Design a lead compensator for the closed-loop (CL) system whose open loop transfer function is given below. Design objectives: reduce the time constant by 50% while increase the damping ratio to sqrt(3)/2 for the dominant poles. Please note that H(s)=1. Please use the method based on root locus plot.

G(s)=2 / [s(s+2)]

Please include detailed step.

Obtain the location of the desired dominant poles.
Draw the root loci of the CL system without the lead compensator
Calculate the angle deficiency.
Determine the location of the pole associated with the lead compensator if the zero is chosen to be at (-2.5, 0)
Obtain the gain value of the compensator (Hint: use the Magnitude Condition)
Write the complete expression of the lead compensator.
The following requires the use of Matlab (please write a Matlab script file):

Upon finishing the design, please use Matlab to plot the root loci of CL systems with and without the lead compensator. Mark the locations of the desired dominant poles. Please make sure that the root loci of CL systems with the lead compensator pass through the desired dominant poles.
Simulate and compare the unit step responses of the uncompensated and compensated system. Please observe from the plots and comment if the design objectives have been achieved.