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?

Transcribed Image Text:

R(s) + K C(s) (s + 1)(s + 2)(s + 3)(s + 4) (a) K(s + a) (s+ 1)(s+ 2)(s+ 3)(s+4) R(s) + C(s) (b) FIGURE P8.8