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

Project

Aim: -

Use the Proportional, Integral, and Derivative (PID) control design knowledge gained in the training to design, develop and test a controller to maintain a desired speed for the motor.

Solution:

PID Control of a DC Motor

DC Machine:

• A DC machine functions as a generator or motor.
• Rotor with an armature winding providing the electric circuited.
• Stator with field winding serves as a magnet when energized.
• A prime mover is coupled with the rotor, allowing it to rotate in the magnetic field created by the field winding.
• This mechanism induces EMF in the conductors mounted on the rotor contributing to voltage generation.
• The electrical energy supplied to armature winding and the field winding contributes to a rotating magnetic field that forces the rotor to rotate.

When a Mechanical Load is applied:

• Using Krichoff’s voltage law, one can derive

Vs = Ra.ia + La + Vb

Vs = Supply Voltage

Ra = Armature Resistance

Ia = Armature Current

La = Armature Inductance

Vb = Back EMF.

• Back EMF, angular velocity, and torque are related by,

Vb = Km t =kti

• Here km and kt are the back EMF and torque constant.
• The open loop transfer function for the motor with the speed (w) and supply voltage (Vs) can be derived as,
• A PID controller design is demonstrated to obtain the desired angular speed using the appropriate supply voltage.

PID – Design for speed control of a DC motor:

• Build a Simulink model of PID controller to regulate the speed of the DC Motor.
• We will assume that the input of the system is the voltage source (V) applied to the motor's armature, while the output is the rotational speed of the shaft.
• Assume a viscous friction model, that is, the friction torque is proportional to shaft angular velocity.
• The physical parameters for our example are:

(J) Moment of inertia of the rotor 0.01 kg.m^2

(b) Motor viscous friction constant 0.1 N.m.s

(Ke) electromotive force constant 0.01 V/rad/sec

(Kt) motor torque constant 0.01 N.m/Amp

(R) Electric resistance 1 Ohm

(L) Electric inductance 0.5 H

• The torque generated by a DC motor is proportional to the armature current and the strength of the magnetic field.
• The open loop transfer function for the motor with the speed (w) and supply voltage (Vs) can be derived as,
• A PID controller design is demonstrated to obtain the desired angular speed using the appropriate supply voltage.
• For a unit step command in motor speed, the control system's output should meet the following requirements.

Settling time less than 2 seconds

Overshoot less than 5%

Steady-state error less than 1%

MATLAB representation

• We can represent the above open-loop transfer function of the motor in MATLAB by defining the parameters and transfer function as follows. Running this code in the command window produces the output shown below.

% Design Parameters

J=0.01;

B=0.1;

Km=0.01;

Kt=0.01;

Ra=1.0;

La=0.5;

• Save the file as ‘pid_controller.m’.

Simulink Model

• The range of numbers 0:0.1:5 specify that the step response plot should include data points for times from 0 to 5 seconds in steps of 0.1 seconds. The resulting plot is shown in the figure below,
• Save the simulated file and run
• The plots are prepared in matlab by using various plotting parameters. Are discussed below.

% Plot the outputs

%Plot Supply Voltage and speed

subplot(411);

plot(out.w);grid;hold;

plot(out.Vs,'r-');title('Supply voltage');

%Plot Back emf

subplot(412);

plot(out.Vb,'b-');grid;title('Back emf');hold;

plot(out.Cs,'m--');

% Plot Armature current

subplot(413);grid;

plot(out.la);title('Armature current');grid;

%Plot Torque Current

subplot(414);grid;

plot(out.i);title('Torque current');

• The plotted graph as shown below.

Conclusion:

Overall, this response seems to meet our goals of bringing the PID speed control of DC machine. The various responses are explained with detailed plots of various parameters of dc machine.