One version of a space station is shown in Figure E7.6 [28]. It is critical to keep

Question:

One version of a space station is shown in Figure E7.6 [28]. It is critical to keep this station in the proper orientation toward the Sun and the Earth for generating power and communications. The orientation controller may be represented by a unity feedback system with an actuator and controller, such as
Gc(s)G(s) = 15 K / s(s2 + 15s + 75).
Sketch the root locus of the system as K increases. Find the value of K that results in an unstable system.