase-crossover frequency, (Sketch the bode diagram by hand) 2 Consider the system shown as below. Use MATLAB to draw a bode diagram of the open-loop transfer function G(s). Show the gain-crossover frequency and phase-crossover frequency in the Bode diagram and determine the phase margin and gain margin. 3. Consider the system shown as below. Design a...
Question 13 10 poi Given the open loop gan Bode plot diagram of a system, Chose...
Question 13 10 poi Given the open loop gan Bode plot diagram of a system, Chose the best sentonce that describes the closed loop system Bode Diagram 50 45 35 30 25 20 15 45 30 15 0 -15 -30 45. -60 75 -105 -120 -135 10 10 10 Frequency (radsec) O The system is stable O The system is unstable only because the gain is greater than 0 when the phase is-180 O The system is unstable only because...
consider a negative unity feedback system whose feedforward transfer function is: (s) - 1/((s+0.11(s+1)(s+10) Brawa Bode...
consider a negative unity feedback system whose feedforward transfer function is: (s) - 1/((s+0.11(s+1)(s+10) Brawa Bode plot of the open loop transfer function that includes an asymptotic and approximate estimate for both magnitude and phase. Answer he following questions Asymptotic phase lag at 1 rad/sec is _ degrees 0 -45 -90 0-135 -180 225 270 325 -360 Asymptotic phase lag at 10 rad/sec is _ degrees 0 -45 -90 0 -135 -180 -225 -270 360 none of these Asymptotic phase...
10 GH = 60 B) For the system shown in 6A calculate the magnitude and phase of response for a unit...
10 GH = 60 B) For the system shown in 6A calculate the magnitude and phase of response for a unit input with an operating speed of w=1.0 rad/sec. C) Identify the system's bandwidth, phase and gain margin as applicable directly on the asymptotic Bode plot drawn in 6A. D) Based on the phase and gain margin values found in 6C is the system stable?Yes / No) E) Apply gain compensation and solve for a new value of K for...
Prob. 5 (30 pts): You are to design a compensator for a radar antenna as shown...
Prob. 5 (30 pts): You are to design a compensator for a radar antenna as shown below. Determine G. (s) so that (a)* The closed-loop system has a bandwidth of approximately 20 rad/s. (b) The closed loop system must have positive phase margin. (6) Increase the attenuation at 200 rad/sec or higher. *You can assume that the bandwidth of the closed system is equal to the gain crossover frequency of the open loop system. You may wish to use the...
Y(s) C(s) G(s) R(S) Figure 1: Closed-loop system Q2 Consider the setup in Figure 1 with S s1 (i) ...
Y(s) C(s) G(s) R(S) Figure 1: Closed-loop system Q2 Consider the setup in Figure 1 with S s1 (i) Design a K,τ, α in the lead compensator 1TOS so that the closed-loop system shown in Figure 1 has a steady state error of.0 for a unit ramp reference input at R and a phase margin of about 45 degrees K, α, τ without Bode plots. When you add phase with the lead compensator add an additional 10 degrees of phase....
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 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?...
You are asked to design a compensator to increase the phase
margin to about 45degree without affecting the steady state
behavior and with the system bandwidth at least 4 rad/s. Would you
use a lag or lead compensator? Briefly explain.
R6 18-01-2018) as In the diagram, the block C(s) represents a compensator. The frequency response of the plant G(s) is shown below. Rode Data Magnitude (c) 40L 135 Phase (deg) .180 Frequency (rad/sec) (a) Suppose a compensator C(s) = 1...
Answers are given.. Explain with calculations how to see from
bode plot which compensator it is and how is the d(s) written?
The next two questions require the following diagram -10 -15 -20 50 -50 100 Frequency (rad/sec) 10 4. The given Bode diagram is that of a lead compensator □ lag compensator lead-lag compensator D lag-lead compensator 5. Write the transfer function of the system represented by the given Bode diagram Solution The low frequency region indicates a lag...
Question 13 10 poi Given the open loop gan Bode plot diagram of a system, Chose the best sentonce that describes the closed loop system Bode Diagram 50 45 35 30 25 20 15 45 30 15 0 -15 -30 45. -60 75 -105 -120 -135 10 10 10 Frequency (radsec) O The system is stable O The system is unstable only because the gain is greater than 0 when the phase is-180 O The system is unstable only because...
consider a negative unity feedback system whose feedforward transfer function is: (s) - 1/((s+0.11(s+1)(s+10) Brawa Bode plot of the open loop transfer function that includes an asymptotic and approximate estimate for both magnitude and phase. Answer he following questions Asymptotic phase lag at 1 rad/sec is _ degrees 0 -45 -90 0-135 -180 225 270 325 -360 Asymptotic phase lag at 10 rad/sec is _ degrees 0 -45 -90 0 -135 -180 -225 -270 360 none of these Asymptotic phase...
10 GH = 60 B) For the system shown in 6A calculate the magnitude and phase of response for a unit input with an operating speed of w=1.0 rad/sec. C) Identify the system's bandwidth, phase and gain margin as applicable directly on the asymptotic Bode plot drawn in 6A. D) Based on the phase and gain margin values found in 6C is the system stable?Yes / No) E) Apply gain compensation and solve for a new value of K for...
Prob. 5 (30 pts): You are to design a compensator for a radar antenna as shown below. Determine G. (s) so that (a)* The closed-loop system has a bandwidth of approximately 20 rad/s. (b) The closed loop system must have positive phase margin. (6) Increase the attenuation at 200 rad/sec or higher. *You can assume that the bandwidth of the closed system is equal to the gain crossover frequency of the open loop system. You may wish to use the...
Y(s) C(s) G(s) R(S) Figure 1: Closed-loop system Q2 Consider the setup in Figure 1 with S s1 (i) Design a K,τ, α in the lead compensator 1TOS so that the closed-loop system shown in Figure 1 has a steady state error of.0 for a unit ramp reference input at R and a phase margin of about 45 degrees K, α, τ without Bode plots. When you add phase with the lead compensator add an additional 10 degrees of phase....
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