. A feedback control system is illustrated in Fig. 2. The plant, compensator and sensor transfer functions are given by Gp(s) = R(s) 5 0.2s+1' Ge(s)= 10, H(s) = 1 Compensator G_(s) E(s) Sensor HG) MG) Plant G(s) C(s) Fig. 2. a) Write the differential equation of plant Gp(s). This equation relates c(t) and m(t). b) Find closed-loop transfer function C(s)/R(s). c) Find transfer function E(s)/R(s). d) If R (s) is the unit step, find steady-state output Css.