Modern Control Theory

Lecturer:

Tutor:

Supervisor:

Department of Control Engineering

Synopsis:

The objective of the subject is to introduce a general design methodology how to translate an engineering problem into an optimization problem and interpret the mathematical results. This approach is illustrated on methods developed during last three decades (state-space and algebraic methods for LQ, time optimal and model matching problems, adaptive control). Basic methods of uncertainty description are introduced and the effect of uncertainty on design is analyzed.

Requirements:

Syllabus of lectures:

1. Norms of signals and systems

2. Feedback systém properties

3. Uncertainty modelling, robustness

4. Stabilizing controllers

5. Algebraic design methods, time optimal control

6. Quadratic optimal control

7. Discrete-time LQ controller, dynamic programming

8. Continuous-time LQ controller, properties of LQ controller

9. LQ tracking, servo and program control formulations

10. Predictive and feedback control strategy, predictive controller

11. MS and LMS estimation

12. Stochastic systém, optimal filtering - algebraic design (Wiener filter)

13. Optimal filtering - state-space design (Kalman filter)

14. LQG controller, separation principle

Syllabus of tutorials:

1. Introduction to laboratory equipment and Matlab toolboxes

2.-4. Algebraic design methods, polynomial toolbox

5.-7. Solution of discrete and continuous time Riccati equation, LQ controller, properties

8.-10. Wiener and Kalman filter - examples, analysis

11.-13. LQ vs. LQG controller, properties

14. Presentation of results

Study Objective:

Study materials:

1. Lewis, F.L.: Optimal Control. J.Wiley and Sons, N.Y. 1994

2. Kučera, V.: Analysis and design of discrete linear control systems. Academia, Prague 1991

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans:

• Cybernetics and Measurements - Control Engineering- structured studies (compulsory course)