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I got A,B,C done can you do D,E,F
Also can you check my solutions please. Thank...
A unity feedback control system has the open loop TF as
A unity feedback control system has the open loop TF as: \(G(s)=\frac{K(s+a+1)(s+b)}{s(s+a)(s+a+2)}\)a) Find analytical expressions for the magnitude and phase response for \(\mathrm{G}(\mathrm{s}) .\left[K=K_{1}\right]\)b) Make a plot of the log-magnitude and the phase, using log-frequency in rad/s as the ordinate. \(\left[K=K_{1}\right]\)c) Sketch the Bode asymptotic magnitude and asymptotic phase plots. \(\left[K=K_{1}\right]\)d) Compare the results from \((a),(b)\), and \((c) .\left[K=K_{1}\right]\)e) Using the Nyquist criterion, find out if system is stable. Show your steps. \(\left[K=K_{1}\right]\)f) Using the Nyquist criterion, find the range...
Let G,()+3s+5) , K-1 and Ge 1 I Determine the loop transfer function L(s)-KG.G. Use 'margin' command in matlab to generate the Bode Plot for L(s). (a) What are its gain and phase margins (the...
Let G,()+3s+5) , K-1 and Ge 1 I Determine the loop transfer function L(s)-KG.G. Use 'margin' command in matlab to generate the Bode Plot for L(s). (a) What are its gain and phase margins (these should be available in the plots). (b) Convert the gain margin in dB to absolute value. (c) For what value of the gain K would the closed loop system become marginally stable? (d) Show that, for this value of K, the closed loop system does...
Problem 4: Given L(s) = K(8 + 1) s(s+3) (a) Use method 2 to sketch the...
Problem 4: Given L(s) = K(8 + 1) s(s+3) (a) Use method 2 to sketch the Nyquist plot of L(s). Do not include the pole at s = 0 in the RHP contour (i.e. assume P = O unstable open-loop poles). Note: The Bode phase function is not monotonic, but you may still use method 2. (b) Using the Nyquist stability criterion, determine the range of positive K values that will result in closed-loop stability. (c) Repeat (a) and (b),...
please solve the (a) (b) (d) 6.19 Sketch the Nyquist plot based on the Bode plots for each of the following systems, an...
please solve the (a) (b) (d)
6.19 Sketch the Nyquist plot based on the Bode plots for each of the following systems, and then compare your result with that obtained by using the Matlab command nyquist: Don't be concerned with the details of exactly where the curve goes, but do make sure it crosses the real axis at the right spot, has the correct number of -I encirclements, and goes off to infinity in the correct direction. GH (s) =...
please do part D only the matlab. thank you 3. Consider the following system s(s2 +4s...
please do part D only the matlab. thank you
3. Consider the following system s(s2 +4s 13) (a) Draw the root locus. b) Use Routh's criterion to find the range of the gain K for which the closed-loop system is stable. (continued on next page) (c) The range of K for which the system is stable can also be obtained by finding a point of the root locus that crosses the Imaginary axis. When you have an Im-axis crossing, the...
Please show all work and answer all the questions so I can learn how to do it on my own. Thank yo...
Please show all work and answer all the questions so I can learn
how to do it on my own. Thank you in advance.
(GM,PM,wcg,wepl-margin(sys) computes the gain margin GM, the phase margin PM, and the associated frequencies weg and wep. They can also be read from the Bode plot. G(s) R(s) EX G(s)- (s +10(s+1)2 Questions Draw the Bode plot when K-1, find the gain margin, and determine the closed-loop stability. (b) Convert the gain margin to a normal...
7. Consider the system with transfer function 100 G(s) = (s + 202 (a) Sketch the...
7. Consider the system with transfer function 100 G(s) = (s + 202 (a) Sketch the bode plot and Nyquist diagrams and determine the range of proportional closed loop gain K for stability. (b) What positive gain K will yield a phase margin of 30 degrees ?
6) (15 total points) For the root locus plot shown below: a) b) c) Find the...
6) (15 total points) For the root locus plot shown below: a) b) c) Find the open-loop transfer function G(s) (show as factors) (3 points) Assuming unity feedback H-1, find the characteristic equation of the closed loop transfer function (3 points). Find the gain K that the system goes unstable. Hint: express the characteristic equation in (a) as s2 + 2ơs + -0, and determine the point ơ becomes negative (6 points). Find the natural frequency of the closed loop...
Q.3(a) Transfer function model of a plant is, G(s) The controller is Ge(s)-K, where K is a constant. Find the value of K such that steady-state error for unit ramp input is 0.1. Find the gain margin...
Q.3(a) Transfer function model of a plant is, G(s) The controller is Ge(s)-K, where K is a constant. Find the value of K such that steady-state error for unit ramp input is 0.1. Find the gain margin and the phase mar gin (6 marks) (b) What are the effects on gain margin, phase margin and steady-state error, if the gain K is increased? (3 marks (c) Can the closed loop be unstable if the controller of Q.3(a) is implemented digi...
Sketch the Nyquist plots of the following loop transfer functions L(S) = Gc(s)G(s), and determine whether...
Sketch the Nyquist plots of the following loop transfer functions L(S) = Gc(s)G(s), and determine whether the system is stable by applying the Nyquist criterion: KS + 1) (b) L(s) = G (9)G(s) = 318+) If the system is stable, find the maximum value for K by determining the point where the Nyquist plot crosses the u-axis.
Let G,()+3s+5) , K-1 and Ge 1 I Determine the loop transfer function L(s)-KG.G. Use 'margin' command in matlab to generate the Bode Plot for L(s). (a) What are its gain and phase margins (these should be available in the plots). (b) Convert the gain margin in dB to absolute value. (c) For what value of the gain K would the closed loop system become marginally stable? (d) Show that, for this value of K, the closed loop system does...
Problem 4: Given L(s) = K(8 + 1) s(s+3) (a) Use method 2 to sketch the Nyquist plot of L(s). Do not include the pole at s = 0 in the RHP contour (i.e. assume P = O unstable open-loop poles). Note: The Bode phase function is not monotonic, but you may still use method 2. (b) Using the Nyquist stability criterion, determine the range of positive K values that will result in closed-loop stability. (c) Repeat (a) and (b),...
please solve the (a) (b) (d)
6.19 Sketch the Nyquist plot based on the Bode plots for each of the following systems, and then compare your result with that obtained by using the Matlab command nyquist: Don't be concerned with the details of exactly where the curve goes, but do make sure it crosses the real axis at the right spot, has the correct number of -I encirclements, and goes off to infinity in the correct direction. GH (s) =...
please do part D only the matlab. thank you
3. Consider the following system s(s2 +4s 13) (a) Draw the root locus. b) Use Routh's criterion to find the range of the gain K for which the closed-loop system is stable. (continued on next page) (c) The range of K for which the system is stable can also be obtained by finding a point of the root locus that crosses the Imaginary axis. When you have an Im-axis crossing, the...
Please show all work and answer all the questions so I can learn
how to do it on my own. Thank you in advance.
(GM,PM,wcg,wepl-margin(sys) computes the gain margin GM, the phase margin PM, and the associated frequencies weg and wep. They can also be read from the Bode plot. G(s) R(s) EX G(s)- (s +10(s+1)2 Questions Draw the Bode plot when K-1, find the gain margin, and determine the closed-loop stability. (b) Convert the gain margin to a normal...
7. Consider the system with transfer function 100 G(s) = (s + 202 (a) Sketch the bode plot and Nyquist diagrams and determine the range of proportional closed loop gain K for stability. (b) What positive gain K will yield a phase margin of 30 degrees ?
6) (15 total points) For the root locus plot shown below: a) b) c) Find the open-loop transfer function G(s) (show as factors) (3 points) Assuming unity feedback H-1, find the characteristic equation of the closed loop transfer function (3 points). Find the gain K that the system goes unstable. Hint: express the characteristic equation in (a) as s2 + 2ơs + -0, and determine the point ơ becomes negative (6 points). Find the natural frequency of the closed loop...
Q.3(a) Transfer function model of a plant is, G(s) The controller is Ge(s)-K, where K is a constant. Find the value of K such that steady-state error for unit ramp input is 0.1. Find the gain margin and the phase mar gin (6 marks) (b) What are the effects on gain margin, phase margin and steady-state error, if the gain K is increased? (3 marks (c) Can the closed loop be unstable if the controller of Q.3(a) is implemented digi...
Sketch the Nyquist plots of the following loop transfer functions L(S) = Gc(s)G(s), and determine whether the system is stable by applying the Nyquist criterion: KS + 1) (b) L(s) = G (9)G(s) = 318+) If the system is stable, find the maximum value for K by determining the point where the Nyquist plot crosses the u-axis.
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