AP4.7 A feedback control system with sensor noise and a disturbance input is shown in Figure AP4.7. The goal is to reduce the effects of the noise and the disturbance.

Let R1s2 = 0.

(a) Determine the effect of the disturbance on Y1s2.

(b) Determine the effect of the noise on Y1s2.

(c) Select the best value for K when 1 … K … 100 so that the effect of steady-state error due to the disturbance and the noise is minimized. Assume Td1s2 = A>s, and N1s2 = B>s.

FIGURE AP4.7 Feedback system with noise. Controller Disturbance T(s) Dynamics K R(s) S N(s) Sensor noise s+ Sensor K =1 Y(s)