Root$-$Locus

Automatic control of helicopters is necessary because, unlike fixed$-$wing aircraft which possess a fair degree of inherent stability, the helicopter is quite unstable. A helicopter control system that utilizes an automatic control loop is shown in Figure I. The dynamics of the helicopter are represented by the transfer function :

$G(s)=\frac{25(s+0\mathrm{.}03)}{(s^3+0\mathrm{.}04s^2+0\mathrm{.}016s+0\mathrm{.}064)}$

Draw the root locus for the automatic stabilization loop using the MATLAB function "rlocus". The open loop transfer function is $G(s)H(s).$

Find the gain $K_2$ that results in a damping for the complex poles equal to $=0\mathrm{.}7.$ Determine all the closed$-$loop poles of this feedback system.

Simulate the feedback loop in Simulink and show the step response of the system.

Submit a matlab figure of the root$-$locus along with the Simulink model.