Determine the transfer function of the phase-lead compensator that can be used with the follow open-loop transfer function in order to give a phase margin of 45°.

Include the Bode plots for the original system (𝐺(𝑠)) and the
compensated system (𝐺𝑐(𝑠)𝐺(𝑠), where 𝐺𝑐(𝑠) is the transfer function
of the phase-lead compensator). The Bode plots should show the
phase margin (use the **margin** command or
**ltiview** in MATLAB). Using a unit step input
(𝑋(𝑠)=1/𝑠), also plot the response to the closed-loop system with
and without the phase-lead compensator (see figures below). Include
both step responses on the same plot (use **ltiview**
in MATLAB). How did changing the phase margin affect the step
response? Include the MATLAB commands used.

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