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Mathematical foundations of the theory of automatic control

All lectures: All lectures on the discipline: mathematical foundations of the theory of automatic control are collected here. These fascinating lectures provide us with the opportunity to explore the deep principles and phenomena underlying our knowledge and our desire to understand the world.


1. Introduction Mathematical foundations of the theory of automatic control
2. Introduction Fractional rational and impulse functions.
3. Fourier and Laplace transforms.
4. The concept of linear dynamic link. Transfer function, block diagram, time characteristics of a dynamic link.
5. Frequency response dynamic link
6. Elementary (typical) dynamic links
7. Time and frequency characteristics of links
8. The rules of equivalent transformations of block diagrams of automatic control systems
9. Oriented graphs of automatic control systems
10. Logarithmic frequency characteristics of dynamic links
11. Logarithmic frequency characteristics of automatic control systems
12. Time and frequency characteristics of the oscillatory level
13. The concept of a multidimensional system used in control theory.
14. Structural matrix schemes and transfer matrices
15. Математические модели в пространстве состояний
16. 15. Interrelation of types of mathematical models of multidimensional systems.
17. Methods for assessing the quality of management systems
18. 17 Quality assessment with harmonic effects
19. 18 Calculation of linear integral estimates
20. 19 Quadratic integral estimate taking into account the derivative
21. 20 Root Criteria for Transient Quality
22. 21 Definitions and problems of identification of mathematical models
23. Transformation of structural schemes. Control system graph. Correspondence of structural diagrams to graphs.
24. 1.1 Cybernetic concepts and the subject of control theory
25. 1.2 Structure and functional components of ACS
26. 1.3 Tasks for managing complex systems
27. 1.4 Local management and control tasks
28. 1.5 Blocks and control algorithms
29. 2.1 Linear input-output models
30. 2.2 Transients and characteristics of input-output models
31. 2.3 Elementary links
32. 2.4 Building Input / Output Models
33. 3.1 The concept of state space and the state-exit model
34. 3.2 Models of Managed Systems
35. 3.3 Phase trajectories of an autonomous second order system
36. 3.4 Equivalent transformations of VSV models and canonical representations
37. 4.1 Models of electromechanical objects
38. 4.2 Models of driver units and external influences
39. 4.3 Principles of control, models of regulators and closed systems
40. Transfer function of a linear stationary system
41. Structural transformation systems. Structural schemes. The main types of connection elements. Examples of tasks
42. Rules for the conversion of structural schemes. negative connections. problem solving examples
43. Preparation of equations of automatic control system (ACS)
44. Temporal characteristics of linear stationary systems. transients. Examples of problem solving
45. Amplitude-phase, frequency, logarithmic frequency characteristics. problem solving examples
46. Stability of linear stationary systems. Criteria of stability. Examples of problem solving
47. Example Definition of parameters of dynamic characteristics of linear links of automatic control systems
48. Example of transfer function modeling
49. State space method and system state