A process with the transfer function Gp = 1/+1is to be controlled by a PD controller. Gc = Kc(1+Ds). The measurement element Gm(s) is =1//6+1 . The control valve (Gv) and Km are both 1. Derive the closed loop transfer function and based on the characteristic equation derive expressions for and (Hint: compare the characteristic equation with the standard second order,2s2+2s+1, system to get and ). Determine the value of for (a) D = 0 and Kc = 4.167 (b) D = 0.05 and Kc = 22. In which case (a) or (b), do you expect more oscillatory response. Compare the offset in the two cases.