Consider the process under feedback control with transfer functions below. Gc=5Gf=1Gp=(s+1)(3s+1)2Gd=(s+1)(3s+1)1Gm=1 For a set point step change of magnitude 2 a) Derive an expression for the closed loop response in the Laplace domain. b) Find how the closed loop output responds with time to the set point change above. c) Compute the maximum value of y(t). d) Compute the offset of the final steady state. e) Compute the period of oscillation of the closed loop response. f) Give a qualitative sketch of the closed loop response