where Consider the following feedback system shown below, R(s)- G(s) G(s) H(s) Gc(s) = kp S Y(s) Gp(s) = (s + 3) + 16 H(s) = e-sto a) For the feedback system shown above, determine the expressions for the sensitivity of the poles with respect to the proportional gain, kp, and the delay time, to. b) In general, determining the exact poles of a feedback system with delay is nontrivial. However, when to is sufficiently small, we may consider the system without delay as the nominal system, and use certain characteristics of the nominal system to approximate the poles of the system with delay. For the nominal system, kp = 6. Find the approximate poles of the system shown above if Akp = 0.48 (change in the proportional gain) and to = 0.0025 (which we may assume to be sufficiently small).