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.

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.

Recommended optional programme components

Not applicable.

Recommended or required reading

Havlena, V., Štecha, J.: Moderní teorie řízení, Skriptum ČVUT, Praha 2000 (CS)
Doyle, J. C., Francis, B. A., Tannenbaum, A. R.: Feedback Control Theory, Dover Publications, 2009, ISBN-13: 978-0486469331. (EN)
Scherer, C., Weiland, S.: Linear matrix inequalities in control. DISC, 2005 (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.
Final written exam. Max 70 points.

Language of instruction

Czech

Work placements

Not applicable.

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.

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.

Classification of course in study plans

• Programme MPC-KAM Master's, 1. year of study, summer semester, 6 credits, compulsory-optional

#### Type of course unit

Lecture

26 hours, optionally

Teacher / Lecturer

Fundamentals seminar

26 hours, compulsory

Teacher / Lecturer

eLearning