Given the open-loop transfer function of a unit-feedback system: G(s) = K/s(s + 1)(s2 + 4s + 5)
For the related (P-controlled) closed-loop system:
a) Make a sketch of the branches of the loci on the real axis, as the gain K varies from zero to infinity.
b) Find the closed loop system asymptotes as K??:
-Determine the angles that they make with the real axis
-Determine the location where the asymptotes cross the real axis, i. e.: the root-locus centroid
c) Which of the following poles corresponds to the breakaway (or break-in) point of the loci on the real axis?
a. - s=-1.57
b. - s=-0.895
c. - s=-0.393
d. - s=-0.111
d) Determine the range of K values for which the closed loop system is absolutely stable.
e) Determine (if any) the frequency (in rad/sec) at which the system becomes unstable.
f) Find the departure angle from the complex-conjugate open-loop poles.
g) Sketch the root-locus plot, clearly indicating its most significant characteristics"
-Branches on the real-axis
-Asymptotes and their centroid
-Breakaway and/or break-in point(s)
-Loci crossings on the imaginary axis (if any)
-The corresponding gains at the most significant loci locations, i. e.: at the breakaway, break-in points at the real axis and at the imaginary axis crossings (if any)
-Departure angles from complex-conjugate open-loop poles
h) For what value of gain K, the closed loop system will have a critical dampint condition (?=1)?