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MINISTRY OF EDUCATION AND SCIENCE OF UKRAIN

Zaporizhzhya National Technical University

METHODICAL DIRECTIONS

to laboratory works execution on the curse of

"MODELING of ELECTROMECHANICAL SYSTEMS"

for students of the specialty 7.092206.02

for all study forms

2006

METHODICAL DIRECTIONS to laboratory works execution on the curse of "MODELING of ELECTROMECHANICAL SYSTEMS" for students of the specialty 7.092206.02 for all study forms / Author T. KORNUS – Zaporizhzhya: ZNTU, 2006. – 68p.

Author: T. KORNUS

Reviewer: L. GORNJAK

Editor-in chief: A. RASSAL'SKY

Approved

by the chair of "Electrical apparatus"

The protocol #14 from 06.06.2006 y.

Contents

page

1 LABORATORY WORK #1 ………………….……………………. 4

2 LABORATORY WORK #2………………………….………….….14

3 LABORATORY WORK #3……………………………………….. 22

4 LABORATORY WORK #4……………………………………….. 30

5 LABORATORY WORK #5……………………………………….. 35

6 LABORATORY WORK #6……………………………………….. 41

7 LABORATORY WORK #7……………………………………….. 46

8 LABORATORY WORK #8……………………………………….. 52

9 LABORATORY WORK #9……………………………………….. 59

10 LABORATORY WORK #10……………………………………… 65

List of literature…………………………………………………………68

1 LAboratory work # 1

TOPIC: Modeling of steady-state electric processes in MATLAB environment. Part 1.

PURPOSE OF THE WORK: Studying of basic statements and operators of MATLAB, kinds of M-files, organization of input and output of information, processing of modeling results.

Mathematical model

Let's consider the example of working out of mathematical model of electric processes and their analysis in the elementary circuit (Fig.1.1) with the help of system MATLAB.

Figure 1.1 - Modeled electric circuit

Let parameters of elements of the circuit are given:

e1 (t) =100sin (t +/6) V; e2 (t) =200sin ((t +/3) V; =2f; f=50 Hz;

R1=1 Ohm; R2=2 Ohm; R3=3 Ohm;

C3=1*10^-4 F; L2=1*10^-3 H.

It is required to define the steady-state currents of branches.

Before to make the program, we shall write down system of Kirchhoff’s equations in the complex form.

Then the complex images of sine wave EMF are

The reactances are as

The complex images of impedances of branches

System of Kirchhoff’s equations for definition of branch currents

Let's copy this system of the equations as

Let's present factors before unknowns as a matrix

Vector of the right parts

Then the above-stated system of the equations written down by a matrix form will look as

where

- a column-vector of defined currents.

The solution of this matrix equation is a vector I of defined branch currents.

Stages of a program elaboration

To work out the program realizing the above-stated mathematical model in MATLAB environment, it is necessary to carry out the following steps:

1. Organize entering of the input data.

2. Make matrixes of system of the linear equations.

3. Solve this system of the linear equations.

4. Define an error of calculations.

5. Organize an output of results of calculation by using numerical or\and a graphic form.

Call Desktop matlab

MATLAB session starts by call one from the menu “Start”. Enter and run of the program should be executed directly from a Command window type and enter statements, operators and commands in turn. However, it is more expedient to use for this purpose a window of the editor of programs (Editor/Debugger). For this purpose, we shall click FileNew from the main menu or press to the corresponding icon button (New) on the panel of tools. The window of the text editor will appear. You can type the program text here.