Nonlinear Systems of Automatic Control
Description: Basic concepts, stability analysis and quality issues of nonlinear systems management. The types and features of nonlinear systems are studied. The main methods of analysis of nonlinear systems: the phase space method, the point image method and harmonic linearity, stabilization of relay systems. Methods of stability analysis: methods of the first and second Lyapunov, as well as methods of absolute stability research. Discrete control systems are considered.
Amount of credits: 5
Course Workload:
| Types of classes | hours |
|---|---|
| Lectures | 15 |
| Practical works | 30 |
| Laboratory works | |
| SAWTG (Student Autonomous Work under Teacher Guidance) | 30 |
| SAW (Student autonomous work) | 75 |
| Form of final control | Exam |
| Final assessment method | writing Exam |
Component: University component
Cycle: Base disciplines
Goal
- Formation of students' knowledge on the construction and use of nonlinear systems of automatic regulation and control of technical systems in various industries, preparation for independent solution of theoretical and applied problems in the field of application of such systems.
Objective
- Preparation for independent solution of theoretical and applied problems in the field of non-linear automatic control systems.
Learning outcome: knowledge and understanding
- – principles of construction of nonlinear systems; - types and features of the description of nonlinear elements; – phase space method; – method of harmonic linearization; – stabilization of relay systems; – the first and second Lyapunov methods for studying the stability of control systems; – methods for studying absolute stability; – bases of construction of discrete control systems.
Learning outcome: applying knowledge and understanding
- Apply knowledge of the principles of constructing nonlinear systems in practical and research activities.
Learning outcome: formation of judgments
- The ability to independently apply the methods and means of cognition, learning and self-control, to be aware of the prospects of intellectual, cultural, moral, physical and professional self-development and self-improvement, to be able to critically assess their own strengths and weaknesses.
Learning outcome: communicative abilities
- The ability to work effectively individually and as a member of a team, demonstrating the skills of managing separate groups of performers, including on interdisciplinary projects, be able to show personal responsibility, adherence to professional ethics and standards of professional conduct.
Learning outcome: learning skills or learning abilities
- The ability to master new equipment being introduced, to check the technical condition and residual life of the existing equipment of automation systems, if necessary, to provide repair and restoration work at the production sites of the enterprise.
Teaching methods
When conducting training sessions, it is planned to use the following educational technologies: - interactive lecture (application of the following active forms of learning: guided discussion or conversation; moderation; demonstration of slides or educational films; brainstorming; motivational speech); - construction of scenarios for the development of various situations based on the specified conditions; - information and communication (for example, classes in a computer classroom using professional application software packages); - search and research (independent research activity of students in the learning process); - solving educational tasks.
Assessment of the student's knowledge
Teacher oversees various tasks related to ongoing assessment and determines students' current performance twice during each academic period. Ratings 1 and 2 are formulated based on the outcomes of this ongoing assessment. The student's learning achievements are assessed using a 100-point scale, and the final grades P1 and P2 are calculated as the average of their ongoing performance evaluations. The teacher evaluates the student's work throughout the academic period in alignment with the assignment submission schedule for the discipline. The assessment system may incorporate a mix of written and oral, group and individual formats.
| Period | Type of task | Total |
|---|---|---|
| 1 rating | Estimated work | 0-100 |
| Estimated work | ||
| Estimated work | ||
| Estimated work | ||
| Estimated work | ||
| Estimated work | ||
| Test | ||
| 2 rating | Estimated work | 0-100 |
| Estimated work | ||
| Estimated work | ||
| Estimated work | ||
| Estimated work | ||
| Estimated work | ||
| Test | ||
| Total control | Exam | 0-100 |
The evaluating policy of learning outcomes by work type
| Type of task | 90-100 | 70-89 | 50-69 | 0-49 |
|---|---|---|---|---|
| Excellent | Good | Satisfactory | Unsatisfactory |
Evaluation form
The student's final grade in the course is calculated on a 100 point grading scale, it includes:
- 40% of the examination result;
- 60% of current control result.
The final grade is calculated by the formula:
| FG = 0,6 | MT1+MT2 | +0,4E |
| 2 |
Where Midterm 1, Midterm 2are digital equivalents of the grades of Midterm 1 and 2;
E is a digital equivalent of the exam grade.
Final alphabetical grade and its equivalent in points:
The letter grading system for students' academic achievements, corresponding to the numerical equivalent on a four-point scale:
| Alphabetical grade | Numerical value | Points (%) | Traditional grade |
|---|---|---|---|
| A | 4.0 | 95-100 | Excellent |
| A- | 3.67 | 90-94 | |
| B+ | 3.33 | 85-89 | Good |
| B | 3.0 | 80-84 | |
| B- | 2.67 | 75-79 | |
| C+ | 2.33 | 70-74 | |
| C | 2.0 | 65-69 | Satisfactory |
| C- | 1.67 | 60-64 | |
| D+ | 1.33 | 55-59 | |
| D | 1.0 | 50-54 | |
| FX | 0.5 | 25-49 | Unsatisfactory |
| F | 0 | 0-24 |
Topics of lectures
- Introduction
- Methods for describing control systems
- Representation of systems in the state space
- Image of processes in the phase space
- Linear and non-linear control systems
- Methods for the analysis of nonlinear systems on a plane
- Method of point mappings
- Initial provisions of the method of harmonic linearization
- Calculation of coefficients of harmonic linearization
- Algebraic method for determining self-oscillations
- Stability of non-linear systems
- Lyapunov function
- Absolute stability
- Discrete control systems
- Transfer functions of discrete systems
Key reading
- CHernov B.A. Lineinye sistemy avtomaticheskogo regulirovaniıa: Uchebnoe posobie (dlıa studentov vysşih uchebnyh zavedenii spetsialnosti «Avtomatizatsiıa i upravlenie»). – Almaty: NAO AUS, 2015. – 80 s
- Besekerskii V.A., Popov E.P. Teoriıa sistem avtomaticheskogo upravleniıa. – SPb.: Izd-vo «Professiıa», 2004. – 752 s. (Seriıa: Spetsialist).
- Kim D.P. Teoriıa avtomaticheskogo upravleniıa. V 2-h t. T.2. Mnogomernye, nelineinye, optimalnye i adaptivnye sistemy. – M.: FIZMATLIT, 2007. – 440 s.
- Teoriıa avtomaticheskogo upravleniıa: Ucheb. dlıa vuzov / Pod red. V.B. Iakovleva. – M.: Vysşaıa şkola, 2009. – 567 s.
- Pevzner L.D. Teoriıa sistem upravleniıa: Uchebnoe posobie. – SPb.: Izdatelstvo «Lan», 2013. – 424 s. – (Uchebniki dlıa vuzov. Spetsialnaıa literatura).
- Malafeev S.I., Malafeeva A.A. Teoriıa avtomaticheskogo upravleniıa: Uchebnik dlıa stud. uchrej. vysş. obrazovaniıa. – M.: Izdatelskii tsentr «Akademiıa», 2014. – 384 s. – (Ser. Bakalavriat).
- Gaiduk A.R., Belıaev V.E., Pıavchenko T.A. Teoriıa avtomaticheskogo upravleniıa v primerah i zadachah s reşeniıami v MATLAV: Uchebnoe posobie. - SPb.: Izdatelstvo «Lan», 2011. – 464 s. (Uchebniki dlıa vuzov).
- Pevzner L.D. Teoriıa avtomaticheskogo upravleniıa. Zadachi i reşeniıa: Uchebnoe posobie. – SPb.: Izdatelstvo «Lan», 2016. – 604 s. – (Uchebniki dlıa vuzov. Spetsialnaıa literatura).
- Pervozvanskii A.A. Kurs teorii avtomaticheskogo upravleniıa: Uchebnoe posobie. – SPb.: Izdatelstvo «Lan», 2010. - 624 s.- (Uchebniki dlıa vuzov. Spetsialnaıa literatura).
- Kudinov IY.I., Paşenko F.F. Teoriıa avtomaticheskogo upravleniıa (s ispolzovaniem MATLAB-SIMULINK): Uchebnoe posobie. – SPb.: Izdatelstvo «Lan», 2016. – 256 s. – (Uchebniki dlıa vuzov. Spetsialnaıa literatura).
- Şişmarev V.IY. Osnovy avtomaticheskogo upravleniıa: Ucheb. posobie dlıa studentov vuzov. – M.: Izdatelskii tsentr «Akademiıa», 2008. – 352 s.
- IYrevich E.I. Teoriıa avtomaticheskogo upravleniıa. – SPb.: BHV-Peterburg, 2007. – 560 s.
- Pupkov K.A., Konkov V.G. Teoriıa nelineinyh sistem avtomaticheskogo regulirovaniıa: Uchebnoe posobie. – M.: RUDN, 2009. – 258 s.
- Volobueva O.P. Osnovy teorii upravleniıa. Uchebnik dlıa vuzov. – Almaty: KazNTU, 2005. – 256 s
- Rotach V.Ia. Teoriıa avtomaticheskogo upravleniıa: Uchebnik dlıa vuzov. – M.: Izdatelstvo MI, 2008. – 400 s.
- Galperin M.V. Avtomaticheskoe upravlenie: Uchebnik. – M.: ID «FORUM»: INFRA-M, 2007. – 224 s. (Professionalnoe obrazovanie). 75
