For the given system, design a lead compensator such that the system achieves $(1)$ a peak time smaller than $50\%$ of the uncompensated system while $(2)$ maintaining a maximum overshoot of at most $10\%$ for a step input. Follow the steps below: $1.$ Set Unique Performance Criteria: Determine your own unique performance criteria for peak time $($tr$)$ and maximum overshoot $($Mp$).$ Since the project requirements are deliberately flexible, each group must establish unique design criteria. These values should not be excessively repeated among groups. Submitting projects with the same design poles as other groups will be considered misconduct or cheating. $2.$Determine Dominant Pole Locations: Based on your unique performance criteria, determine algebraically where the dominant poles must be located in the s$-$plane. $3.$ Design a Lead Compensator: Design a lead compensator using any of the methods discusses in the lectures or provided in the reference books. The general form of a lead compensator is: G$\_$c$($s$)=$ K$\_$c$($s $+$ z$\_$c$)($s $+$ p$\_$c$),$ where zc is the zero, pc is the pole $($pc $>$ zc$),$ and Kc is the gain. Note that both the zero and the pole are on the real axes by design. Your design must include the derivation of these parameters in detail supported by relevant drawings.