Consider the following feedback control system. Assume H(s)=F(s)=1 and 4 (s)=D(s)=0. The plant transfer function is: P(s) = Consider a Proportional (P) Control %3D (2s+1)(0.5s+1) (s) = Kp. (a) What is the closed-loop transfer function? What are the expressions of the closed-loop poles? (b) What is the allowed region of the closed-loop poles on the complex plane such that the %OS is less than 10% and that the 2% settling time is less than 6 sec? What is the corresponding range of K,? (c) Plot the step response of the closed-loop system when K, = 0.5. (d) Does the response obtained in (c) satisfy the requirements in (b)? Is the steady-state error zero? Disturbance D(s) Actuating Signal EA(s) Output Reference nput R(s) Control Input Y(s) F(s) C(s) P(s) U(s) + Plant Pre-filter Controller H(s) Noise N(s) Consider the same feedback control system as in Problem 1. Again, assume 4 |(s)=F(s)=l and N(s)=D(s)=0. The plant transfer function is still: P(s) = Now, consider a (2s+1)(0.5s+1) roportional-Integral (PI) Control C(s) = Kp + K; -. (a) What is the closed-loop transfer function? (b) Plot the step response of the closed-loop system when Kp = 5 and K¡ = 3. %3D (c) From the plot, is the steady-state error zero?