Project - Speed Control of a Direct Current (DC) motor

Aim :

To design, develop and test a controller to maintain a desired speed for the motor.

Mathematical model of DC motor :

w(s)/Vs(s) = Kt/(J * La * s^2 + (J * Ra + B * La) * s +(B * Ra +kt * km))

Parameters for DC motor :

To plot result :

subplot(321);plot(out.time,out.supply_voltage,'k-');grid;title('Supply voltage');

subplot(322);plot(out.time,out.ia,'k-');grid;title('Armature current');

subplot(323);plot(out.time,out.t,'k-');grid;title('Torque');

subplot(324);plot(out.time,out.W,'k-');grid;title('Angular velocity');

subplot(325);plot(out.time,out.vb,'k-');grid;title('Back EMF');

DC motor simulink model :

Graphical response :

Parameters for PID controller :

J = 0.01; % Moment of inertia of the rotor in kg-m^2

B = 0.1; % Motor viscus friction constant in N-m-s

Km = 0.01; % Back emf constant in v/rad/s

kt = 0.01; % Motor torque constant in N-m/amp

Ra = 1.0; % Resistance of the armature circuit in ohms

La = 0.5; % Inductunce of the armature circuit in henries

%PID parameters case 1

kp = 16200;

kd = 1000;

ki = 61700;

%PID parameters case 2

kp = 1000;

kd = 150;

ki = 2500;

To plot result :

subplot(321);plot(out.time,out.supply_voltage,'k-');grid;title('Supply voltage');

subplot(322);plot(out.time,out.g,'k-');grid;title('Gain');

subplot(323);plot(out.time,out.ia,'k-');grid;title('Armature current');

subplot(324);plot(out.time,out.t,'k-');grid;title('Torque');

subplot(325);plot(out.time,out.W,'k-');grid;title('Angular velocity');

subplot(326);plot(out.time,out.vb,'k-');grid;title('Back EMF');

PID controller simulink model :

Result :

For case 1:

For case 2:

Conclusion :

Speed of the DC motor has been controlled using PID controller model