Consider a feedback control system with a PID controller: R + Kp + K S C(s) + KDS + + D 1 S +3.65 +9 P(s) Y where R, D, and Yare reference, disturbance, and output respectively. C(s) and P(s) are transfer functions of the controller and plant respectively. A. Please give the expressions of the (two) closed-loop transfer functions for the responses from R to Y and from D to Y. They should have the same denominator (bottom) polynomial (a.k.a., the closed-loop characteristic polynomial). B. Assume that it's desirable to have the closed-loop poles located at p =-10, P3 = -2 j23 for a good balance of response and stability. In other words, it is desirable to have the closed-loop characteristic polynomial equal to (s-P) (s - P) (SP3). What should the P, I, and D gains equal to?