Read more
COMPUTER MODELS OF PROCESS DYNAMICS
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.
List 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.
About the author
Olis Rubin, DSc. Eng., has held many positions in control engineering throughout his career including at Denel, PBMR, ContrOlis, Kentron, and CSIR. He was also an honorary post graduate professor in Control Systems at the University of Pretoria. He previously published
Control Engineering in Development Projects (2016) and
The Design of Automatic Control Systems (1986) with Artech House.
