The course will be given in academic year 2023/2024. The course will
start on Wednesday, January 17, 2024.
The lectures will take place in Nollstället (Entrance 25, room 3D:550)
Room:
| No. | Date, time | Contents | ZDG | SP | HO |
|---|---|---|---|---|---|
| 1 | 2024-01-17 13:15 | Introduction, why need for robust design, sensitivity functions, uncertainties, overview of course | 1-3 | en ex.pdf | |
| 2 | 2024-01-24 13:15 | Vector and matrix norms, induced norms, dynamic linear systems, Lyapunov equations, balancing, H2 and H∞. | 2.1, 2.2, 2.7, 2.8, 2.11, 3.1-3.10, (3.11), 4.1, (4.2, 4.3), 4.4-4.7 | 4.1, 4.10, 11.3, A.5 | en |
| 3 | 2024-01-31 13:15 | Feedback, internal stability, performance specifications, performance limitations. | 5.1-5.3, 5.5-5.7, 6 | 4.3-4.7, 5, 6 | en |
| 4 | 2024-02-07 13:15 | Parametrization of stabilizing controllers (Youla), Riccati equations, coprime factorization, LQR, H2 synthesis | 5.4, 12.1-12.6, 13.1, 13.2, 13.8, 14.1-14.6, 14.8-14.10 | 4.8, 9.2, 9.3 | en |
| 5 | 2024-02-14 13:15 | H∞ synthesis | 16.1-16.10, 17.1, (17.3, 17.4), 17.5, 17.8 | 9.3 | en |
| 6 | 2024-02-21 13:15 | LMIs | en LMI sdpfilt.m | ||
| 7 | 2024-02-28 13:15 | Loop shaping, model reduction | 9.3.3, 18.1-18.3, 7, 19.1, 19.2, (19.3), 19.4 | 4.10.4, 9.4. 11 | en |
| 8 | 2024-03-13 13:15 | Model uncertainties, small gain theorem, stability margins, LFTs | 9, 10 | 3.8, 4.9, A.7 | en |
| 9 | 2024-03-20 13:15 | µ-analysis and synthesis | 11.1-11.4 | 8.1-8.13 | en µ-ex loopshaping-ex ellipfilt.m |
| 10 | 2024-03-27 13:15 | Summary | |
|
en |
A hand-in exercise 1 is available here ex1 . Please try to solve the problems and hand in your solution before March 8.
A hand-in exercise 2 is available here
ex2 .
Please try to solve the problems and hand in your solution before April
10.
[ZDG] Robust and Optimal Control by Zhou, Doyle and Glover, Prentice Hall, 1995, ISBN 0-13-456567-3. The book is available in cloth cover from Prentice Hall.
[SP1] Multivariable Feedback Control: Analysis and Design by Skogestad and Postlethwaite, John Wiley and sons, ISBN 0-471-94330-4, or
[SP2] Multivariable Feedback Control: Analysis and Design, Second Edition by Skogestad and Postlethwaite, John Wiley and sons, ISBN 0-470-01168-8.
[SP1] and [SP2] are equivalent.
[HO] Handouts or lecture notes.
Short notes on Linear Matrix Inequalities. This document gives a short introduction on how to use LMIs to solve H∞ synthesis problems.
| Lecture | SP1 | SP2 | comment |
|---|---|---|---|
| 2 | 3.19, 3.23 | 3.22, 3.26 | |
| 4.16 | 4.16 | H2, H∞ | |
| 11.1, 11.2 | 11.1, 11.2 | ||
| 4 | 9.2, 9.3 | 9.2 | LQR |
| 4.1 | 4.1 | Coprime | |
| 4.13, 4.15 | 4.13, 4.15 | IMC/Youla | |
| 5 | 9.6 | H∞ Compleib exercises: AC3, AC4, AC8, AC10, AC13, AC14, AC18 (pick 3 or 4 examples). Unpack "compleib.zip" and put it in your Matlab path. The type "[g, dim] = complib('AC8')", where "dim" defines number of measurements and controls. | |
| 7 | 9.6, 9.7, 9.8, 11.2, 11.3 | 9.7, 9.8, 9.9, 11.2, 11.3 | Loop shaping |
| genring example | |||
| 8 | 8.1, 8.2, 8.3, 8.12 | 8.1, 8.2, 8.3, 8.13 | Uncertainties |
hinflmi.m. This Matlab file can be used for H∞ synthesis. Requires Yalmip and SeDuMi. You also need recoverP.m.
ellipfilt.m. This Matlab file can be used for defining low pass filters with a specified cut-off frequency and damping.
genbeam.m. This Matlab file generates a model of a flexible beam.
beam.pdf. A short description of the flexible beam model.
robkurs.tar.gz. This archive file contains Matlab files for solving the pendulum problem, which was handed out during the first lecture.
loopshaping.m. This script file uses loop shaping for solving the pendulum problem.
Extra exercises intended as a preparation for your examination. Solutions.