Challenge

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

PPrakash Turankar7 Nov 2022

Project

Project Name :- Speed Control of Direct Current (DC) Method.

Aim :- 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.

Diagram :-

Using Kirchhoff's voltage law,

Vs = Ra*Ia+La*di/dt+Vb

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

Vb = Km*dtheta/dt T = Kt*i

Here, Km and Kt are the back emf and torque constants

respectively.

angular Veloscity W = theta

The Open loop transfer function for motor the speed (W) and supply voltage (Vs) can be control.

W(s)/Va(s)= Kt/JLa S^2+(JRa+BLa)S+(BRa+K-Km)

PID Design for Speed Control Of a DC Motor

Parameter

J - Moment of inertia of the rotor - 0.01 Kgm ^2

B - Motor viscous friction constant - 0.1 Nms

Km- Back EMF Constant - 0.01 V/radian /s

Kr - Motor Torque constant - 0.01 Nm/Ampere

Ra - Armature Resistance - 1ohm

La - Armature inducatancce - 0.5 Henry

Control design Objectives

Setting Time < 2S

Overshoot < 5 %

Steady State error <1 %

State Space Model

d/dt = [-B/J:KT/J:-km/La:-Ra/La] [theeta i]+ [0 L/La]Vs

Y = [1 0]

Program :-

% This file contains the parameter for DC Motor Design

clear all

clc

b = 0.1; % Moment of inertia of the rotor in kg-m^2

J = 0.01; % Motor viscous 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

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

Ra = 1; % Resistan of the armature circuit in ohm

% Design of PID Controller

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

B = [0; 1/La];

% Placement of pole

fn = 1;

wn = 2*pi*fn;

Zeeta = 0.5;

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

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

P = [p1 p2];

K = place(A,B,P)

Kp =K(1);

Kd=K(2);

ScreeShot

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

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in your own course.

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Ship work like thisin your own course.

Talk to a career counsellor

Ship work like this
in your own course.