Problem $1($Motor Position Control$).$ A servo motor is used in the position control system where the plant is $G(s)=\frac{61\mathrm{.}75}{s(s+35\mathrm{.}1)}.$ Design a lag compensator for the system so that the system has at most $5\%$ overshoot for a step input and no more than $2\%$ steady state error for a ramp input. Once the design is complete, simulate the loop gain to verify the specifications are met and determine the bandwidth $($crossover frequency$).$