Modeling and analysis of dynamic systems

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Title:

Personal Author:

Esfandiari, Ramin S., author

Edition:

Second edition

Publication Information:

Boca Raton : CRC Press, Taylor & Francis, 2014

Physical Description:

xvii, 548 pages : illustrations ; 27 cm.

ISBN:

9781466574939

Abstract:

"The goal of this second edition is essentially the same as that of the first edition, to provide the reader with a thorough knowledge of mathematical modeling and analysis of dynamic systems. Matlab, Simulink, and Simscape are introduced at the outset and are utilized throughout the book to perform symbolic, graphical, numerical, and simulation tasks. The textbook written at junior level, meticulously covers techniques for modeling dynamic systems, methods of response analysis, and in introduction to vibration and control systems. "--provided by publisher

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Library	Item Barcode	Call Number	Material Type	Item Category 1	Status
Searching... PSZ JB	30000010337038	TA342 E88 2014	Open Access Book	Book	Searching... Unknown

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Summary

Modeling and Analysis of Dynamic Systems, Second Editionintroduces MATLAB®, Simulink®, and Simscape(tm) and then uses them throughout the text to perform symbolic, graphical, numerical, and simulation tasks. Written for junior or senior level courses, the textbook meticulously covers techniques for modeling dynamic systems, methods of response analysis, and provides an introduction to vibration and control systems. These features combine to provide students with a thorough knowledge of the mathematical modeling and analysis of dynamic systems.

See What's New in the Second Edition:

Coverage of modeling and analysis of dynamic systems ranging from mechanical to thermal using Simscape Utilization of Simulink for linearization as well as simulation of nonlinear dynamic systems Integration of Simscape into Simulink for control system analysis and design

Each topic covered includes at least one example, giving students better comprehension of the subject matter. More complex topics are accompanied by multiple, painstakingly worked-out examples. Each section of each chapter is followed by several exercises so that students can immediately apply the ideas just learned. End-of-chapter review exercises help in learning how a combination of different ideas can be used to analyze a problem.

This second edition of a bestselling textbook fully integrates the MATLAB Simscape Toolbox and covers the usage of Simulink for new purposes. It gives students better insight into the involvement of actual physical components rather than their mathematical representations.

Preface	p. xiii
Acknowledgment	p. xv
Authors	p. xvii
Chapter 1 Introduction to MATLAB®, Simulink®, and Simscape®	p. 1
1.1 MATLAB Command Window and Command Prompt	p. 1
1.2 User-Defined Functions and Script Files	p. 2
1.2.1 Creating a Script File	p. 3
1.3 Defining and Evaluating Functions	p. 3
1.4 Iterative Calculations	p. 4
1.5 Matrices and Vectors	p. 5
1.6 Differentiation and Integration	p. 6
1.7 Plotting in MATLAB	p. 8
1.7.1 Plotting Data Points	p. 8
1.7.2 Plotting Analytical Expressions	p. 9
1.8 Simulink	p. 10
1.8.1 Block Library	p. 10
1.8.2 Building a New Model	p. 12
1.8.3 Simulation	p. 13
1.9 Simscape	p. 14
1.9.1 Block Library	p. 15
1.9.2 Building a New Model and Simulation	p. 15
1.9.3 Simulation	p. 18
Chapter 2 Complex Analysis, Differential Equations, and Laplace Transformation	p. 23
2.1 Complex Analysis	p. 23
2.1.1 Complex Numbers in Rectangular Form	p. 23
2.1.1.1 Magnitude	p. 24
2.1.1.2 Complex Conjugate	p. 25
2.1.2 Complex Numbers in Polar Form	p. 26
2.1.2.1 Complex Algebra Using the Polar Form	p. 28
2.1.2.2 Integer Powers of Complex Numbers	p. 30
2.1.2.3 Roots of Complex Numbers	p. 30
2.1.3 Complex Variables and Functions	p. 31
2.2 Differential Equations	p. 32
2.2.1 Linear, First-Order Differential Equations	p. 32
2.2.2 Second-Order Differential Equations with Constant Coefficients	p. 33
2.2.2.1 Homogeneous Solution	p. 33
2.2.2.2 Particular Solution	p. 34
2.3 Laplace Transformation	p. 37
2.3.1 Linearity of Laplace and Inverse Laplace Transforms	p. 40
2.3.2 Differentiation and Integration of Laplace Transforms	p. 40
2.3.2.1 Differentiation of Laplace Transforms	p. 40
2.3.2.2 Integration of Laplace Transforms	p. 41
2.3.3 Special Functions	p. 42
2.3.3.1 Unit-Step Function	p. 42
2.3.3.2 Unit-Ramp Function	p. 44
2.3.3.3 Unit-Pulse Function	p. 44
2.3.3.4 Unit-Impulse (Dirac Delta) Function	p. 45
2.3.3.5 The Relation between Unit-Impulse and Unit-Step Functions	p. 46
2.3.3.6 Periodic Functions	p. 46
2.3.4 Laplace Transforms of Derivatives and Integrals	p. 47
2.3.4.1 Laplace Transforms of Derivatives	p. 47
2.3.4.2 Laplace Transforms of Integrals	p. 48
2.3.5 Inverse Laplace Transformation	p. 48
2.3.5.1 Partial-Fraction Expansion Method	p. 49
2.3.5.2 $$$ Performing Partial Fractions in MATLAB	p. 51
2.3.5.3 Convolution Method	p. 53
2.3.6 Final-Value Theorem and Initial-Value Theorem	p. 55
2.3.6.1 Final-Value Theorem	p. 55
2.3.6.2 Initial-Value Theorem	p. 57
2.4 Summary	p. 60
Chapter 3 Matrix Analysis	p. 65
3.1 Vectors and Matrices	p. 65
3.1.1 Special Matrices	p. 67
3.1.2 Elementary Row Operations	p. 67
3.1.3 Rank of a Matrix	p. 68
3.1.4 Determinant of a Matrix	p. 69
3.1.4.1 Properties of Determinant	p. 70
3.1.4.2 Rank in Terms of Determinant	p. 70
3.1.4.3 Block Diagonal and Block Triangular Matrices	p. 71
3.1.5 Inverse of a Matrix	p. 72
3.1.5.1 Adjoint Matrix	p. 72
3.2 Solution of Linear Systems of Equations	p. 77
3.2.1 Gauss Elimination Method	p. 78
3.2.2 Using the Inverse of the Coefficient Matrix	p. 79
3.2.3 Cramer's Rule	p. 79
3.2.4 Homogeneous Systems	p. 81
3.3 Matrix Eigenvalue Problem	p. 83
3.3.1 Solving the Eigenvalue Problem	p. 83
3.3.2 Algebraic Multiplicity and Geometric Multiplicity	p. 86
3.3.2.1 Generalized Eigenvectors	p. 86
3.3.2.2 Similarity Transformations	p. 87
3.3.2.3 Matrix Diagonalization	p. 88
3.3.2.4 Defective Matrices	p. 88
3.4 Summary	p. 90
Chapter 4 System Model Representation	p. 95
4.1 Configuration Form	p. 95
4.1.1 Second-Order Matrix Form	p. 96
4.2 State-Space Form	p. 98
4.2.1 State Variables, State-Variable Equations, State Equation	p. 98
4.2.1.1 State-Variable Equations	p. 99
4.2.1.2 State Equation	p. 100
4.2.2 Output Equation, State-Space Form	p. 101
4.2.2.1 Output Equation	p. 102
4.2.2.2 State-Space Form	p. 103
4.2.3 Decoupling the State Equation	p. 105
4.3 Input-Output Equation, Transfer Function	p. 108
4.3.1 Input-Output Equations from the System Model	p. 108
4.3.2 Transfer Functions from the System Model	p. 110
4.4 Relations between State-Space Form, Input-Output Equation and Transfer Matrix	p. 114
4.4.1 Input-Output Equation to State-Space Form	p. 114
4.4.1.1 Controller Canonical Form $$$	p. 116
4.4.2 State-Space Form to Transfer Matrix	p. 118
4.5 Block Diagram Representation	p. 123
4.5.1 Block Diagram Operations	p. 123
4.5.1.1 Summing Junction	p. 123
4.5.1.2 Series Combinations of Blocks	p. 123
4.5.1.3 Parallel Combinations of Blocks	p. 124
4.5.1.4 Integration	p. 126
4.5.1.5 Closed-Loop Systems	p. 126
4.5.2 Block Diagram Reduction Techniques	p. 128
4.5.2.1 Moving a Branch Point	p. 128
4.5.2.2 Moving a Summing Junction	p. 128
4.5.2.3 Mason's Rule	p. 130
4.5.3 Block Diagram Construction from System Model	p. 132
4.6 Linearization	p. 138
4.6.1 Linearization of a Nonlinear Element	p. 138
4.6.1.1 Functions of Two Variables	p. 140
4.6.2 Linearization of a Nonlinear Model	p. 140
4.6.2.1 Operating Point	p. 140
4.6.2.2 Linearization Procedure	p. 141
4.6.2.3 Small-Angle Linearization	p. 143
4.6.3 Linearization with MATLAB Simulink	p. 145
4.7 Summary	p. 148
Chapter 5 Mechanical Systems	p. 155
5.1 Mechanical Elements	p. 155
5.1.1 Mass Elements	p. 155
5.1.2 Spring Elements	p. 157
5.1.3 Damper Elements	p. 158
5.1.4 Equivalence	p. 160
5.2 Translational Systems	p. 167
5.2.1 Degrees of Freedom	p. 167
5.2.2 Newton's Second Law	p. 168
5.2.3 Free-Body Diagrams	p. 168
5.2.4 Static Equilibrium Position and Coordinate Reference	p. 171
5.2.5 Massless Junctions	p. 176
5.2.6 D'Alembert's Principle	p. 178
5.3 Rotational Systems	p. 184
5.3.1 General Moment Equation	p. 184
5.3.2 Modeling of Rigid Bodies in Plane Motion	p. 185
5.3.3 Mass Moment of Inertia	p. 188
5.3.4 Pure Rolling Motion	p. 192
5.4 Mixed Systems: Translational and Rotational	p. 199
5.4.1 Force and Moment Equations	p. 199
5.4.2 Energy Method	p. 206
5.5 Gear-Train Systems	p. 214
5.6 System Modeling with Simulink and Simscape	p. 219
5.6.1 Translational Systems	p. 219
5.6.2 Rotational Systems	p. 226
5.7 Summary	p. 231
Chapter 6 Electrical, Electronic, and Electromechanical Systems	p. 239
6.1 Electrical Elements	p. 239
6.1.1 Resistors	p. 240
6.1.2 Inductors	p. 242
6.1.3 Capacitors	p. 243
6.2 Electric Circuits	p. 247
6.2.1 Kirchhoff s Voltage Law	p. 247
6.2.2 Kirchhoff's Current Law	p. 249
6.2.3 Node Method	p. 252
6.2.4 Loop Method	p. 255
6.2.5 State Variables of Circuits	p. 257
6.3 Operational Amplifiers	p. 261
6.4 Electromechanical Systems	p. 266
6.4.1 Elemental Relations of Electromechanical Systems	p. 266
6.4.2 Armature-Controlled Motors	p. 268
6.4.3 Field-Controlled Motors	p. 272
6.5 Impedance Methods	p. 275
6.5.1 Impedances of Electric Elements	p. 276
6.5.2 Series and Parallel Impedances	p. 276
6.5.3 Mechanical Impedances	p. 280
6.6 System Modeling with Simulink and Simscape	p. 281
6.6.1 Electric Circuits	p. 281
6.6.2 Operational Amplifiers	p. 286
6.6.3 DC Motors	p. 287
6.7 Summary	p. 292
Chapter 7 Fluid and Thermal Systems	p. 299
7.1 Pneumatic Systems	p. 299
7.1.1 Ideal Gases	p. 299
7.1.2 Pneumatic Capacitance	p. 300
7.1.3 Modeling of Pneumatic Systems	p. 301
7.2 Liquid-Level Systems	p. 304
7.2.1 Hydraulic Capacitance	p. 305
7.2.2 Hydraulic Resistance	p. 307
7.2.3 Modeling of Liquid-Level Systems	p. 308
7.3 Thermal Systems	p. 316
7.3.1 First Law of Thermodynamics	p. 316
7.3.2 Thermal Capacitance	p. 317
7.3.3 Thermal Resistance	p. 318
7.3.4 Modeling of Heat Transfer Systems	p. 321
7.4 System Modeling with Simulink and Simscape	p. 329
7.5 Summary	p. 337
Chapter 8 System Response	p. 341
8.1 Types of Response	p. 341
8.2 Transient Response and Steady-State Response	p. 341
8.2.1 Transient Response of First-Order Systems	p. 342
8.2.1.1 Free Response of First-Order Systems	p. 342
8.2.1.2 Impulse Response of First-Order Systems	p. 343
8.2.1.3 Step Response of First-Order Systems	p. 343
8.2.1.4 Ramp Response of First-Order Systems	p. 345
8.3 Transient Response of Second-Order Systems	p. 347
8.3.1 Free Response of Second-Order Systems	p. 349
8.3.1.1 $$$ Initial Response in MATLAB	p. 350
8.3.2 Impulse Response of Second-Order Systems	p. 351
8.3.2.1 $$$ Impulse Response in MATLAB	p. 353
8.3.3 Step Response of Second-Order Systems	p. 354
8.3.3.1 $$$ Step Response in MATLAB	p. 355
8.3.3.2 $$$ Response Analysis Using MATLAB Simulink	p. 357
8.4 Frequency Response	p. 365
8.4.1 Frequency Response of Stable, Linear Systems	p. 366
8.4.1.1 Frequency Response of First-Order Systems	p. 367
8.4.1.2 Frequency Response of Second-Order Systems	p. 368
8.4.2 Bode Diagram	p. 370
8.4.2.1 $$$ Plotting Bode Diagrams in MATLAB	p. 371
8.4.2.2 Bode Diagram of First-Order Systems	p. 371
8.4.2.3 Bode Diagram of Second-Order Systems	p. 373
8.5 Solving the State Equation	p. 379
8.5.1 Formal Solution of the State Equation	p. 379
8.5.1.1 Matrix Exponential	p. 379
8.5.1.2 $$$ Formal Solution in MATLAB	p. 381
8.5.2 Solution of the State Equation via Laplace Transformation	p. 382
8.5.3 Solution of the State Equation via State-Transition Matrix	p. 383
8.6 Response of Nonlinear Systems $$$	p. 385
8.6.1 Numerical Solution of the State-Variable Equations	p. 385
8.6.1.1 Fourth-Order Runge-Kutta Method	p. 385
8.6.2 Response via MATLAB Simulink	p. 388
8.6.3 Response of the Linearized Model	p. 388
8.7 Summary	p. 391
Chapter 9 Introduction to Vibrations	p. 397
9.1 Free Vibration	p. 397
9.1.1 Logarithmic Decrement	p. 398
9.1.2 Coulomb Damping	p. 400
9.2 Forced Vibration	p. 405
9.2.1 Half-Power Bandwidth	p. 406
9.2.2 Rotating Unbalance	p. 409
9.2.3 Harmonic Base Excitation	p. 411
9.3 Vibration Suppressions	p. 415
9.3.1 Vibration Isolators	p. 415
9.3.2 Vibration Absorbers	p. 418
9.4 Modal Analysis	p. 423
9.4.1 Eigenvalue Problem	p. 423
9.4.2 Orthogonality of Modes	p. 428
9.4.3 Response to Initial Excitations	p. 430
9.4.4 Response to Harmonic Excitations	p. 433
9.5 Vibration Measurement and Analysis	p. 436
9.5.1 Vibration Measurement	p. 437
9.5.2 System Identification	p. 438
9.6 Summary	p. 442
Chapter 10 Introduction to Feedback Control Systems	p. 449
10.1 Basic Concepts and Terminologies	p. 449
10.2 Stability and Performance	p. 452
10.2.1 Stability of Linear Time-Invariant Systems	p. 453
10.2.2 Time-Domain Performance Specifications	p. 455
10.2.3 Frequency-Domain Performance Specifications	p. 460
10.3 Benefits of Feedback Control	p. 462
10.3.1 Stabilization	p. 462
10.3.2 Disturbance Rejection	p. 465
10.3.3 Reference Tracking	p. 467
10.3.4 Sensitivity to Parameter Variations	p. 470
10.4 Proportional-Integral-Derivative Control	p. 473
10.4.1 Proportional Control	p. 474
10.4.2 Proportional-Integral Control	p. 476
10.4.3 PID Control	p. 478
10.4.4 Ziegler-Nichols Timing of PID Controllers	p. 481
10.5 Root Locus	p. 485
10.5.1 Root Locus of a Basic Feedback System	p. 486
10.5.2 Analysis Using Root Locus	p. 491
10.5.3 Control Design Using Root Locus	p. 493
10.6 Bode Plot	p. 498
10.6.1 Bode Plot of a Basic Feedback System	p. 498
10.6.2 Analysis Using Bode Plot	p. 505
10.6.3 Control Design Using Bode Plot	p. 507
10.7 Full-State Feedback	p. 511
10.7.1 Analysis of State-Space Equations	p. 511
10.7.2 Control Design for Full-State Feedback	p. 515
10.8 Integration of Simulink and Simscape into Control Design	p. 520
10.8.1 Control System Simulation Using Simulink	p. 520
10.8.2 Integration of Simscape into Control System Simulation	p. 521
10.9 Summary	p. 525
Bibliography	p. 531
Appendix A p. 533
Appendix B Useful Formulas	p. 535
Index	p. 537

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