Problem # 2: (60%) Consider the following proportional feedback control system, R(s) + E(s) U(s) K G₁(s) r(t) e(t) u(t) V(s) v(t) 2 of 3 where G(s) is a first-order system with the following transfer function, G,(s) = 20 5+2 V(s) (2a) Find the transfer function of the closed-loop system. (10%) R(s) E(s) (2b) Find the transfer function of the closed-loop system. (10%) R(s) (2c) Find the characteristic equation of the closed-loop system. (10%) (2d) Determine the value of K so that the time constant of the closed-loop system is 0.05 second. (10%) (2e) Let K be the value determined in (2d) and assume the reference input R(s) is an unit step function. Compute the steady-state error e = lim e(t). (10%) 1-500 (2f) Use the results of (2d) and (2e) to plot the step response v(t) and comment on how the feedback control has changed the dynamics of the system. (10%)