$(25$ pts$)$ Consider the open$-$loop system shown below. Design a full$-$state feedback servo tracking loop to track the output variable with zero steady$-$state error to a unitstep input. Determine the feedback gains by solving a linear quadratic regulator problem. Choose a design that has a reasonable step$-$response to a unit step overshoot, reasonable settling time$).$ Plot the unit$-$step response and error as a function of time.