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Consider a unity feedback system with forward (open-loop) Transfer Function, G(s)= K s+1/s(s+2) a) What are the open-loop poles and zeros? Plot them on the complex plane as we discussed in class. b) Find the closed-loop transfer function T(s) = C(s)/R(s). c) Solve for the closed-loop poles as a function of K. d) What are the closed-loop poles for K = 0, 1, 10, 100? Plot them on the complex plane as we discussed in class. e) Discuss what happens to each of the closed-loop poles as K increases. Where do they approaches ∞.

Consider a unity feedback system with forward (open-loop) Transfer Function, G(s)= K s+1/s(s+2) a) What are the open-loop poles and zeros? Plot them on the complex plane as we discussed in class. b) Find the closed-loop transfer function T(s) = C(s)/R(s). c) Solve for the closed-loop poles as a function of K. d) What are the closed-loop poles for K = 0, 1, 10, 100? Plot them on the complex plane as we discussed in class. e) Discuss what happens to each of the closed-loop poles as K increases. Where do they approaches ∞.

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Consider a unity feedback system with forward (open-loop) Transfer Function, G(s)= K s+1/s(s+2) a) What are the open-loop poles and zeros? Plot them on the complex plane as we discussed in class. b) Find the closed-loop transfer function T(s) = C(s)/R(s). c) Solve for the closed-loop poles as a function of K. d) What are the closed-loop poles for K = 0, 1, 10, 100? Plot them on the complex plane as we discussed in class. e) Discuss what happens to each of the closed-loop poles as K increases. Where do they approaches ∞.

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Problem 7. For the feedback control system given in the figure on the right, (a) Find the closed-loop transfer function, C(s)/R(s). (b) Determine the system's stability range for gain K using Routh-Hurwitz criterion. (c) What is the type of the system? (You need to convert the system to a simple unity feedback. ) (d) Sketch the root-locus in Matlab (you need to use the open-loop transfer function with K = 1 ) and validate the stability region you found in (b). (e) Plot the step response up to 10 seconds for the input of 1.5u(t) and the gain value that makes the system marginally stable. (f) Find the steady-state error for an input step of 1.5u(t) for K = 22 and plot this response together with the input up to 10 seconds in order to display the steady-state error you computed. (g) Find the steady-state error for an input ramp of 1.5tu(t) for K = 22 and plot this response together with the input up to 10 seconds in order to indicate the steady-state error you computed.

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(a) Find the closed-loop transfer function, C(s)/R(s). (b) Determine the system's stability range for gain K using Routh-Hurwitz criterion. (c) What is the type of the system? (You need to convert the system to a simple unity feedback. ) (d) Sketch the root-locus in Matlab (you need to use the open-loop transfer function with K = 1) and validate the stability region you found in (b). (e) Plot the step response up to 10 seconds for the input of 1.5u(t) and the gain value that makes the system marginally stable. (f) Find the steady-state error for an input step of 1.5u(t) for K = 22 and plot this response together with the input up to 10 seconds in order to display the steady-state error you computed. (g) Find the steady-state error for an input ramp of 1.5tu(t) for K = 22 and plot this response together with the input up to 10 seconds in order to indicate the steady-state error you computed.

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