***USE MATLAB OR SIMULINK***

A field-controlled DC motor can be described by the following differential equation.

ay'''(t) + by''(t) + cy'(t) = dx(t)

Where y(t) is the angle displacement of the motors load and x(t) is the applied voltage to the motor. The applied voltage is DC that turns on at t = 0, which is a step function.

The values for a,b,c and d are derived from the model of the field controlled DC motor.

% Motor Parameters

J = .01; % Gain (positive)

f = .10; % Friction (0

Rf = 10;

Lf = .01;

kt = 10;

% System coefficients

a = J;

b = f+ J*Rf/Lf;

c = f*Rf/Lf;

d = kt/Lf;

1.) Plot the impulse response and the step response of the system.

2.) Analyze the plots by answering these questions:

a.) If an impulse is applied, how many degrees does the motor turn? And how long does it take to turn those degrees?

b.) After 1 minute of applying a step voltage (1 volt DC), how many revolutions of the motor ? How many revolutions if the DC voltage applied is 12 volts ?

c.) The only parameters we can control in the motor are J, f, and the input voltage x(t) Play with these to evaluate the motor. In other words try a few different sets of values for J, f, and the input voltage x(t) and explain what happens.