2. Consider a first order process with transfer function Gp(s)=s+15 Assume the transfer functions for the measuring device (Gm(s)) and control valve (G1(s)) are equal to unity. If the process is feedback controlled with a proportional controller, P with Kc=1, a) Derive the closed loop feedback response of the system to unit step change in the set point. b) Compute the value of offset for the close loop system in part (a). If the above process is feedback controlled with a proportional-integral controller, PI with Kc and 1. c) Derive an expression for the closed loop feedback response of the system to unit step change in the set point. d) Compute the value of offset if the closed loop response exhibits an offset to a unit step change in the set point. e) For Kc=1, find the value of 1 which produces an underdamped response with a decay ratio 1/4. (decayratio=exp(122))(Gc(s)=Kc(1+cs1)forPIcontrollerGc(s)=KcforPcontroller)