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.