Robust Invariant Systems

Description: The discipline is devoted to the study of modern control theory and systems theory, methods of analysis and synthesis of control systems under conditions of incomplete certainty. Non-adaptive methods for controlling objects with parametric uncertainties, synthesis of parametrically invariant systems, robust stabilization and control are considered. Examples and solutions to problems of synthesis of robust control systems for technical systems are given. Tasks on the analysis and synthesis of control systems are considered using application packages Simulink Toolbox, Robust Control Toolbox of the MatLab integrated environment.

Amount of credits: 5

Пререквизиты:

• Automation of Engineering Systems

Course Workload:

Component: Component by selection

Cycle: Profiling disciplines

Goal

• Formation in students of professional competencies in the application of methods of modern automatic control theory, intended for the synthesis of control systems that are stable according to a given criterion under the condition of parametric or structural uncertainty.

Objective

• studying methods of robust control theory, basic techniques for synthesizing robust regulators of automatic systems, methods for studying complex phenomena in control processes of technical systems under conditions of a priori uncertainty;
• mastering the mathematical apparatus that underlies the methods of synthesis and analysis of robust and invariant control systems;
• mastering of application packages Simulink Toolbox, Robust Control Toolbox of the MatLab environment to solve applied problems;
• acquisition of practical skills in the synthesis of robust regulators of automatic systems.

Learning outcome: knowledge and understanding

• demonstrate knowledge of modern control theory and systems theory, methods and means of synthesizing control systems under conditions of incomplete certainty;
• evaluate calculations for analyzing the stability of robust and invariant control systems;

Learning outcome: applying knowledge and understanding

• analyze existing and independently develop technical documentation, clearly present and defend the results of complex engineering and scientific activities in the field of automation and control;

Learning outcome: formation of judgments

• apply independently methods and means of cognition, realize the prospects of professional self-development and self-improvement, be able to critically evaluate one’s strengths and weaknesses;

Learning outcome: communicative abilities

• present the results of engineering problems and scientific research

Learning outcome: learning skills or learning abilities

• apply methods of automatic control theory to synthesize robust and invariant systems;
• apply computer software for the analysis and synthesis of robust and invariant systems.

Teaching methods

interactive lecture (use of the following active forms of learning: guided discussion or conversation; moderation; demonstration of slides or educational films; motivational speech);

information and communication (for example, classes in a computer class using professional application software packages);

search and research (independent research activities of students during the learning process).

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.

The evaluating policy of learning outcomes by work type

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:

 

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:

Topics of lectures

• Introduction to robust systems
• Types of uncertainty
• Basic methods for managing uncertain objects
• Analysis of systems with uncertainties
• Methods of sensitivity theory
• Systems with interval parameters
• Non-adaptive methods for controlling objects with parametric uncertainties
• Synthesis of parametrically invariant systems
• Robust interval control
• Synthesis of robust control systems
• Synthesis of robust systems with a PID controller
• Robust system with internal model
• Robust stabilization and control
• First order object management
• Nonlinear robust control of a multidimensional object

Key reading

• Bobcov A.A., Nikiforov V.O., Pyrkin A.A., Slita O.V., Ushakov A.V. Metody adaptivnogo i robastnogo upravleniya nelinejnymi ob"ektami v priborostroenii: uchebnoe posobie dlya vysshih uchebnyh zavedenij. – SPb: NIU ITMO, 2013. – 277 c.
• Polyak B.T. Robastnaya ustojchivost' i upravlenie / B.T.Polyak, P.S. Shcherbakov. – M.:Nauka, 2002.-303s.
• Dorf Richard. Sovremennye sistemy upravleniya / R. Dorf, R. Bishop; Per. s angl. B. I. Kopylova. - Moskva : Lab. Bazovyh Znanij : YuNIMEDIASTAJL, 2002. - 831 s.
• Gerasimov, D. N. Adaptivnoe i robastnoe upravlenie dinamicheskimi sistemami. Praktikum dlya vypolneniya laboratornyh, prakticheskih i kursovyh rabot : uchebnoe posobie / D. N. Gerasimov, A. V. Paramonov, V. O. Nikiforov. — Sankt-Peterburg : NIU ITMO, 2020. — 149 s.

Further reading

• Kim, D. P. Teoriya avtomaticheskogo upravleniya. Mnogomernye, nelinejnye, optimal'nye i adaptivnye sistemy : uchebnik i praktikum dlya vuzov. – Moskva: Izdatel'stvo Yurajt, 2023. - 441 s. URL: https://urait.ru/bcode/513236.
• Bobcov A.A., Pyrkin A.A. Adaptivnoe i robastnoe upravlenie s kompensaciej neopredelennostej. Uchebnoe posobie. - SPb.: NIU ITMO, 2013. - 135s.
• Cykunov A.M. Robastnoe upravlenie s kompensaciej vozmushchenij. - Moskva : Fizmatlit, 2012. – 298 s.
• Modelirovanie sistem : uchebnoe posobie / I.A. Elizarov, Yu.F. Martem'yanov, A.G. Skhirtladze, A.A. Tret'yakov. – Tambov : Izd-vo FGBOU VPO «TGTU», 2011. – 96 s.
• Lazarev V.L. Robastnoe upravlenie v biotekhnologicheskoj promyshlennosti: Ucheb. posobie. SPb.: Universitet ITMO; IHiBT, 2015. 196 s