Let

in Figure P8.3.

a. Find the range of K for closed-loop stability.

b. Plot the root locus for K > 0.

c. Plot the root locus for K < 0.

d. Assuming a step input, what value of K will result in the smallest attainable settling time?

e. Calculate the system’s e_{ss} for a unit step input assuming the value of K obtained in Part d.

f. Make an approximate hand sketch of the unit step response of the system if K has the value obtained in Part d.