Solve d and e • The unity feedback control structure has the following block diagram:wC(s)P(s) Suppose the open-loop unstable plant,1P(s) =s2s +4and the controller,ksC(s) =(s + 10)are structured in a unity feedback control scheme.(a)Find the closed-loop transfer function from r to y as a ratio of polynomials in s:Y(s)G(s) =R(s)bmsm + bm-1sm-1ans" + an-18n-1 ++ bịs + bo+ a1s + ao+......(b)Find the range of k such that the closed-loop system G(s) is stable.(c)Regarding the steady-state error for tracking, what is the System TYPE?(d)Assume k = 10. Can this system track the reference input r(t) = 1 perfectly? If YES,justify your answer. If NO, what is the actual steady-state error e(0)?(e)Suppose the above controller is replaced by a controller of the form:kC1(s)Determine whether a controller of this form can produce a stable closed-loop system capableof tracking a step reference with zero steady-state-error e()step = 0.

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(d) justify your answer. If NO, what is the actual steady-state error e(0)? Assume k = 10. Can this system track the reference input r(t) = 1 perfectly? If YES, (e) Suppose the above controller is replaced by a controller of the form: k Ci (s): Determine whether a controller of this form can produce a stable closed-loop system capable of tracking a step reference with zero steady-state-error e()step = 0.