View source for 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 <math>\omega</math> or angular velocity as a function of time.

[[Image:Step_response_dc_motor.png]]

Here is the system response with the output being <math>\omega</math> and the input being the input voltage.

[[Image:Bode_Plot_DC_Motor.png]]