It is desired to design a feedback control system on a TESLA Model S to reach desired speed as fast as possible. For this purpose Newtons First equation of motion as shown below was used which relates dynamic velocity with accelaration and decelaration due to friction .

V=Vo+a.dt-.dt

In the equation above a is the accelaration and is decelaration due to friction which are dependent on time. Vo and V are the initial and dynamic velocity of the car.

By the information given above:

a)Develop a transfer function model that relates velocity of the car to accelaration and decelaration due to friction.

b)Design a control system which uses accelaration as a manipulated variable and as a disturbance variable and which involves I(mA)/a(mph/s) transducer and a sensor (mA/mph) and a proportional controller with a gain of 1. There is a time delay of 5 seconds in the sensor.

Top speed of Tesla MODEL S is 200mph

Maximum accelaration is 60mph/1.99s

Sensor output current range is from 0 to 10mA

Lets say it is desired to speed up the car from 50 mph to 80mph. Therefore determine the dynamic velocity profile and the rise time and offset.

c) For part b use PID controller and analyze the effect of controller parameters (Kc, T and T_D) on the dynamic velocity profile, rise time, overshoot and offset.

Hint: In order to analyze the effect of controller parameters fix two parameters and change the remaining parameter.