Challenge

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

SSaurabh Goel25 Aug 2022

Aim: To design a Simulink model for the DC motor shown in Figure 1. amd aslo by Using 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.

Answer:

Here the Speed control of a DC motor is either done manually by the operator or by means of an automatic control device.
This is different to speed regulation where the speed is trying to be maintained or regulated against the natural change in speed due to a change in the load on the shaft
so the speed can be varied by changing:
1. The terminal voltage of the armature V
2. The external resistance in armature circuit R_a
3. The flux per pole
So Terminal voltage and external resistance involve a change that affects the armature circuit while flux involves a change in the maginetic field
so Therefore speed control of DC motor can be classified into:
1. Armature Control Methods
2. Field Control Methods

the comparison of three DC motor control techniques for tracking setpoint commands and reducing sensitivity to load disturbances:

feedforward command
integral feedback control
LQR regulation

In armature-controlled DC motors, the applied voltage Va controls the angular velocity w of the shaft.

This example shows two DC motor control techniques for reducing the sensitivity of w to load variations (changes in the torque opposed by the motor load).

A simplified model of the DC motor is shown above. The torque Td models load disturbances. You must minimize the speed variations induced by such disturbance

Simulink model :

Here first we need to creat simulink model of the DC motor and make it as subsytem called the DC motor
So next the subsytem of DC motor is connected to the discrete PID controller which helps in maintaining the desired speed
So after the PID controller we need to start with the kp ki kd such as 1.0 1.0 0 after tunin accordingly so by this we can adjust the kp /ki/ kd values as 31.5/ 82.3 /2.3
Which is used to obtaine the control design objectives

Simulink model for DC motor:

Over all Simulink block:

MATLAB COMMAND:

%DC motor Parameters

Jm = 0.01; %Moment of Inertia of Rotor (Kgm^2)

Bm = 0.1; %Motor viscous friction constant (Nms)

Km = 0.01; %Back EMF constant (V/rad/s)

Kt = 0.01; %Motor Torque constant (Nm/Ampere)

Ra = 1; %Armature Resistance (ohm)

La = 0.5; %Armature Inductance (H)

%PID design from DC_motor_PID_design.m

%Load the parameters of DC motor

%PD design

A = [-Bm/Jm Kt/Jm; -Km/La -Ra/La];

B = [0; 1/La];

%pole placement design

f = 1;

wn = 2*pi*f;

zeta = 0.5;

p1 = -zeta*wn + wn*sqrt(zeta^2-1);

p2 = -zeta*wn - wn*sqrt(zeta^2-1);

P = [p1;p2];

K = place(A,B,P);

Kp = K(1);

Kd = K(2);

Kp = 20;

Kd = -0.9;

Ki = 3;

%Plotting the graphs from dc_motor_plot.m

figure(1)

subplot(321);grid;title('Supply Voltage (V)');

subplot(322);grid;title('Back EMF (V)');

subplot(323);grid;title('Armature Current (A)');

subplot(324);grid;title('Torque (Nm)');

subplot(325);grid;hold;title('Refernce Speed (rad/s)');

Output Waveform:

speed reference given as 5:

speed reference given as 55:

By optimising the Ki value, the Steady state response error is minimised.

Now go to APP sectionand then select PID tuner

Then IMPORT a file as shown in below figure:

Then select PID from TYPE menu as shown in figure

change the response time and transient behaviour as shown in figure

ecall that the transfer function for a PID controller is:

(4)

Here we consider the PID control paramters as :

Kp =1 ki = 1 kd 0

But after tuning we set kp ki kd to 31.5 82.3 2.3 which is used to obtaine the control objectives of the settling time overshoot time and steady state error

Plot for when tuning settling time as 1.5sec:

Plot for tuning as overshoot is less than 5%:

Plot for tuning as steadt state error less than 1 %

Final plot:

Now For maintaing the stabilty of a dynamic system :

Output results:

Case : 1 When maintaining a desired speed of the motor at 100 :

Case : 2 When maintaining a desired speed of the motor at 230v :

Here by observing the above two graphs we change the desired speed as 100 in the case1 and 230 in the case 2
But here both the plots reamains same
So by this we can say that we maintained desired speed of a DC motor

Conclusion:

we have desined In this project a Simulink model for the DC motor as shown in Figure 1.and also we 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

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

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Ship work like thisin your own course.

Talk to a career counsellor

Ship work like this
in your own course.