![28. Consider the system in Figure P10.9. ISection: 10.12] 50 C(s) Delay s+2+5) FIGURE P10.9 a. Find the phase margin if the s](http://img.homeworklib.com/images/01c5b214-6825-441a-aefc-c0a87dd5b133.png?x-oss-process=image/resize,w_560)
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28. Consider the system in Figure P10.9. ISection: 10.12] 50 C(s) Delay s+2+5) FIGURE P10.9 a. Fi...
2) For the system below, find the phase margin if the system is stable for time...
2) For the system below, find the phase margin if the system is stable for time delays of 0.1 and 0.2 second. Please use Matlab to plot the frequency response of G(s) (10 pts) Delay 50 (s +2s +5) G(s)
3. Consider a unity feedback system with G(s)=- s(s+1)(s+2) a) Sketch the bode plot and find...
3. Consider a unity feedback system with G(s)=- s(s+1)(s+2) a) Sketch the bode plot and find the phase margin, gain crossover frequency, gain margin, and phase crossover frequency. b) Suppose G(s) is replaced with — - Kets s(s+1)(s+2) i. For the phase margin you have computed in (a), find the minimum value for t that makes the system marginally stable. Suppose t is 1 second. What is the range of K for stability? (You can use MATLAB for this part.)...
em Q5. Consider the Nyquist plot of the frequency response of the open-loop syst 10000 Go(s)...
em Q5. Consider the Nyquist plot of the frequency response of the open-loop syst 10000 Go(s) )(s +10) (s+50) which is shown in Figure Q5 below Real Axil 0.5 Figure Q5 (a) Write down the expression of the frequency response for this system, clearly showing the overall gain. why maximum value of an additional gain K for which the closed loop would still be stable? the corresponding point on the plot occurs at 12rad/s, what is the maximum delay xphian...
For the system shown in Figure 1, the plant transfer function is given by 50 Gp(s) = 1s + 1)(s + 2)(s+5) ( The frequenc...
For the system shown in Figure 1, the plant transfer function is given by 50 Gp(s) = 1s + 1)(s + 2)(s+5) ( The frequency response Gp(jw) is given in Table 1. Assume that the sensor gain is Hk 1.0 (a) Find the approximate gain margin and phase margin of the uncompensated sys- tem. Required Pre-Practical Work (b) Use the analytical method to design a phase-lead compensator of unity DC gain that results i a phase margin of approximately 45°...
automatic control systems
QUESTION 1: (35 points)
The transfer function of the components of a control system is given as follows:
?????: ?(?) =
2
5?
2 + 1.6? + 4
??????????: ??
(?) = ??(1 +
0.5
?
)
a) Obtain the values of ?? that makes the system stable. (10 pts.)
b) If gain margin is 1.185, find the value of ??. (5 pts.)
c) For the value of ?? found in part (b), find the phase margin. (10 pts.)
d)...
Find a & b Figure 1 shows a closed-loop control system in which G(S)-40/1 (S+2) (S+3)],...
Find a & b
Figure 1 shows a closed-loop control system in which G(S)-40/1 (S+2) (S+3)], and H(S)-1/(S+4) Y(s) H(s) Figure 2 shows the Nyquist plot for the open-loop transfer function. System: sys Real: -0.187 Imag: 2.56e-05 Frequency: (rad/s): -5.16 Using the Nyquist criterion a) Find out the gain margin expressed in dB. Is the system stable or unstable? (25 points) b) What is the value of the gain expressed in dB that makes the system marginally stable? (25 points)
Figure 1 shows a closed-loop control system in which G(S)-40/1 (5+2) (5+3)], and H(S)-1/15+4) R(s) E(S)...
Figure 1 shows a closed-loop control system in which G(S)-40/1 (5+2) (5+3)], and H(S)-1/15+4) R(s) E(S) Y(5) G(s) H(s) Figure 2 shows the Nyquist plot for the open-loop transfer function. Systemsys Real: -0.187 Imag: 2.56e-05 Frequency: (rad/s): -5.16 Using the Nyquist criterion a) Find out the gain margin expressed in dB. Is the system stable or unstable? (25 points) b) What is the value of the gain expressed in dB that makes the system marginally stable?(25 points)
P10.35 A unity feedback system has the loop transfer function -Ts Ks + 0.54 L(s) =...
P10.35 A unity feedback system has the loop transfer function -Ts Ks + 0.54 L(s) = Gc(s)G(s) = *S cos(s + 1.76) where T is a time delay and K is the controller propor- tional gain. The block diagram is illustrated in Figure P10.35. The nominal value of K = 2. Plot the phase margin of the system for 0 < T = 2 s when K = 2. What happens to the phase margin as the time delay LUDronel...
Figure 1 shows a closed-loop control system in which G(S)=40/[ (S+2) (S+3)], and H(S)=1/(S+4) R(S) E(S)...
Figure 1 shows a closed-loop control system in which G(S)=40/[ (S+2) (S+3)], and H(S)=1/(S+4) R(S) E(S) Y(s) G(S) HS) Figure 2 shows the Nyquist plot for the open-loop transfer function. Figure 2 shows the Nyquist plot for the open-loop transfer function System: sys Real: -0.187 Imag: 2.56e-05 Frequency: (rad/s): -5.16 Using the Nyquist criterion: a) Find out the gain margin expressed in dB. Is the system stable or unstable? (25 points) b) What is the value of the gain expressed...
SS10. The unity-feedback system of Figure P11.1 with K (s +4) G (s) (s 2) (s 5) (s +12) is operat...
SS10. The unity-feedback system of Figure P11.1 with K (s +4) G (s) (s 2) (s 5) (s +12) is operating with 20% overshoot. [Section: 114] a. Find the settling time. b. Find Kp c. Find the phase margin and the phase-margin frequency d. Using frequency response techniques, design a compensator that will yield a threefold improvement in Kp and a twofold reduction in settling time while keeping the overshoot at 20%.
SS10. The unity-feedback system of Figure P11.1 with...
2) For the system below, find the phase margin if the system is stable for time delays of 0.1 and 0.2 second. Please use Matlab to plot the frequency response of G(s) (10 pts) Delay 50 (s +2s +5) G(s)
3. Consider a unity feedback system with G(s)=- s(s+1)(s+2) a) Sketch the bode plot and find the phase margin, gain crossover frequency, gain margin, and phase crossover frequency. b) Suppose G(s) is replaced with — - Kets s(s+1)(s+2) i. For the phase margin you have computed in (a), find the minimum value for t that makes the system marginally stable. Suppose t is 1 second. What is the range of K for stability? (You can use MATLAB for this part.)...
em Q5. Consider the Nyquist plot of the frequency response of the open-loop syst 10000 Go(s) )(s +10) (s+50) which is shown in Figure Q5 below Real Axil 0.5 Figure Q5 (a) Write down the expression of the frequency response for this system, clearly showing the overall gain. why maximum value of an additional gain K for which the closed loop would still be stable? the corresponding point on the plot occurs at 12rad/s, what is the maximum delay xphian...
For the system shown in Figure 1, the plant transfer function is given by 50 Gp(s) = 1s + 1)(s + 2)(s+5) ( The frequency response Gp(jw) is given in Table 1. Assume that the sensor gain is Hk 1.0 (a) Find the approximate gain margin and phase margin of the uncompensated sys- tem. Required Pre-Practical Work (b) Use the analytical method to design a phase-lead compensator of unity DC gain that results i a phase margin of approximately 45°...
Find a & b
Figure 1 shows a closed-loop control system in which G(S)-40/1 (S+2) (S+3)], and H(S)-1/(S+4) Y(s) H(s) Figure 2 shows the Nyquist plot for the open-loop transfer function. System: sys Real: -0.187 Imag: 2.56e-05 Frequency: (rad/s): -5.16 Using the Nyquist criterion a) Find out the gain margin expressed in dB. Is the system stable or unstable? (25 points) b) What is the value of the gain expressed in dB that makes the system marginally stable? (25 points)
Figure 1 shows a closed-loop control system in which G(S)-40/1 (5+2) (5+3)], and H(S)-1/15+4) R(s) E(S) Y(5) G(s) H(s) Figure 2 shows the Nyquist plot for the open-loop transfer function. Systemsys Real: -0.187 Imag: 2.56e-05 Frequency: (rad/s): -5.16 Using the Nyquist criterion a) Find out the gain margin expressed in dB. Is the system stable or unstable? (25 points) b) What is the value of the gain expressed in dB that makes the system marginally stable?(25 points)
P10.35 A unity feedback system has the loop transfer function -Ts Ks + 0.54 L(s) = Gc(s)G(s) = *S cos(s + 1.76) where T is a time delay and K is the controller propor- tional gain. The block diagram is illustrated in Figure P10.35. The nominal value of K = 2. Plot the phase margin of the system for 0 < T = 2 s when K = 2. What happens to the phase margin as the time delay LUDronel...
Figure 1 shows a closed-loop control system in which G(S)=40/[ (S+2) (S+3)], and H(S)=1/(S+4) R(S) E(S) Y(s) G(S) HS) Figure 2 shows the Nyquist plot for the open-loop transfer function. Figure 2 shows the Nyquist plot for the open-loop transfer function System: sys Real: -0.187 Imag: 2.56e-05 Frequency: (rad/s): -5.16 Using the Nyquist criterion: a) Find out the gain margin expressed in dB. Is the system stable or unstable? (25 points) b) What is the value of the gain expressed...
SS10. The unity-feedback system of Figure P11.1 with K (s +4) G (s) (s 2) (s 5) (s +12) is operating with 20% overshoot. [Section: 114] a. Find the settling time. b. Find Kp c. Find the phase margin and the phase-margin frequency d. Using frequency response techniques, design a compensator that will yield a threefold improvement in Kp and a twofold reduction in settling time while keeping the overshoot at 20%.
SS10. The unity-feedback system of Figure P11.1 with...
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