A mobile robot using s vision system as the measurement device is shown in figure $($a$)$ below. The control system in block diagram is also shown in figure $($b$).$ A PI controller is to be designed so that the steady state error for a step input is zero, i$.$e$.$ Using the root locus method, design the PI controller so that $($a$)$ the percent maximum overshoot for a step input is $5\%$ or less; $($b$)$ the settling time $(2\%$ definition$)$ is $5$ seconds or less; $($c$)$ the system velocity error constant is greater than $1\mathrm{.}5.$