Answer Happy

Consider the control system with negative and unity feedback
The open-loop transfer function is given by
With respect to the location of the roots of the closed-loop system, determine in a justified and detailed way
look:
a) the place of the roots on the real axis;
b) the asymptote angles;
c) the intersection of the asymptotes with the real axis;
d) the arrival or departure points of the real axis, if any;
e) the departure angles of the complex conjugated poles;
f) the points where the locus of the roots crosses the imaginary axis and the associated gain;
g) the range of K gain values ​​in which the system is unstable;
h) the value of the real pole of the closed-loop transfer function associated with the gain K, where the pair of dominant closed-loop conjugate complex poles is purely imaginary;
i) the sketch of the place of the roots in the complex plane.
R(s) + E(s) G(s) C(s)
G(s) = K s(s² + 6s + 18)