For the system of Figure P8.8(a), sketch the root locus and find the following:
a. Asymptotes
b. Breakaway points
c. The range of K for stability
d. The value of K to yield a 0.7 damping ratio for the dominant second order pair
To improve stability, we desire the root locus to cross the jω-axis at j5.5. To accomplish this, the open-loop function is cascaded with a zero, as shown in Figure P8.8(b).
e. Find the value of α and sketch the new root locus.
f. Repeat Part c for the new locus.
g. Compare the results of Part c and Part f. What improvement in transient response do you notice?
