Challenge

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

DDeepak Pandey17 Nov 2022

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

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 : -

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

Here the Speed control of a DC motor is either done manually by the operator or by means of an automatic control device. so the speed can be varied by changing:

The terminal voltage of the armature V.

What do you mean by speed control of motor?

Jan. 1, 2008. Speed, torque, and horsepower are three inter-related parameters in motor control.

The speed of a motor, measured in revolutions per minute (rpm), defines a motor's ability to spin at a rate per unit time.

What is speed control called?

Cruise control (also known as speed control, cruise command, autocruise, or tempomat) is a system that automatically controls the speed of a motor vehicle.

Which device is used for speed control of motor?

MATLAB CODE : -

%DC Motor parameters for PID control

J=0.01; %Moment of Inertia of rotor in kg/m^2

B=0.1; %Motor Viscous friction in Nms

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

Kt=0.01; %Motor torque constant in Nm/A

Ra=1; %Resistance of Armature ckt in ohm

La=0.5; %Inductance of Armature ckt in Henry

%Kp, Ki and Kd used in PID design of Speed control of DC motor

Kp=3.8602; %Proportional gain

Kd=6.2832; %Derivative gain

Ki=0; %Intergral Gain

%In the above code and values the value of Ki is taken as 0 because when the value was assigned to the

%Ki other than zero the parameters were approaching infinity,

% which is not a favorable condition for speed control of DC motor.

Below is the Model of the DC motor according to the circuit shown above.

Where,

value of Kt = 0.01

and Kb = 0.01,

VALUE OF STEP FUNCTION : -

OUTPUT GRAPH FOR DC CIRCUIT : -

Below is the Model for the PID controller for the speed control of the DC motor.

MATLAB CODE :-

Basic eqn: u(t) = Kp*e(t) + Ki*int(e(t)dt) + kd*diff e(t)/dt

Modified eqn: Vs = Kp*(wref - w) + Ki*int((wref - w)dt) - Kd*Ia

Matrix A and B are found from the state space model of a DC motor,

(d/dt)*[teta_dot;i] = [-B/J Kt/J;-Km/La -Ra/La]*[teta_dot;i] + [0 1/La]*Vs

y = [1;0] * [teta_dot;i]

%Matrix - Plant model

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

C=[0;1/La];

%Poles

Matrix P is found from the open loop Transfer function of the DC motor denominator

Eqn: w(S)/Vs(S) = Kt/(J*La(S^2) + J*Ra+B*La(S) + B*Ra+Kt*Km)

P=roots([J*La J*Ra+B*La B*Ra+Kt*Km]);

K=place(A,C,P);

In this model the PID controllers are added with the values shown above.

Here we consider the PID control paramters as :

Kp =3.8602,

ki =80,

kd =6.2832

The input and control designs were kept under certain conditions such as

Settling time <2sec

Overshoot<5%

Steady-state error<1%

These parameters can be considered that it will keep the system in a stable state as fast as possible.

In the case shown below the value of Ki is kept as 80 which results in a ramp-like output that approaches infinity and hence the system doesn't achieve stability.

GRAPH FOR PID CONTROLLEDR FOR THE SPEED CONTROL OF DC MOTOR : -

Then Ki = 0

Hence here is the speed control of the DC Motor.

I have used the tools to construct the these models:

Clock : output the current simulation time.

Constant : Output the constant input value.

Step : Output a step.

Integrator : Continous time integration of input signal.

Sum : Add or subtract the inputs.

Add : Add or subtract the inputs.

Scope : Display input signals with respect to the simulation time.

Gain : The Gain block multiplies the input by a constant value (gain).

Integral : The Integrator block outputs the value of the integral of its input signal with respect to time.

To Workspace : The To Workspace block logs the data connected to its input port to a workspace from a Simulink model.

Transfer fcn : It gives the numerator and denominator values.

Summary:

Initially, the DC motor model was made and the values for PID design were calculated and the PID model was incorporated into the DC motor model.

The supply voltage was set to 30 and the simulation time was 10s.

The solver was set to Fixed-type and to be solved by ode4(Runge-Kutta method).

The parameters of the dc motor were given.

The poles were calculated using the place function and values of Kp, Kd, and Ki to get a stable speed.

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.