Question

Please solve part b and c and d !!

Consider the closed loop system shown in Figure 4. The root locus of that system is shown in Figure 5 (s+40s+8) R(s) Y(s) Figure 4 System block diagram of Problem 4 a) On the root locus plot, sketch the region of possible roots of the dominant closed-loop poles such that the system response to a unit step has the following time domain specifications. [5] i. Damping ratio, 20.76 ii. Natural frequency,. 24.5 rad iii. Settling time, ts 1.2 seconds (for 2% criterion) b) Using the root-locus plot and the possible root region, identify one of the complex closed-loop roots such that the system would have the least settling time. Find the corresponding value of k. 15] c) Using the root-locus plot and the possible root region, identify closed-loop roots such that the system would have the least overshoot yet the fastest possible response. Find the corresponding value of k. 15) d) Using the root-locus plot and the possible root region, identify one of the closed-loop roots such that the system would have the least steady-state error. Find the corresponding value of k. [5] 0.88 0.760. 05 0.34 0.16 0.94 0.985 0.985 -3 0.94 0.86 0.760.6 0.5 0 34 0.16 -2 Real Axis (seconds Figure 5 Root locus plot of Problem 4

Answer 1