Problem 7. For the feedback control system given in the figure on the right, R(s) +...

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Problem 7. For the feedback control system given in the figure on the right, R(s) + 1 C(s) K s(s + 2)(s + 5) (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. () 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. Problem 7. For the feedback control system given in the figure on the right, R(s) + 1 C(s) K s(s + 2)(s + 5) (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. () 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.