Course detail

Robust and Algebraic Control

FEKT-MRALAcad. year: 2018/2019

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.

Language of instruction

Czech

Number of ECTS credits

5

Mode of study

Not applicable.

Guarantor

doc. Ing. Petr Blaha, Ph.D.

Department

Department of Control and Instrumentation (UAMT)

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.

Prerequisites

The subject knowledge on the Bachelor´s degree level is requested.

Co-requisites

Not applicable.

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.

Course curriculum

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

Work placements

Not applicable.

Aims

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.

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Doyle, Francis, Tannenbaum: Feedback Control Theory, Macmillan Publishing (EN)
Kučera:Algebraická teorie reg.,Academia Press (CS)
Scherer, Weiland: Linear matrix inequalities in control. DISC, 2000 (EN)
Štecha, Havlena: Moderní teorie řízení, ČVUT Praha (CS)

Recommended reading

Not applicable.

Classification of course in study plans

  • Programme EEKR-M Master's

    branch M-KAM , 1 year of study, summer semester, elective specialised

  • Programme EEKR-CZV lifelong learning

    branch EE-FLE , 1 year of study, summer semester, elective specialised

Type of course unit

 

Lecture

26 hod., optionally

Teacher / Lecturer

doc. Ing. Petr Blaha, Ph.D.

Syllabus

Introduction. Summary of needed mathematics.
Introduction to algebraic theory of control.
Using of algebraic theory for design of controllers, stabilizing controllers.
Discrete time optimal control.
Feedback and feed forward quadratic optimal control.
Discrete time stochastic control, MVC and generalized MVC controllers.
Sensitivity function shaping and disturbance rejection.
Algebraic theory for multivariable systems.
Control design of multivariable systems.
Parametric uncertainties, interval polynomials, stability of interval polynomials.
Nonparametric uncertainties, norms of signals and systems.
Robust control.
Sliding mode control.

Fundamentals seminar

14 hod., compulsory

Teacher / Lecturer

doc. Ing. Petr Blaha, Ph.D.

Syllabus

Mathematic tools for algebraic theory.
Solution of polynomial equation.
Calculation of stabilizing class of controllers for given system.
Time optimal controller design.
Interval polynomials and their stability.
Robust controllers.
Evaluation.

Exercise in computer lab

12 hod., compulsory

Teacher / Lecturer

Ing. Luděk Buchta, Ph.D.
Ing. Lukáš Pohl, Ph.D.

Syllabus

Introduction to usage of Symbolic Toolbox in Matlab.
Solution of polynomial equations using Matlab.
Exact model matching problem design and simulation.
Minimum variance control design.
Sensitivity function shaping design of controller.
Sliding mode controller design.