Practical MATLAB Modeling with Simulink (eBook)

Table of Contents 5
About the Author 13
About the Technical Reviewer 14
Acknowledgments 15
Introduction 16
Part I: Ordinary Differential Equations 20
Chapter 1: Analytical Solutions for ODEs 21
Classifying ODEs 22
Example 1 23
Example 2 24
Example 3 24
Analytical Solutions of ODEs 26
dsolve() 26
Example 4 26
Example 5 27
Example 6 29
Example 7 29
Second-Order ODEs and a System of ODEs 31
Example 8 31
Example 9 32
Example 10 33
Example 11 34
Example 12 34
Example 13 35
Laplace Transforms 40
Example 14 42
laplace/ilaplace 43
Example 15 43
Example 16 44
Example 17 44
Example 18 44
Example 19 48
Example 20 52
Example 21 54
References 58
Chapter 2: Numerical Methods for First-Order ODEs 59
Euler Method 59
Example 1 60
Improved Euler Method 62
Backward Euler Method 63
Example 2 65
Midpoint Rule Method 68
Example 3 69
Ralston Method 73
Runge-Kutta Method 74
Example 4 75
Runge-Kutta-Gill Method 78
Runge-Kutta-Fehlberg Method 81
Adams-Bashforth Method 84
Example 5 84
Milne Method 90
Example 6 91
Taylor Series Method 93
Example 7 93
Adams-Moulton Method 96
Example 8 98
MATLAB’s Built-in ODE Solvers 103
Example 9 105
The OPTIONS, ODESET, and ODEPLOT Tools of Solvers 111
Example 10 113
Example 11 116
Simulink Modeling 121
Example 12 121
SIMSET 129
References 130
Chapter 3: Numerical Methods for Second-Order ODEs 131
Euler Method 132
Example 1 132
Example 2 136
Example 3 138
Example 4 140
Example 5 142
Runge-Kutta Method 146
Example 6 146
Example 7 149
Example 8 152
Example 9 154
Example 10 156
Adams-Moulton Method 159
Example 11 159
Example 12 164
Simulink Modeling 169
Example 13 169
Example 14 171
Example 15 174
Example 16 175
Nonzero Starting Initial Conditions 176
Example 17 177
ODEx Solvers 180
Example 18 181
Example 19 183
Example 20 184
Example 21 187
diff() 190
Example 22 190
Chapter 4: Stiff ODEs 194
Example 1 194
Example 2 196
Example 3 197
Example 4 200
Jacobian Matrix 202
Example 5 203
Example 6 206
Chapter 5: Higher-Order and Coupled ODEs 210
Fourth-Order ODE Problem 210
Robertson Problem 214
Akzo-Nobel Problem 216
HIRES Problem 223
Reference 228
Chapter 6: Implicit ODEs 229
Example 1 230
Example 2 234
Example 3 236
Example 4 239
Example 5 242
Example 6 245
References 248
Chapter 7: Comparative Analysis of ODE Solution Methods 249
Example 1 250
Drill Exercises 267
Exercise 1 267
Exercise 2 268
Exercise 3 268
Exercise 4 269
Exercise 5 269
Exercise 6 270
Exercise 7 271
Exercise 8 272
Exercise 9 273
Exercise 10 274
Exercise 11 274
Exercise 12 275
Exercise 13 275
Part II: Boundary Value Problems in Ordinary Differential Equations 276
Chapter 8: Boundary Value Problems 277
Dirichlet Boundary Condition Problem 281
Example 1 281
Example 2 285
Robin Boundary Condition Problem 288
Example 3 288
Sturm-Liouville Boundary Value Problem 293
Example 4 294
Stiff Boundary Value Problem 299
Example 5 299
References 303
Drill Exercises 303
Exercise 1 304
Exercise 2 304
Exercise 3 304
Exercise 4 304
Exercise 5 304
Exercise 6 305
Exercise 7 305
Exercise 8 305
Exercise 9 305
Exercise 10 306
Exercise 11 306
Exercise 12 306
Exercise 13 306
Part III: Applications of Ordinary Differential Equations 307
Chapter 9: Spring-Mass-Damper Systems 308
Single Degree of Freedom System 308
Case 1: Free Vibration (Motion) 308
Case 2: Forced Vibration (Motion) 322
Two Degrees of Freedom System 333
Three Degrees of Freedom System 341
Matrix Approach for n-Degree of Freedom System 349
References 356
Chapter 10: Electromechanical and Mechanical Systems 358
Modeling a DC Motor 358
Modeling a DC Motor with Flexible Load 363
Modeling a Microphone 369
Modeling Motor: Pump Gear Box 374
Modeling Double Pendulum 384
Reference 397
Chapter 11: Trajectory Problems 398
Falling Object 398
Thrown Ball Trajectories 401
References 413
Chapter 12: Simulation Problems 414
Lorenz System 414
Lotka-Voltera Problem 420
References 424
Drill Exercises 425
Exercise 1 425
Exercise 2 426
Exercise 3 426
Exercise 4 426
Exercise 5 427
Exercise 6 427
Exercise 7 428
Exercise 8 428
Exercise 9 429
Exercise 10 429
Exercise 11 429
Exercise 12 430
Exercise 13 430
Exercise 14 431
Exercise 15 432
Exercise 16 433
Exercise 17 435
Exercise 18 436
Part IV: Partial Differential Equations 439
Chapter 13: Solving Partial Differential Equations 440
pdepe() 441
One-Dimensional Heat Transfer Problem 442
Example 1 443
Two-Dimensional Heat Transfer: Solving an Elliptic PDE with the Gauss-Seidel Method 447
Example 2 449
del2(): Laplace Operator 454
Example 3 455
Wave Equation 458
Solving a One-Dimensional Wave Equation 459
Example 4 462
Solving a Two-Dimensional Wave Equation 466
Example 5 467
References 470
Drill Exercises 471
Exercise 1 471
Exercise 2 471
Exercise 3 471
Exercise 4 472
Exercise 5 472
Exercise 6 472
Exercise 7 472
Exercise 8 472
Exercise 9 473
Exercise 10 473
Exercise 11 473
Exercise 12 474
Exercise 13 474
Index 475