Orchard Publications www.orchardpublications.com Introduction to Simulink® with Engineering Applications Steven T. Karris Introduction to Simulink ® with Engineering Applications Steven T. Karris Orchard Publications www.orchardpublications.com Introduction to Simulink ® with Engineering Applications Copyright ® 2006 Orchard Publications. All rights reserved. Printed in the United States of America. No part of this publication may be reproduced or distributed in any form or by any means, or stored in a data base or retrieval system, without the prior written permission of the publisher. Direct all inquiries to Orchard Publications, info@orchardpublications.com Product and corporate names are trademarks or registered trademarks of The MathWorks™, Inc. They are used only for identification and explanation, without intent to infringe. Library of Congress Cataloging-in-Publication Data Library of Congress Control Number (LCCN) 2006926850 ISBN 0-9744239-8-X ISBN 978-0-9744239-8-2 Disclaimer The author has made every effort to make this text as complete and accurate as possible, but no warranty is implied. The author and publisher shall have neither liability nor responsibility to any person or entity with respect to any loss or damages arising from the information contained in this text. Preface This text is an introduction to Simulink ®, a companion application to MATLAB ®. It is written for students at the undergraduate and graduate programs, as well as for the working professional. Although some previous knowledge of MATLAB would be helpful, it is not absolutely necessary; Appendix A of this text is an introduction to MATLAB to enable the reader to begin learning both MATLAB and Simulink simultaneously, and to perform graphical computations and programming. Chapters 2 through 18 describe the blocks of all Simulink libraries. Their application is illustrated with practical examples through Simulink models, some of which are supplemented with MATLAB functions, commands, and statements. Some background information is provided for lesser known definitions and topics. Chapters 1 and 19 contain several Simulink models to illustrate various applied math and engineering applications. Appendix B is an introduction to difference equations as they apply to discrete -time systems, and Appendix C introduces the reader to random generation procedures. This text supplements our Numerical Analysis with MATLAB and Spreadsheet Applications, ISBN 0 −9709511−1−6. It is self-contained; the blocks of each library are described in an orderly fashion that is consistent with Simulink’s documentation. This arrangement provides insight into how a model is used and how its parts interact with each another. Like MATLAB, Simulink can be used with both linear and nonlinear systems, which can be modeled in continuous time, sample time, or a hybrid of these. Examples are provided in this text. Most of the examples presented in this book can be implemented with the Student Versions of MATLAB and Simulink. A few may require the full versions of these outstanding packages, and these examples may be skipped. Some add −ons, known as Toolboxes and Blocksets can be obtained from The MathWorks,™ Inc., 3 Apple Hill Drive, Natick, MA, 01760-2098, USA, www.mathworks.com. To get the most out of this outstanding application, it is highly recommended that this text is used in conjunction with the MATLAB and Simulink User’s Guides. Other references are provided in the reference section of this text. The author wishes to express his gratitude to the staff of The MathWorks™, the developers of MATLAB® and Simulink®, especially to Ms. Courtney Esposito, for the encouragement and unlimited support they have provided me with during the production of this text. This is the first edition of this title, and although every effort was made to correct possible typographical errors and erroneous references to figures and tables, some may have been overlooked. Accordingly, the author will appreciate it very much if any such errors are brought to his attention so that corrections can be made for the next edition. Orchard Publications www.orchardpublications.com info@orchardpublications.com Introduction to Simulink with Engineering Applications i Copyright © Orchard Publications Table of Contents 1 Introduction to Simulink 1−1 1.1 Simulink and its Relation to MATLAB 1−1 1.2 Simulink Demos 1 −20 1.3 Summary 1−28 1.4 Exercises 1 −29 1.5 Solutions to End −of−Chapter Exercises 1−30 2 The Commonly Used Blocks Library 2−1 2.1 The Inport, Outport, and Subsystem Blocks 2−2 2.2 The Ground Block 2 −4 2.3 The Terminator Block 2−5 2.4 The Constant and Product Blocks 2 −6 2.5 The Scope Block 2 −7 2.6 The Bus Creator and Bus Selector Blocks 2−7 2.7 The Mux and Demux Blocks 2 −11 2.8 The Switch Block 2 −14 2.9 The Sum Block 2−15 2.10 The Gain Block 2 −16 2.11 The Relational Operator Block 2 −17 2.12 The Logical Operator Block 2−18 2.13 The Saturation Block 2 −19 2.14 The Integrator Block 2 −20 2.15 The Unit Delay Block 2−24 2.16 The Discrete −Time Integrator Block 2−26 2.17 Data Types and The Data Type Conversion Block 2 −29 2.18 Summary 2 −35 2.19 Exercises 2 −39 2.20 Solutions to End −of−Chapter Exercises 2−41 3 The Continuous Blocks Library 3−1 3.1 The Continuous−Time Linear Systems Sub−Library 3−2 3.1.1 The Integrator Block 3 −2 3.1.2 The Derivative Block 3 −2 3.1.3 The State −Space Block 3−6 3.1.4 The Transfer Fcn Block 3 −6 3.1.5 The Zero −Pole Block 3−8 3.2 The Continuous−Time Delays Sub−Library 3−10 ii Introduction to Simulink with Engineering Applications Copyright © Orchard Publications 3.2.1 The Transport Delay Block 3−10 3.2.2 The Variable Time Delay Block 3−11 3.2.3 The Variable Transport Delay Block 3 −12 3.3 Summary 3 −14 3.4 Exercises 3−16 3.5 Solutions to End −of−Chapter Exercises 3−17 4 The Discontinuities Blocks Library 4−1 4.1 The Saturation Block 4−2 4.2 The Saturation Dynamic Block 4 −3 4.3 The Dead Zone Block 4 −4 4.4 The Dead Zone Dynamic Block 4−5 4.5 The Rate Limiter Block 4 −6 4.6 The Rate Limiter Dynamic Block 4 −8 4.7 The Backlash Block 4−9 4.8 The Relay Block 4 −11 4.9 The Quantizer Block 4 −12 4.10 The Hit Crossing Block 4−13 4.11 The Coulomb and Viscous Friction Block 4 −14 4.12 The Wrap to Zero Block 4−16 4.13 Summary 4 −17 4.14 Exercises 4 −19 4.15 Solutions to End−of−Chapter Exercises 4−20 5 The Discrete Blocks Library 5−1 5.1 The Discrete−Time Linear Systems Sub−Library 5−2 5.1.1 The Unit Delay Block 5−2 5.1.2 The Integer Delay Block 5 −2 5.1.3 The Tapped Delay Block 5 −3 5.1.4 The Discrete−Time Integrator Block 5−4 5.1.5 The Discrete Transfer Fcn Block 5−4 5.1.6 The Discrete Filter Block 5−5 5.1.7 The Discrete Zero−Pole Block 5−8 5.1.8 The Difference Block 5 −9 5.1.9 The Discrete Derivative Block 5 −10 5.1.10 The Discrete State−Space Block 5− 11 5.1.11 The Transfer Fcn First Order Block 5 −14 5.1.12 The Transfer Fcn Lead or Lag Block 5 −15 5.1.13 The Transfer Fcn Real Zero Block 5 −18 5.1.14 The Weighted Moving Average Block 5 −19 Introduction to Simulink with Engineering Applications iii Copyright © Orchard Publications 5.2 The Sample & Hold Delays Sub−Library 5−21 5.2.1 The Memory Block 5 −21 5.2.2 The First−Order Hold Block 5−22 5.2.3 The Zero −Order Hold Block 5−23 5.3 Summary 5−25 5.4 Exercises 5 −27 5.5 Solutions to End −of−Chapter Exercises 5−29 6 The Logic and Bit Operations Library 6−1 6.1 The Logic Operations Group Sub−Library 6−2 6.1.1 The Logical Operator Block 6 −2 6.1.2 The Relational Operator Block 6−2 6.1.3 The Interval Test Block 6 −2 6.1.4 The Interval Test Dynamic Block 6 −3 6.1.5 The Combinational Logic Block 6−4 6.1.6 The Compare to Zero Block 6 −9 6.1.7 The Compare to Constant Block 6 −10 6.2 The Bit Operations Group Sub−Library 6−11 6.2.1 The Bit Set Block 6 −12 6.2.2 The Bit Clear Block 6 −13 6.2.3 The Bitwise Operator Block 6−14 6.2.4 The Shift Arithmetic Block 6 −16 6.2.5 The Extract Bits Block 6 −17 6.3 The Edge Detection Group Sub−Library 6−18 6.3.1 The Detect Increase Block 6 −18 6.3.2 The Detect Decrease Block 6 −20 6.3.3 The Detect Change Block 6−21 6.3.4 The Detect Rise Positive Block 6 −22 6.3.5 The Detect Rise Nonnegative Block 6 −23 6.3.6 The Detect Fall Negative Block 6 −24 6.3.7 The Detect Fall Nonpositive Block 6 −25 6.4 Summary 6 −27 6.5 Exercises 6 −31 6.6 Solutions to End −of−Chapter Exercises 6−32 7 The Lookup Tables Library 7−1 7.1 The Lookup Table Block 7−2 7.2 The Lookup Table (2 −D) Block 7−3 7.3 The Lookup Table (n −D) Block 7−5 7.4 The PreLookup Index Search Block 7 −7 iv Introduction to Simulink with Engineering Applications Copyright © Orchard Publications 7.5 The Interpolation (n−D) Using PreLookup Block 7−8 7.6 The Direct Lookup Table (n−D) Block 7−9 7.7 The Lookup Table Dynamic Block 7 −15 7.8 The Sine and Cosine Blocks 7 −16 7.9 Summary 7−20 7.10 Exercises 7 −22 7.11 Solutions to End −of−Chapter Exercises 7−23 8 The Math Operations Library 8−1 8.1 The Math Operations Group Sub−Library 8−2 8.1.1 The Sum Block 8 −2 8.1.2 The Add Block 8−2 8.1.3 The Subtract Block 8 −3 8.1.4 The Sum of Elements Block 8 −4 8.1.5 The Bias Block 8−4 8.1.6 The Weighted Sample Time Math Block 8 −5 8.1.7 The Gain Block 8 −6 8.1.8 The Slider Gain Block 8−6 8.1.9 The Product Block 8 −7 8.1.10 The Divide Block 8−7 8.1.11 The Product of Elements Block 8 −7 8.1.12 The Dot Product Block 8 −8 8.1.13 The Sign Block 8−9 8.1.14 The Abs Block 8 −10 8.1.15 The Unary Minus Block 8 −10 8.1.16 The Math Function Block 8−11 8.1.17 The Rounding Function Block 8 −13 8.1.18 The Polynomial Block 8 −14 8.1.19 The MinMax Block 8 −14 8.1.20 The MinMax Running Resettable Block 8 −15 8.1.21 The Trigonometric Function Block 8 −16 8.1.22 The Sine Wave Function Block 8−17 8.1.23 The Algebraic Constraint Block 8 −18 8.2 The Vector / Matrix Operations Group Sub −Library 8−19 8.2.1 The Assignment Block 8−19 8.2.2 The Reshape Block 8 −20 8.2.3 The Matrix Concatenate Block 8 −21 8.2.4 The Vector Concatenate Block 8 −23 8.3 The Complex Vector Conversions Group Sub −Library 8−24 8.3.1 The Complex to Magnitude −Angle Block 8−24 8.3.2 The Magnitude −Angle to Complex Block 8−24 Introduction to Simulink with Engineering Applications v Copyright © Orchard Publications 8.3.3 The Complex to Real−Imag Block 8−25 8.3.4 The Real −Imag to Complex Block 8−26 8.4 Summary 8−28 8.5 Exercises 8 −32 8.6 Solutions to End−of−Chapter Exercises 8−34 9 The Model Verification Library 9−1 9.1 The Check Static Lower Bound Block 9−2 9.2 The Check Static Upper Bound Block 9−3 9.3 The Check Static Range Block 9 −4 9.4 The Check Static Gap Block 9 −5 9.5 The Check Dynamic Lower Bound Block 9−6 9.6 The Check Dynamic Upper Bound Block 9 −8 9.7 The Check Dynamic Range Block 9 −9 9.8 The Check Dynamic Gap Block 9−10 9.9 The Assertion Block 9 −12 9.10 The Check Discrete Gradient Block 9 −13 9.11 The Check Input Resolution Block 9−14 9.12 Summary 9 −16 9.13 Exercises 9 −18 9.14 Solutions to End−of−Chapter Exercises 9−19 10 The Model−Wide Utilities Library 10−1 10.1 The Linearization of Running Models Sub−Library 10−2 10.1.1 The Trigger−Based Linearization Block 10−2 10.1.2 The Time −Based Linearization Block 10−4 10.2 The Documentation Sub −Library 10−6 10.2.1 The Model Info Block 10 −6 10.2.2 The Doc Text Block 10 −8 10.3 The Modeling Guides Sub −Library 10−9 10.4 Summary 10 −11 11 The Ports & Subsystems Library 11−1 11.1 The Inport, Outport, and Subsystem Blocks 11−2 11.2 The Trigger Block 11 −2 11.3 The Enable Block 11 −2 11.4 The Function −Call Generator Block 11−3 11.5 The Atomic Subsystem Block 11 −4 11.6 The Code Reuse Subsystem Block 11 −9 11.7 The Model Block 11−17 [...]... Introduction to Simulink with Engineering Applications Copyright © Orchard Publications Simulink and its Relation to MATLAB x1 y = [1 0 0 0] ⋅ x2 x3 + [ 0 ] sin t (1.39) x4 We invoke MATLAB, we start Simulink by clicking on the Simulink icon, on the Simulink Library Browser, we click on the Create a new model (blank page icon on the left of the top bar), and we save this model as Example_1_2 On the Simulink. .. of Example 1.1 with Simulink To run Simulink, we must first invoke MATLAB Make sure that Simulink is installed in your system In the Command Window, we type: simulink Alternately, we can click on the Simulink icon shown in Figure 1.3 It appears on the top bar on MATLAB s Command Window Figure 1.3 The Simulink icon Upon execution of the Simulink command, the Commonly Used Blocks are shown in Figure 1.4... understanding Simulink, and for this purpose, Appendix A is included as an introduction to MATLAB 1.1 Simulink and its Relation to MATLAB The MATLAB and Simulink environments are integrated into one entity, and thus we can analyze, simulate, and revise our models in either environment at any point We invoke Simulink from within MATLAB We begin with a few examples and we will discuss generalities in subsequent... Introduction to Simulink with Engineering Applications Copyright © Orchard Publications Chapter 1 Introduction to Simulink T his chapter is an introduction to Simulink This author feels that we can best introduce Simulink with a few examples Tools for simulation and model−based designs will be presented in the subsequent chapters Some familiarity with MATLAB is essential in understanding Simulink, and... Systems with MATLAB Applications, ISBN 09709511-6-7, Chapter 5 1−6 Introduction to Simulink with Engineering Applications Copyright © Orchard Publications Simulink and its Relation to MATLAB x1 x2 = –t e –e – 3t –t 1 – 0.75 e + 0.25e – 3t Then, –t x1 = iL = e –e – 3t (1.24) and –t x 2 = v C = 1 – 0.75e + 0.25e – 3t (1.25) Modeling the Differential Equation of Example 1.1 with Simulink To run Simulink, ... diagram Introduction to Simulink with Engineering Applications Copyright © Orchard Publications 1−7 Chapter 1 Introduction to Simulink Figure 1.4 The Simulink Library Browser 2 u0 ( t ) 3 Σ d vC -2 dt ∫ dt dv C -dt ∫ dt vC -4 -3 Figure 1.5 Block diagram for equation (1.26) To model the differential equation (1.26) using Simulink, we perform the following steps: 1 On the Simulink Library Browser,... + v cf ( t ) = k 1 e –s1 t + k2 e –s2 t + v cf ( t ) (1.6) * Please refer to Circuit Analysis II with MATLAB Applications, ISBN 0-9709511−5−9, Appendix B for a thorough discussion 1−2 Introduction to Simulink with Engineering Applications Copyright © Orchard Publications Simulink and its Relation to MATLAB The values of s 1 and s 2 are the roots of the characteristic equation 2 (1.7) s + 4s + 3 = 0... please refer to Circuit Analysis I with MATLAB Applications, ISBN 0−9709511−2−4 † A thorough discussion of partial fraction expansion with MATLAB Applications is presented in Numerical Analysis with MATLAB and Spreadsheet Applications, ISBN 0−9709511−1−6 ‡ For an introduction to Laplace Transform and Inverse Laplace Transform, please refer to Circuit Analysis II with MATLAB Applications, ISBN 0−9709511−5−9... as a blank page on the top title bar A new model window named untitled will appear as shown in Figure 1.6 1−8 Introduction to Simulink with Engineering Applications Copyright © Orchard Publications Simulink and its Relation to MATLAB Figure 1.6 The Untitled model window in Simulink The window of Figure 1.6 is the model window where we enter our blocks to form a block diagram We save this as model file... connect an amplifier with Gain 3 to the unit step function block The gain block in Simulink is under Commonly Used Blocks (first item under Simulink on the Simulink Library Browser) See Figure 1.8 If the Equation_1_26 model window is no longer visible, it can be recalled by clicking on the white page icon on the top bar of the Simulink Library Browser 4 We choose the gain block and we drag it to the right . Publications www.orchardpublications.com info@orchardpublications.com Introduction to Simulink with Engineering Applications i Copyright © Orchard Publications Table of Contents 1 Introduction to Simulink 1−1 1.1 Simulink and its Relation to MATLAB 1−1 1.2 Simulink Demos. for this purpose, Appendix A is included as an introduction to MATLAB. 1.1 Simulink and its Relation to MATLAB The MATLAB and Simulink environments are integrated into one entity, and thus. 19 −31 19.11 Summary 19 −32 x Introduction to Simulink with Engineering Applications Copyright © Orchard Publications A Introduction to MATLAB A−1 A.1 MATLAB and Simulink A−1 A.2 Command Window A −1 A.3