is textbook is ideal for an undergraduate course in Engineering System Dynamics and Controls. It is intended to provide the reader with a thorough understanding of the process of creating mathematical (and computerbased) models of physical systems. The material is restricted to lumped parameter models, which are those models in which time is the only independent variable. It assumes a basic knowledge of engineering mechanics and ordinary differential equations. The new edition has expanded topical coverage and many more new examples and exercises.
P1: KAE 0521864356pre CUFX086/Kulakowski 0 521 86435 6 printer: Sheridan May 11, 2007 20:56 xiv This page intentionally left blank P1: KAE 0521864356pre CUFX086/Kulakowski 0 521 86435 6 printer: Sheridan May 11, 2007 20:56 DYNAMIC MODELING AND CONTROL OF ENGINEERING SYSTEMS THIRD EDITION This textbook is ideal for a course in Engineering System Dynamics and Controls. The work is a comprehensive treatment of the analysis of lumped-parameter physical systems. Starting with a discussion of mathematical models in general, and ordinary differential equations, the book covers input–output and state- space models, computer simulation, and modeling methods and techniques in mechanical, electrical, thermal, and fluid domains. Frequency-domain methods, transfer functions, and frequency response are covered in detail. The book con- cludes with a treatment of stability, feedback control (PID, lag–lead, root locus), and an introduction to discrete-time systems. This new edition features many new and expanded sections on such topics as Solving Stiff Systems, Opera- tional Amplifiers, Electrohydraulic Servovalves, Using MATLAB ® with Trans- fer Functions, Using MATLAB with Frequency Response, MATLAB Tutorial, and an expanded Simulink ® Tutorial. The work has 40 percent more end-of- chapter exercises and 30 percent more examples. Bohdan T. Kulakowski, Ph.D. (1942–2006) was Professor of Mechanical Engi- neering at Pennsylvania State University. He was an internationally recognized expert in automatic control systems, computer simulations and control of indus- trial processes, systems dynamics, vehicle–road dynamic interaction, and trans- portation systems. His fuzzy-logic algorithm for avoiding skidding accidents was recognized in 2000 by Discover magazine as one of its top 10 technological inno- vations of the year. John F. Gardner is Chair of the Mechanical and Biomedical Engineering Depart- ment at Boise State University, where he has been a faculty member since 2000. Before his appointment at Boise State, he was on the faculty of Pennsylvania State University in University Park, where his research in dynamic systems and controls led to publications in diverse fields from railroad freight car dynamics to adaptive control of artificial hearts. He pursues research in modeling and control of engineering and biological systems. J. Lowen Shearer (1921–1992) received his Sc.D. from the Massachusetts Insti- tute of Technology. At MIT, between 1950 and 1963, he served as the group leader in the Dynamic Analysis & Control Laboratory, and as a member of the mechanical engineering faculty. From 1963 until his retirement in 1985, he was on the faculty of Mechanical Engineering at Pennsylvania State University. Profes- sor Shearer was a member of ASME’s Dynamic Systems and Control Division and received that group’s Rufus Oldenberger Award in 1983. In addition, he received the Donald P. Eckman Award (ISA, 1965), and the Richards Memorial Award (ASME, 1966). i P1: KAE 0521864356pre CUFX086/Kulakowski 0 521 86435 6 printer: Sheridan May 11, 2007 20:56 ii P1: KAE 0521864356pre CUFX086/Kulakowski 0 521 86435 6 printer: Sheridan May 11, 2007 20:56 DYNAMIC MODELING AND CONTROL OF ENGINEERING SYSTEMS THIRD EDITION Bohdan T. Kulakowski Deceased, formerly Pennsylvania State University John F. Gardner Boise State University J. Lowen Shearer Deceased, formerly Pennsylvania State University iii CAMBRIDGE UNIVERSITY PRESS Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo Cambridge University Press The Edinburgh Building, Cambridge CB2 8RU, UK First published in print format ISBN-13 978-0-521-86435-0 ISBN-13 978-0-511-28942-2 © John F. Gardner 2007 MATLAB and Simulink are trademarks of The MathWorks, Inc. and are used with permission. The MathWorks does not warrant the accuracy of the text or exercises in this book. This book’s use or discussion of MATLAB® and Simulink® software or related products does not constitute endorsement or sponsorship by The MathWorks of a particular pedagogical approach or particular use of the MATLAB® and Simulink® software. 2007 Information on this title: www.cambridge.org/9780521864350 This publication is in copyright. Subject to statutory exception and to the provision of relevant collective licensing agreements, no reproduction of any part may take place without the written p ermission of Cambrid g e University Press. ISBN-10 0-511-28942-1 ISBN-10 0-521-86435-6 Cambridge University Press has no responsibility for the persistence or accuracy of urls for external or third-party internet websites referred to in this publication, and does not g uarantee that any content on such websites is, or will remain, accurate or a pp ro p riate. Published in the United States of America by Cambridge University Press, New York www.cambridge.org hardback eBook (EBL) eBook (EBL) hardback P1: KAE 0521864356pre CUFX086/Kulakowski 0 521 86435 6 printer: Sheridan May 11, 2007 20:56 Dedicated to the memories of Professor Bohdan T. Kulakowski (1942–2006), the victims of the April 16, 2007 shootings at Virginia Tech, and all who are touched by senseless violence. May we never forget and always strive to learn form history. v P1: KAE 0521864356pre CUFX086/Kulakowski 0 521 86435 6 printer: Sheridan May 11, 2007 20:56 vi P1: KAE 0521864356pre CUFX086/Kulakowski 0 521 86435 6 printer: Sheridan May 11, 2007 20:56 Contents Preface page xi 1 INTRODUCTION 1 1.1 Systems and System Models 1 1.2 System Elements, Their Characteristics, and the Role of Integration 4 Problems 9 2 MECHANICAL SYSTEMS 14 2.1 Introduction 14 2.2 Translational Mechanical Systems 16 2.3 Rotational–Mechanical Systems 30 2.4 Linearization 34 2.5 Synopsis 44 Problems 45 3 MATHEMATICAL MODELS 54 3.1 Introduction 54 3.2 Input–Output Models 55 3.3 State Models 61 3.4 Transition Between Input–Output and State Models 68 3.5 Nonlinearities in Input–Output and State Models 71 3.6 Synopsis 76 Problems 76 4 ANALYTICAL SOLUTIONS OF SYSTEM INPUT–OUTPUT EQUATIONS 81 4.1 Introduction 81 4.2 Analytical Solutions of Linear Differential Equations 82 4.3 First-Order Models 84 4.4 Second-Order Models 92 4.5 Third- and Higher-Order Models 106 4.6 Synopsis 109 Problems 111 5 NUMERICAL SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS 120 5.1 Introduction 120 5.2 Euler’s Method 121 5.3 More Accurate Methods 124 5.4 Integration Step Size 129 vii P1: KAE 0521864356pre CUFX086/Kulakowski 0 521 86435 6 printer: Sheridan May 11, 2007 20:56 viii Contents 5.5 Systems of Differential Equations 133 5.6 Stiff Systems of Differential Equations 133 5.7 Synopsis 138 Problems 139 6 SIMULATION OF DYNAMIC SYSTEMS 141 6.1 Introduction 141 6.2 Simulation Block Diagrams 143 6.3 Building a Simulation 147 6.4 Studying a System with a Simulation 150 6.5 Simulation Case Study: Mechanical Snubber 157 6.6 Synopsis 164 Problems 165 7 ELECTRICAL SYSTEMS 168 7.1 Introduction 168 7.2 Diagrams, Symbols, and Circuit Laws 169 7.3 Elemental Diagrams, Equations, and Energy Storage 170 7.4 Analysis of Systems of Interacting Electrical Elements 175 7.5 Operational Amplifiers 179 7.6 Linear Time-Varying Electrical Elements 186 7.7 Synopsis 188 Problems 189 8 THERMAL SYSTEMS 198 8.1 Introduction 198 8.2 Basic Mechanisms of Heat Transfer 199 8.3 Lumped Models of Thermal Systems 202 8.4 Synopsis 212 Problems 213 9 FLUID SYSTEMS 219 9.1 Introduction 219 9.2 Fluid System Elements 220 9.3 Analysis of Fluid Systems 225 9.4 Electrohydraulic Servoactuator 228 9.5 Pneumatic Systems 235 9.6 Synopsis 243 Problems 244 10 MIXED SYSTEMS 249 10.1 Introduction 249 10.2 Energy-Converting Transducers and Devices 249 10.3 Signal-Converting Transducers 254 10.4 Application Examples 255 10.5 Synopsis 261 Problems 261 [...]... course in control systems However, Chapters 13 and 14 present a very brief discussion of the fundamental concepts in feedback control, stability (and algebraic and numerical stability techniques), closed-loop performance, and PID and simple cascade controllers Similarly, the preponderance of digitally implemented control schemes necessitates a discussion of discrete-time control and the dynamic effects... the middle of the 20th century, the field of systems dynamics and feedback control has rapidly become both a core science for mathematicians and engineers and a remarkably mature field of study As early as 20 years ago, textbooks (and professors) could be found that purported astoundingly different and widely varying approaches and tools for this field From block diagrams to signal flow graphs and bond graphs,... diversity of approaches, and the passion with which they were defended (or attacked), made any meeting of systems and control professionals a lively event Although the various tools of the field still exist, there appears to be a consensus forming that the tools are secondary to the insight they provide The field of system dynamics is nothing short of a unique, useful, and utterly different way of looking... inputs and outputs 1–2 To distinguish among various types of mathematical models used to represent and predict the behavior of systems 1–3 To recognize through (T-type) variables and across (A-type) variables when examining energy transfer within a system 1–4 To recognize analogs between corresponding energy-storage and energydissipation elements in different types of dynamic systems 1–5 To understand... understood as a conceptually isolated part of the universe that is of interest to us Other parts of the universe that interact with the system comprise the system environment, or neighboring systems All existing systems change with time, and when the rates of change are significant, the systems are referred to as dynamic systems A car riding over a road can be considered as a dynamic system (especially on a crooked... the state of the system at any given instant of time; and they are of great importance in the modeling and analysis of dynamic systems Provided the initial state and the input variables have all been specified, the state variables then describe from instant to instant the behavior, or response, of the system The concept of the state of a dynamic system is discussed in more detail in Chap 3 In most cases,... ELEMENTS, THEIR CHARACTERISTICS, AND THE ROLE OF INTEGRATION The modeling techniques developed in this text focus initially on the use of a set of simple ideal system elements found in four main types of systems: mechanical, electrical, fluid, and thermal Transducers, which enable the coupling of these types of system to create mixed-system models, will be introduced later This set of ideal linear elements... which also provides their elemental equations and, in the case of energy-storing elements, their energy-storage equations in simplified form The variables, such as force F and velocity v used in mechanical systems, current i and voltage e in electrical systems, fluid flow rate Q f and pressure P in fluid systems, and heat flow rate Qh and temperature T in thermal systems, have also been classified as either... simplified models of the systems, and their use leads to only approximate predictions of system behavior Figure 1.1 shows a graphical presentation of a dynamic system In addition to the state variables, parameters also characterize the system In the example of the moving car, the input variables would include throttle position, position of the steering wheel, and road conditions such as slope and roughness... criteria: applicability of the principle of superposition, dependence on spatial coordinates as well Table 1.1 Classification of system models Type of model Classification criterion Type of model equation Nonlinear Principle of superposition does not apply Principle of superposition applies Dependent variables are functions of spatial coordinates and time Dependent variables are independent of spatial coordinates . 20:56 DYNAMIC MODELING AND CONTROL OF ENGINEERING SYSTEMS THIRD EDITION This textbook is ideal for a course in Engineering System Dynamics and Controls. The work is a comprehensive treatment of. recognized expert in automatic control systems, computer simulations and control of indus- trial processes, systems dynamics, vehicle–road dynamic interaction, and trans- portation systems. His fuzzy-logic. 1985, he was on the faculty of Mechanical Engineering at Pennsylvania State University. Profes- sor Shearer was a member of ASME’s Dynamic Systems and Control Division and received that group’s