You have a car such that if you give it 9 volt, it will eventually reach a steady state speed of 50 cm/s. if it starts from rest then it takes 0.1 second for it reach 63.2% of the steady state speed. you attach a sensor to the motor which measures its speed "very accurately", the measured speed is used by the proportional controller. a proportional controller of gain k, provides voltage to the motor, with an aim to make the speed of the car same as the desired speed what is the transfer function of the motor, from voltage to speed? draw the block diagram of the system with plant, controller and the feedback path. hint: note you are controlling the speed of the car. the reference command is the desired speed. the closed loop system is from the desired speed to the actual speed. draw the rlocus of gk with a proportional controller what happens to the settling time and overshoot as you increase the proportional gain? if the desired speed is a constant (say 20 cm/s, the value doesn't matter). what should be the gain k of the proportional controller, so that the steady state error in the speed is less than 5%? (ie, what number k will ensure that, (desired speed-actual steady state speed)/desired speed