CP12.4 Consider the feedback control system in Figure CP12.4. The exact value of parameter b is unknown;

however, for design purposes, the nominal value is taken to be b = 4. The value of a = 8 is known very precisely. 

a. Design the proportional controller K so that the closed-loop system response to a unit step input has a settling time (with a 2% criterion) of Ts ≤ 5 s and a percent overshoot of P O. . ≤ 10%. Use the nominal value of b in the design.

b. Investigate the effects of variations in the pa

rameter b on the closed-loop system unit step response. Let b = 0, 1, 4, and 40, and co-plot the step response associated with each value of

b. In all cases, use the proportional controller from part (a). Discuss the results.

FIGURE CP12.4 A feedback control system with uncer- tain parameter b. Controller Plant 1 R(s) K s+bs+a Y(s)