Contents

Introduction

First and second surface: Comics and What we are talking about

(1.) Chapter I: Everything is a system: Philosophy

2. Everything is a system, systems are everywhere
3. Levels of understanding
4. All this is, in fact, philosophy too
5. The big questions: ontology
6. The big questions: epistemology
7. The big questions: ethics
8. The big questions: aesthetics
9. Is there an answer? And if so, how definitive is it?

(10.) Chapter II: Reality and its models

11. System science does not provide definitive answers but helps to create models that actually work
12. Models: similarities and differences
13. Geometry as a basic model
14. Another basic model: motion
15. This is where the concepts of path, velocity and time came from
16. These and similar basic shapes are still the building blocks of our thinking
17. Homomorphism and homology
18. Deterministic or stochastic?
19. Stochastic models and probable frequencies
20. System models also serve as thematic summaries
21. Holistic model building

(22.) Chapter III: Model building in our minds

23. Ancient basic concepts and models
24. World models in circle forms: abstract concepts
25. Symmetries and equilibriums
26. Representation in the mind
27. Logic makes generalizations from connecting shapes (With logical example)
28. Different explanations for relations

(29.) Chapter IV: Model representations

30. Model representations are diverse
31. Mathematics is the most abstract language of system models
32. Mathematical representation became a practical tool with the emergence of computer science
33. New directions in computer design and manufacturing
34. The computational-mathematical model has become the basis of control systems

(35.) Chapter V: Signals and processes

36. Where shall we draw the boundaries of the system?
37. Boundaries: input - output
38. The relationship between the systems: signals
39. Signals
40. Observation of signals
41. Observation of frequencies
42. Audio frequencies
43. Observations in the time and in the frequency domain; the representations and transformations of identical phenomena
44. The measure
45. State variables
46. Noises and disturbances
47. Big Data, highlighting significant signs in extremely large sets of data
48. Between input and output: the process itself
49. The family of processes: self-regulating processes
50. The family of processes: continuous processes
51. State space modelling of continuous processes
52. The family of processes: non-continuous processes
53. The family of processes: Discrete time, sampled processes
54. Linear and non-linear operators
55. Linear is easy, non-linear is difficult to calculate
56. Typical connections of processes

(57.) Chapter VI:  Changes and stationarity

58. Changes: processes in systems
59. Dynamic equilibria: gains and losses
60. The dynamic relations of a system are determined by the principles of changes and stationarity
61. Equilibrium and conservation
62. In all changes something is conserved
63. We think about the problem of changes and conservations for a long while
64. System reserves are important (energy, capital, health status)
65. Reversible and irreversible changes
66. The first dissipation phenomenon observed was friction
67. What is left unchanged?
68. Entropy: an interesting measure of the changes of one-way processes
69. Cause or interaction?

(70.) Chapter VII: Dimensions and spaces

71. Dimensions and spaces
72. Changes can be described in space and time
73. Coordinates and scaling as organizers of the selected spaces
74. Registration and representation
75. Problems are solved in the suitable spaces and coordinate systems
76. This leads to metrics, the measures of the spaces
77. Time is not an independent framework but the relative characteristic of coincidences
78. Hyperbolic spaces
79. Once we thought of space and time as the eternal, fixed framework of the world
80. The spaces of system science
81. The Möbius transformation
82. Hardy spaces

(83.) Chapter VIII: Control

84. Control is goal oriented
85. The aim and the goal function of a control system
86. Lagrange’s observation
87. The “best” solution
88. The irreversible problem
89. Observation and control
90. Feedback is a crucial element in closed-loop control
91. The main problem of control: Stability
92. Stability is sensitive to frequency characteristics of the system
93. Quality specifications
94. Zeros, poles. Design considerations.
95. Control structures
96. About the control algorithms
97. PID control
98. Youla parameterisation, its special case is dead beat control
99. Predictive control
100. State feedback, state estimation
101. Adaptive control
102. The next task is robustness

(103.) Chapter IX: Artificial intelligence

104. Artificial intelligence methods
105. Variables in logic
106. Conceptual generalisations
107. Logical functions
108. Frames and nets
109. Modalities
110. Intensions
111. Non-monotonic logics
112. Stochastic relations
113. Different uncertainties
114. Shapes
115. Learning
116. Design, scheduling
117. Pattern recognition and robots, computational linguistics, cognitive sciences

(118.) Chapter X: The history of control

119. About the history of control

First, second and fourth surface: Mathematical representations

(120.) Chapter XI: Mathematical – computational representation of system theory

121. About the mathematical – computer science representation of system theory
122. Hamilton, Lie and the Erlangen program: the great unifications
123. Group theory (with mathematical representation)
124. Analytical functions, complex variable
125. The significance and unity of the time and frequency based approach (with mathematical representation)
126. Lie groups and Lie algebras (with mathematical representation)
127. Computational spaces (with mathematical representation)
128. Transformations (with mathematical representation)
129. A single view for the variety of approaches
130. Applications of the matrix technics of linear algebra (with mathematical representation)
131. Operation and quality requirements as process space metrics
132. State spaces and process identification
133. Stability and quality - norms
134. The world of  Hardy-spaces – modern world of control theory
135. Managing complex systems with computers
136. The relationship between classic control theory and the modern approach
137. Summary overview

First, second, third and fourth surface: Control course

2. Systems everywhere
11. Models try to describe reality from a given viewpoint
30. System and its model 1.
31. System and its model 2.

Fifth surface: Case studies

1. Cooking
2. Driving a car
3. Energy production and distribution
4. Oil refinery
5. Systems and controls in the human body
6. Medical systems and health education
7. Economical systems
8. Feedback in education and upbringing

JAVA Applets

The JAVA applet demonstrates that by increasing the time period the periodic function approximates an aperiodic function and the frequency spectrum becomes continuous. (Instruction)
Fourier JAVA applet. (Instruction)
The JAVA applet shows the step and impulse responses, the Bode and the Nyquist diagrams of a system, given by its transfer function. The transfer function is described by its numerator and denominator polynomials. (Instruction)
Shower JAVA applet. (Instruction)
Juggler JAVA applet. (Instruction)
The Java applet demonstrates the behavior of the continuous control system with parallel PID controller. (Instruction)
The Java applet demonstrates the behavior of the continuous control system with series PID controller. (Instruction)
The Java applet demonstrates the behavior of the continuous Youla parameterized control. (Instruction)
The Java applet demonstrates the behavior of the discrete Youla parameterized control system. (Instruction)
The JAVA applet shows for the case of a first order system that the output is composed as the sum of the free and forced responses. It also demonstrates for some cases the behavior of predictive control. (Instruction)

Student works

Glossary

References