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

                                                                            Project

                                                Speed Control of a Direct Current (DC) motor

1. In this project, a Simulink model for the DC motor will be first developed per the schematic shown in Figure 1.

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.

ANSWER:

• Here, the operator controls the speed of a DC motor manually or automatically via a control device.

• This differs from speed regulation, which attempts to maintain or control speed in the face of a natural variation in speed brought on by a change in the load on the shaft.

As a result, the speed can be altered by:

1. The armature's terminal voltage is V.
2. The armature circuit's external resistance, Ra
3. flux per polarised
4. Thus, flux entails a change in the magnetic field whereas terminal voltage and external resistance involve a change that impacts the armature circuit. 

5. Hence, the following categories can be used to classify speed control of DC motors:
6. Methods for Armature Control
7. Field Control Procedures

Simulink Model:

Here, we must first create a simulation of the DC motor and turn it into a separate system.

The discrete PID controller is then attached to the DC motor system, helping to maintain the appropriate speed.

Therefore, following the PID controller, we must begin with the kp ki kd such as

Kp = 25;

Ki = 10.2;

Kd = -0.8;

Which is employed in order to achieve the control design objectives.

PID controller design:

Controlling the supplied voltage allows for the modification or control of the DC motor's speed (Vs). The supply voltage is controlled by the PID controller thanks to its clever design (Vs). The equation that follows illustrates this.

The PID controller's fundamental equation, which is, must be used in the design process.

SCOPE: OUTPUT

All six parameters of the plot are observed.

The speed eventually settles at the desired value of 250 after lagging behind the reference value for a short while.

The armature current conforms to the step function's nature and reaches a high value of 2495A.

The reference signal's nature matches that of the back emf, which settles at 2.5V.

The input signal's nature matches that of the torque, which stabilizes at 25 Nm.

Vs has a similar nature to the reference signal and, after some initial overshoot, settles at 2595V.

Here, we can see that the speed signal w's peak value is at 245., well below the 5% overshoot threshold (which would be at 249.5). As a result, the requirement that the overshoot error be less than 5% is met. Additionally, we notice that the signal w reaches the reference value of 250 well before 2 seconds have passed since it began to ascend, leading us to believe that the settling time is shorter than 2 seconds. After the system stabilizes, the response signal and reference speed are in sync, and the difference between the target value and the output value is 0; as a result, the steady state error is 0% (1%).

MATLAB SCRIPT:

%This file contains design parameters to model a DC motor
J = 0.01; % Moment of inertia of rotor in kg-m^2
b = 0.1; % Motor viscous friction constant in N-m-s
Km = 0.01; % Back EMF constant in v/rad/s
Kt = 0.01; % Motor Torque constsnt in N-m/amp
Ra = 1.0; % Resistance of the armature circuit in Ohms
La = 0.5; % Inductance of the armature circuit in henries

% A & B Matrices

A=[-b/J Kt/J; -Km/La -Ra/La]; 
B=[0;1/La];

% Equivalent wn
wn = 6.28; % Sqrt (k/m) rad/sec
fn = 1.0; % wn/(2*pi)   Hz

%Design Parameter
zeta =0.5; % Underdamped system design

% Desired Poles
 
p1 = -zeta*wn+wn*sqrt(zeta^2-1);
p2 = -zeta*wn-wn*sqrt(zeta^2-1);

P=[p1;p2];

% Pole Placement
K=place(A,B,P);

%Kp , Ki & Kd gain are obtained from the Slide Datas Provided

Kp = 25;
Ki = 10.2;
Kd = -0.8;

Command Window:

Workspace:

Conclusion:

The Reference Speed vs and the Speed is tracked is tracked according to the Reference Speed given

The error and the overshoot are reduced and follows the input.

Thus, for the above Question the Specifications provided is successfully proved and verified