Czech

Not applicable.

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

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

Not applicable.

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.

Exercises, individual project. Max. 30 points.
Final written exam. Max 70 points.

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 to robust control. Robustness, signal and system norms.
10. H infinity control. Linear fractional transformation, mixed sensitivity design, gamma iteration.
11. H2 control, comparison with LQ control, H2 optimal state controller design, H2 optimal state observer design, duality of both approaches.
12. Uncertainties description. Classification of uncertainties, affine/polytopic uncertainties, gain scheduling controller design. Additive, multiplicative and feedback uncertainties. Small gain theorem, D-K iteration.
13. Linear Matrix Inequalities (LMI), quadratic form LJ and its conversion to LMI, LQG using LMI, H infinity using LMI

Not applicable.

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.

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.

Not applicable.

Not applicable.

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)

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