Question $6$:

A control system with unity negative feedback has a forward transfer function.

$\backslash [$

G$($s$)=\backslash$frac$\{$K$\}\{$s$($s$+2)($s$+3)\}$

$\backslash ]$

$(20$ marks$)$

a$)$ Determine the open loop poles and zeros of the system

b$)$ Find the point which the asymptotes cross the real axis

c$)$ Provide calculations for the asymptote angles.

d$)$ Determine the crossing points of the loci with the imaginary axis

e$)$ What is the gain $\backslash ($ K $\backslash )$ at those points

f$)$ Sketch the root locus diagram for the system