Consider unity feedback systems with the open$-$loop transfer functions below and $H(s)$ represents the plant and the controller respectively$).$ Sketch their root locus plots by hand.

a$)$ Temperature controller with lead compensation

$G(s)H(s)=\frac{s+1}{s+3}\frac{1}{s^2-2}$

b$)$ Temperature controller with integral control and lead compensation

$G(s)H(s)=\frac{s+1}{s(s+3)}\frac{1}{s^2-2}$