Robust and Algebraic Control
FEKT-MRALAcad. year: 2019/2020
The course is focused on application of algebraic theory for control circuit’s synthesis. It consists of algebraic theory, the controller designs using polynomial methods, structured and unstructured uncertainties of dynamic systems and introduction into robust control.
Learning outcomes of the course unit
The student are able to use algebraic methodes of controller design and they know how to design robust controller.
The subject knowledge on the Bachelor´s degree level is requested.
Recommended optional programme components
Recommended or required reading
Kučera:Algebraická teorie reg.,Academia Press (CS)
Štecha, Havlena: Moderní teorie řízení, ČVUT Praha (CS)
Doyle, Francis, Tannenbaum: Feedback Control Theory, Macmillan Publishing (EN)
Scherer, Weiland: Linear matrix inequalities in control. DISC, 2000 (EN)
Planned learning activities and teaching methods
Teaching methods depend on the type of course unit as specified in the article 7 of BUT Rules for Studies and Examinations. Materials for lectures and exercises are available for students from web pages of the course. Students have to write a single project/assignment during the course.
Assesment methods and criteria linked to learning outcomes
Exercises. Individual project. Max. 30 points.
Written exam. Max 70 points.
Language of instruction
1. Introduction into problematic.
2. Algebraic theory. Solution of polynomial equation, general solution, special solutions, solvability condition.
3. Application of algebraic methods to simple controller designs. Pole placement method, exact model matching problem, the group of stabilizing controllers.
4. Sensitivity function shaping design. Sensitivity function and modulus margin, sensitivity function template, additional polynomials in controller and in its design.
5. Time optimal discrete control. Feedforward control,
6. Quadraticaly optimal discrete control, 1DOF, 2DOF, finite and stable time optimum control with nonzero initial conditions.
7. Stochastic control. Minimum variance control, the evaluation of MVC controllers, generalized minimum variance control.
8. Interval polynomials. Zero exclusion principle, value sets, Mikhailov-Leonard stability criteria, Kharitonov polynomials.
9. Inroduction into robust control. The notion of robustness, norms of the system and signal, LFT, system matrices and their operations.
10. Description of uncertainties. Parametric and nonparametric uncertainties, their description in Matlab Simulink.
11. Mixed sensitivity design, GS controller. Similarities with sensitivity function shaping method.
12. Course summary
To introduce to the students universal tool for solving tasks of automatic control and to became familiar with robust control. and CASE systems.
Specification of controlled education, way of implementation and compensation for absences
The content and forms of instruction in the evaluated course are specified by a regulation issued by the lecturer responsible for the course and updated for every academic year.