# Matlab or Octave Script for this problem.

% This octave/Matlab script demonstrates the state space model of the
J=0.01;
b=0.1;
K=0.01;
R=1;
L=0.5;
A1=[[0,1,0];[0,-b/J,K/J];[0,-K/L,-R/L]];
B1=[0,0,1/L]';
C1=[0,1,0]; % The output is the angular velocity omega.
sys1=ss(A1,B1,C1);  % Note that theta cannot be controlled.
% There is a warning in octave from this.
% So we use only the theta dot, and i_a as state variables.
A2=[[-b/J, K/J];[-K/L,-R/L]];
B2=[0,1/L]';
C2=[1,0];
sys2=ss(A2,B2,C2);
figure(1)
clf;


Here is the unit step response for $\omega$ or angular velocity as a function of time.

Here is the system response with the output being $\omega$ and the input being the input voltage.