Comprehensive overview of techniques for describing physical phenomena by means of computer models that are determined by mathematical analysis
Computer Models of Process Dynamics covers everything required to do computer based mathematical modeling of dynamic systems, including an introduction to a scientific language, its use to program essential operations, and methods to approximate the integration of continuous signals.
From a practical standpoint, readers will learn how to build computer models that simulate differential equations. They are also shown how to model physical objects of increasing complexity, where the most complex objects are simulated by finite element models, and how to follow a formal procedure in order to build a valid computer model. To aid in reader comprehension, a series of case studies is presented that covers myriad different topics to provide a view of the challenges that fall within this discipline. The book concludes with a discussion of how computer models are used in an engineering project where the readers would operate in a team environment.
Other topics covered in Computer Models of Process Dynamics include: - Computer hardware and software, covering algebraic expressions, math functions, computation loops, decision-making, graphics, and user-defined functions - Creative thinking and scientific theories, covering the Ancients, the Renaissance, Galileo, Newton, electricity and magnetism, and newer sciences - Uncertainty and softer science, covering random number generators, statistical analysis of data, the method of least squares, and state/velocity estimators - Flight simulators, covering the motion of an aircraft, the equations of motion, short period pitching motion, and phugoid motion
Established engineers and programmers, along with students and academics in related programs of study, can harness the comprehensive information in Computer Models of Process Dynamics to gain mastery over the subject and be ready to use their knowledge in many practical applications in the field.
Table of Contents
Preface xiii
1 Introduction 1
1.1 Engineering uses of computer models 1
1.1.1 Mission statement 2
1.2 The subject matter 3
1.3 Mathematical material 4
1.4 Some remarks 5
Bibliography 5
2 From Computer Hardware to Software 7
2.1 Introduction 7
2.2 Computing machines 7
2.2.1 The software interface 8
2.3 Computer programming 9
2.3.1 Algebraic expressions 10
2.3.2 Math functions 13
2.3.3 Computation loops 14
2.3.4 Decision making 16
2.3.5 Graphics 17
2.3.6 User defined functions 17
2.4 State transition machines 17
2.4.1 A binary signal generator 18
2.4.2 Operational control of an industrial plant 24
2.5 Difference engines 25
2.5.1 Difference equation to calculate compound interest 26
2.6 Iterative programming 27
2.6.1 Inverse functions 29
2.7 Digital simulation of differential equations 30
2.7.1 Rectangular integration 31
2.7.2 Trapezoidal integration 33
2.7.3 Second-order integration 35
2.7.4 An Example 36
2.8 Discussion 37
Exercises 38
References 41
3 Creative thinking and scientific theories 43
3.1 Introduction 43
3.2 The dawn of astronomy 44
3.3 The renaissance 45
3.3.1 Galileo 45
3.3.2 Newton 46
3.4 Electromagnetism 49
3.4.1 Magnetic fields 50
3.4.2 Electromagnetic induction 50
3.4.3 Electromagnetic radiation 51
3.5 Aerodynamics 52
3.5.1 Vector flow fields 53
3.6 Discussion 54
References 56
4 Calculus and the computer 57
4.1 Introduction 57
4.2 Mathematical solution of differential equations 58
4.3 From physical analogs to analog computers 60
4.4 Picard’s method for solving a nonlinear differential equation 61
4.4.1 Mechanization of Picard’s method 62
4.4.2 Feedback model of the differential equation 62
4.4.3 Approximate solution by Taylor series 64
4.5 Exponential functions and linear differential equations 65
4.5.1 Taylor series to approximate exponential functions 66
4.6 Sinusoidal functions and phasors 67
4.6.1 Taylor series to approximate sinusoids 69
4.7 Bessel’s equation 70
4.8 Discussion 72
Exercises 73
Bibliography 74
5 Science and computer models 75
5.1 Introduction 75
5.2 A planetary orbit around a stationary Sun 76
5.2.1 An analytic solution for planetary orbits 79
5.2.2 A difference equation to model planetary orbits 80
5.3 Simulation of a swinging pendulum 81
5.3.1 A graphical construction to show the motion of a pendulum 83
5.3.2 Truncation and roundoff errors 84
5.4 Lagrange’s equations of motion 85
5.4.1 A double pendulum 87
5.4.2 A few comments 90
5.4.3 Modes of motion of a double pendulum 90
5.4.4 Structural vibrations in an aircraft 91
5.5 Discussion 94
Exercises 94
Bibliography 95
6 Flight simulators 97
6.1 Introduction 97
6.2 The motion of an aircraft 98
6.2.1 The equations of motion 99
6.3 Short period pitching motion 101
6.3.1 Case study of short period pitching motion 104
6.3.2 State equations of short period pitching 105
6.3.3 Transfer functions of short period pitching 107
6.3.4 Frequency response of short period pitching 108
6.4 Phugoid motion 110
6.5 User interfaces 111
6.6 Discussion 112
Exercises 113
Bibliography 114
7 Finite element models and the diffusion of heat 115
7.1 Introduction 115
7.2 A thermal model 117
7.2.1 A finite element model based on an electrical ladder network 118
7.2.2 Free settling from an initial temperature profile 119
7.2.3 Step response test 121
7.2.4 State space model of diffusion 126
7.3 A practical application 129
7.4 Two-dimensional steady-state model 131
7.5 Discussion 132
Exercises 134
Bibliography 135
8 Wave equations 137
8.1 Introduction 137
8.2 Energy storage mechanisms 138
8.2.1 Partial differential equation describing propagation in a transmission line 140
8.3 A finite element model of a transmission line 141
8.4 State space model of a standing wave in a vibrating system 145
8.4.1 State space model of a multiple compound pendulum 147
8.5 A two-dimensional electromagnetic field 148
8.6 A two-dimensional potential flow model 151
8.7 Discussion 155
Exercises 156
Bibliography 159
9 Uncertainty and softer science 161
9.1 Introduction 161
9.2 Empirical and “black box” models 162
9.2.1 An imperfect model of a simple physical object 163
9.2.2 Finite impulse response models 164
9.3 Randomness within computer models 166
9.3.1 Random number generators and data analysis 167
9.3.2 Statistical estimation and the method of least squares 168
9.3.3 A state estimator 171
9.3.4 A velocity estimator 175
9.3.5 An FIR filter 176
9.4 Economic, Geo-, Bio-, and other sciences 179
9.4.1 A pricing strategy 181
9.4.2 The productivity of money 184
9.4.3 Comments on business models 187
9.5 Digital images 189
9.5.1 An image processor 190
9.6 Discussion 193
Exercises 194
Bibliography 196
10 Computer models in a development project 197
10.1 Introduction 197
10.1.1 The scope of this chapter 198
10.2 A motor drive model 198
10.2.1 A conceptual model 200
10.2.2 The motor drive parameters 202
10.2.3 Creating the simulation model 203
10.2.4 The electrical and mechanical subsystems 204
10.2.5 System integration 206
10.2.6 Configuration management 208
10.3 The definition phase 208
10.3.1 Selection of the motor 209
10.3.2 Simulation of load disturbances 210
10.4 The design phase 213
10.4.1 Calculation of frequency response 213
10.4.2 The current control loop 214
10.4.3 Design review and further actions 217
10.4.4 Rate feedback 219
10.5 A setback to the project 222
10.5.1 Elastic coupling between motor and load 222
10.6 Discussion 227
Exercises 229
Bibliography 230
11 Postscript 231
11.1 Looking back 231
11.2 The operation of a simulation facility 233
11.3 Looking forward 234
Bibliography 235
Appendix A Frequency response methods 237
Appendix B Vector analysis 261
Appendix C Scalar and vector fields 269
Appendix D Probability and statistical models 287
Index 297
