Use matlab to solve the following:
A field-controlled DC motor can be described by the followingdifferential equation:
ay3(t)+by2(t)+cy1(t) =dx(t)
Where y(t) is the angle displacement of the motor’s load andx(t) is the applied voltage to the motor. The applied voltage is DCthat turns on at t = 0, which is a step function. Thevalues for a,b,c and d are derived from the model of the fieldcontrolled DC motor. This is a concept that is slightly advancedfrom this class. For now, go with this:
% 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 thesystem.
(2) Analyze the plots by answering these questions:
(a)If an impulse is applied, how many degrees does the motorturn? And how long does it take to turn those degrees?
(b)After 1 minute of applying a step voltage (1 volt DC), howmany revolutions of the motor ? How many revolutions if the DCvoltage applied is 12 volts ?
(c)The only parameters we can control in the motor are J, f, andthe input voltage x(t). Play with these to evaluate the motor. Inother words try a few different sets of values for J, f, and theinput voltage x(t) and explain what happens.
