Given the unity feedback system wheredo the following sketch the root locus

1. Nise, Chapter 8, Q.13a: For the system shown in Figure P8.6, make an accurate plot of the root locus and find the following:

Figure 1: Nise, Figure P8.6.

Solution
Root locus crosses the imaginary axis at j0.65 for K = 0.79. Thus, the system is stable for K < 0.79.

Solution
a) Root locus crosses the imaginary axis at ±j3.162 at K = 52.

b) Since the gain is the product of pole lengths to −5, K = (1)(42 + 12)(42 + 12) = 17.

c) Find the value of gain that will make the system marginally stable.

d) Find the value of gain for which the closed-loop transfer function will have a pole on the real axis at -0.5.

(c) Root locus crosses imaginary axis at j4.28 with K = 140.8.

(d) K = 13.125.

Solution