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Vilnius Gediminas technical university

Andrius Petrovas,

Roma Rinkevičienė

AUTOMATIC CONTROL THEORY 1, 2

Description of laboratory works

Vilnius 2012

A. Petrovas, R. Rinkevičienė. Automatic Control Theory 1,2: description of laboratory works. Vilnius: Technika, 2012. 98 p. [2,5 aut. l. 2012 06 18]

Descriptionsoflaboratoryworksareforstudentsoftechnologysciencesstudyfield, electrical engineering study branch, automation study programme, taking course in automatic control theory. Descriptions of laboratory works will also be useful for incoming students in the frame of Erasmus program or other students of Exchange programs in energetic systems and mechatronics study branches. Every description of the laboratory work includes the aim of the work, a wide theoretical part, tasks, content of the report and control questions. Basic knowledge of MATLAB application is presented and specialized commands for this purpose are considered.

Descriptions of laboratory works were recommended by Study the Committee of VGTU Faculty of Electronics

Reviewed by:

Saulius Lisauskas, Assoc. Prof PhD of VGTU Department of Automation

Zita Savickienė,Assoc. Prof PhD

The publication has been produced and financed byVGTU and Europe Social Fund

(Contract Nr. VP1-2.2-ŠMM-07-K-01-047). The book is part of the project “Key update I graduate study programs of VGTU Faculty of Electronics”

VGTU leidyklos TECHNIKA 1335-S mokomosios metodinės literatūros knyga

http://leidykla.vgtu.lt

eISBN 978-609-457-162-6 doi: 10.3846/1335-S

©Petrovas, A., 2012

©Rinkevičienė, R., 2012

©VGTU leidykla TECHNIKA, 2012

Contents

Introduction . . . . . . . . . . . . . . . . . . . 5

The main knowledge about MATLAB and Simulink . . . . .5

MATRIXES. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7 Entering Matrices. . . . . . . . . . . . . . . . . . .7 Commands sum, transpose, and diag. . . . . . . . . . . 8 Subscripts. . . . . . . . . . . . . . . . . . . . . 10 The Colon Operator. . . . . . . . . . . . . . . . . 10 Numbers. . . . . . . . . . . . . . . . . . . . . .12 Functions . . . . . . . . . . . . . . . . . . . . . 13 The Colon Operator. . . . . . . . . . . . . . . . . 14 Building Tables . . . . . . . . . . . . . . . . . . .15 Representing Polynomials. . . . . . . . . . . . . . .16 Evaluating Polynomials. . . . . . . . . . . . . . . .16 Roots . . . . . . . . . . . . . . . . . . . . . . .16 MATLAB Commands List. . . . . . . . . . . . . . .17 Introduction to MATLAB Functions . . . . . . . . . . .20

Composition of dynamic systems in MATLAB. . . . . . . .22 Laboratory work Nr. 1. . . . . . . . . . . . . . . . 22 Theoretical part . . . . . . . . . . . . . . . . . . .22 Examples of dynamic system modeling and analysis . . . . 27 Content of the report:. . . . . . . . . . . . . . . . .31 Control questions: . . . . . . . . . . . . . . . . . .31

Frequency response of dynamic systems. . . . . . . . . . 32 Laboratory work №2. . . . . . . . . . . . . . . . .32 Teoretical part. . . . . . . . . . . . . . . . . . . .32 Content of the report . . . . . . . . . . . . . . . . .39 Control questions. . . . . . . . . . . . . . . . . . 40

The First Order Dynamic Systems . . . . . . . . . . . . .41 Laboratory work No. 3. . . . . . . . . . . . . . . . 41 Theoretical part . . . . . . . . . . . . . . . . . . .41 Content of the report . . . . . . . . . . . . . . . . .62 Control questions. . . . . . . . . . . . . . . . . . 62

The second order systems. . . . . . . . . . . . . . . . 63 Laboratory work No 4. . . . . . . . . . . . . . . . 63 Theoretical part . . . . . . . . . . . . . . . . . . .63 Problems of the second order system analysis. . . . . . . 79 Content of the report . . . . . . . . . . . . . . . . .82 Control questions. . . . . . . . . . . . . . . . . . 82

Analysis of algebraic methods of stability. . . . . . . . . .83 Laboratory work No 5. . . . . . . . . . . . . . . . 83 Theoretical part . . . . . . . . . . . . . . . . . . .83 Examples of algebraic stability metods application. . . . . 93 Content of report . . . . . . . . . . . . . . . . . . 97 Control questions. . . . . . . . . . . . . . . . . . 97

References. . . . . . . . . . . . . . . . . . . . . . 98

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