$(40\%)$ Given the identified motor resistance R$\_($a$)=8\mathrm{.}80$hms$,$ the EMF

constant K$\_($B$)=0\mathrm{.}22$volt$($s$)/($r$)$a$($d$)/($s$),$ and K$\_($t$)=34\mathrm{.}7$oz$-$i$($n$)/($a$)$mpere$,$ the

relationship between PWM $($Pulse Width Modulation$)$ and RPM

$($Revolutions Per Minute$)$ is shown below. The applied battery

voltage is $7\mathrm{.}2$ V $.$

Left motor: PWM: $40,60,90,$ resulting in RPMs of $124,152,$ and $166,$

respectively.

Right motor: PWM: $40,60,90,$ resulting in RPMs of $110,140,$ and $156,$

respectively.

Questions:

Design experiments to determine the damping coefficient f using all the above data.

For the left motor, with a PWM of $60,$ you measured an RPM of $96$ at $0\mathrm{.}3$ seconds. Estimate the

moment of inertia l of the left motor.

For the right motor, with a PWM of $60,$ you measured an RPM of $70$ at $0\mathrm{.}3$ seconds. Estimate the

moment of inertia I of the right motor.

You aim to control the car to move straight forward at a linear velocity of $0\mathrm{.}2$ meter$($s$)/($second from$)$

an initial stall state. Determine the necessary PWM to be applied to the left and right motors,

respectively, assuming the wheel diameter is $70$ mm and a frictionless system.

Obtain the dynamic response of both the left and right wheels given the applied voltage in step $4.$

Will the car move straight forward continuously? If not, determine when it will start to move

straight forward $($assuming a frictionless system$).$