Course detail

Robust and Algebraic Control

FEKT-MPC-RALAcad. year: 2020/2021

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 to robust control.

Language of instruction

Czech

Number of ECTS credits

6

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

After passing the course, student should be able to
- solve algebraic equations and understand algebraic theory
- utilize basic algebraic methods for controller designs
- explain the relationship between sensitivity function and modulus stability margin
- describe the possibilities of sensitivity function shaping and use them for robust controller design
- determine stability of interval polynomials
- utilize parametric and non-parametric uncertainties in the environment of MATLAB Simulink
- design the controller using H infinity mixed sensitivity method

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.
Final 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. Quadratically 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. Introduction into robust control. The notion of robustness, norms of the system and signal, LFT, system matrices and their operations.
10. H2 and H infinity controller. Mixed sensitivity design method.
11. Description of uncertainties. Parametric and nonparametric uncertainties, their description in MATLAB Simulink.
12. Linear matrix inequalities (LMI), quadratic form LJ and its conversion to LMI, LQR using LMI, H infinity using LMI.
13. Recapitulation, course summary.

Work placements

Not applicable.

Aims

The aim of the course is to introduce students with algebraic theory as a universal tool for solving tasks of automatic control and to became familiar with robust control methods.

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, J. C., Francis, B. A., Tannenbaum, A. R.: Feedback Control Theory, Dover Publications, 2009, ISBN-13: 978-0486469331. (EN)
Havlena, V., Štecha, J.: Moderní teorie řízení, Skriptum ČVUT, Praha 2000 (CS)

Recommended reading

Scherer, C., Weiland, S.: Linear matrix inequalities in control. DISC, 2005 (EN)

Elearning

eLearning: currently opened course

Classification of course in study plans

  • Programme MPC-KAM Master's 1 year of study, summer semester, compulsory-optional

Type of course unit

 

Lecture

26 hod., optionally

Teacher / Lecturer

Ing. Lukáš Pohl, Ph.D.
doc. Ing. Petr Blaha, Ph.D.

Syllabus

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. Quadratically 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. Introduction into robust control. The notion of robustness, norms of the system and signal, LFT, system matrices and their operations.
10. H2 and H infinity controller. Mixed sensitivity design method.
11. Description of uncertainties. Parametric and nonparametric uncertainties, their description in MATLAB Simulink.
12. Linear matrix inequalities (LMI), quadratic form LJ and its conversion to LMI, LQR using LMI, H infinity using LMI.
13. Course summary.

Fundamentals seminar

26 hod., compulsory

Teacher / Lecturer

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

Syllabus

1. Becoming familiar with functions from Symbolic Math Toolbox in MATLAB.
2. Basic notations in algebraic methods.
3. Preparation of function for the computation of the general and particular solution of polynomial equation.
4. Stabilizing controller design, modal controller, EMMP problem solution.
5. Design of time optimal controllers for one degree of freedom control structure.
6. Design of time optimal controllers for two degrees of freedom control structure.
7. The work on the project. Design of the controller using sensitivity function shaping.
8. Computation with parametric uncertainties. Interval uncertainties. Conversion to structured uncertainties.
9. H infinity controller design. Loop shaping design method.
10. H infinity controller design. Mixed sensitivity design.
11. H infinity controller design , inverted pendulum example.
12. Robust controller design for MIMO systems.
13. Reserve, conclusions.

Elearning

eLearning: currently opened course