For the system shown below do the following:

Design a proportional controller with $=0\mathrm{.}4($Sketch the root locus$).$

Design a PI controller with $=0\mathrm{.}4($Sketch the root locus$).$

Design a PD controller with $=0\mathrm{.}4$ with half reduction in settling time $($Sketch the root locus$).$

Design a PID controller with $=0\mathrm{.}4$ with half reduction in settling time and zero steady state error for a step input $($Sketch the root locus$).$

Plot the system response for each controller, Compare the performance and write the conclusion.