Course information (NOTE! Under CONSTRUCTION!!!)

EL2620 Nonlinear control

Nonlinear Control treats the analysis and synthesis of nonlinear control systems. It is a 7,5 credits course given in the second quarter (lp2), Fall 2015.

Instructors: Course responsible and lectures: Elling W Jacobsen jacobsen@kth.se

Teaching assistant: Niklas Everitt neveritt@kth.se

Teaching assistant: Arda Aytekin aytekin@kth.se

STEX: Course administration, results, registrations, Course material, homework, exams etc. Osquldasv. 10, floor 3 (entrance floor), stex@ee.kth.se

The course consists of three main parts: an analysis part presenting the theoretical foundation; a design part introducing important control design methods; and a part dealing with other nonlinear control methods. The outline of the course is as follows:

* Introduction: nonlinear models and nonlinear phenomena, computer simulation (L1-L2)
* Feedback analysis: linearization, stability theory, describing function (L3-L6)
* Control design: compensation, high-gain design, Lyapunov methods (L7-L10)
* Alternative methods: gain scheduling, optimal control, neural networks, fuzzy control (L11-L13)
* Summary (L14)
Literature Lecture notes and exercises can be bought at STEX. The package costs 120 kronor. They are also made available on the homepage under "Course Material".

Highly recommended textbook is Khalil, H. K., Nonlinear Systems (3rd ed., 2002, Prentice Hall, ISBN 0-13-067389-7). As of 2015 this book is only available in the USA. The international edition Khalil, H.K., Nonlinear systems Pearson New International Edition (Pearson, ISBN 9781292039213) is equivalent except that chapter 14 as well as all appendices are missing. The missing parts will be made available electronically on the course homepage to all registered students (thanks to Hassan Khalil).

It will be possible to follow the course also without Khalil. Some other textbooks that might be useful are (in order of increasing mathematical level) Glad, T., and Ljung, L., Reglerteori, flervariabla och olinjara metoder (1997, Studentlitteratur, ISBN 91-44-00472-9); Slotine, J.-J., and Li,W., Applied Nonlinear Control (1991, Prentice Hall, ISBN 0-13-040049-1); Sastry, S., Nonlinear Systems: Analysis, Stability and Control (1999, Springer-Verlag, ISBN 0-38-798513-1); and Vidyasagar, M., Nonlinear Systems Analysis (1993, Prentice Hall, ISBN 0-13-623513-1).

Schedule The schedule is given below. A link to the official schedule can be found in the menu above left.

Lectures Lecture notes are sold by STEX. Minor changes to these will be made during the course and the updated notes will be posted under the menu item "Course Material" as they become available. Page numbers refer to Khalil, 3rd ed.

LecDayDate/TimeContents 1 Tue 151103, 10-12 Introduction: nonlinear problems and phenomena. [pp 1-23,87-95] 2 Thu 14511065, 13-15 Simulation in Simulink. 3 MonTue 1451110, 10-12 Linearisation, phase-plane analysis, equilibria, oscillations. [35-54,54-59,111-113,133-135,139] 4 WedThu 1451112, 153-175 Stability theory: Lyapunov methods. [pp 113-133,135-144] 5 MonTue 1451117, 10-12 Stability theory: input-output methods. [pp 263-275,209-210,217-219,227-229] 6 Thu 14112051119, 103-125 Describing function analysis. [pp 280-289] 7 Tue 14511254, 150-172 Compensation for saturation (anti-windup) and friction. 8 Thu 1451127, 13-15 Compensation for back-lash and quantization. 9 Tue 1451202, 10-12 High-gain design methods: linearization by high gain and sliding modes. [pp 551-563] 10 Thu 1451204, 13-15 Nonlinear observers, Lyapunov design methods, and feedback linearization. [pp 469-478,505-509,589-597] 11 Mon 1451208, 13-15 Gain scheduling and nonlinear controllability. [pp 485-489,496-499] 12 Wed 1451210, 13-15 Optimal control. 13 Mon 1451216, 10-12 Neural networks and fuzzy control. [pp 14-16,131-133] 14 Wed 141217, 13-15 Course summary and the future. Exercises An Exercise compendium can be purchased at STEX (can also be found under "Course Material" on the main course homepage.). Here are the exercises we are doing in class.

Exercise/ListDayDate/TimeIn classSuggested 1 Wed 141105, 08-10 1.1, 1.2, 1.6, 1.7 1.3, 1.4, 1.5 2 Fri 141107, 13-15 Computer ex 2.1-2.5 3 Tue 141111, 15-17 3.1a,b, 3.4, 3.5, 3.7, 4.5a 3.1, 3.2,3.3,3.6,3.8, 3.9 4 Fri 141114, 13-15 4.1, 4.2, 4.3, 4.5b 4.4, 4.6, 4.9, 4.10 5 Tue 141118, 10-12 4.7, 4.8 6 Thu 141120, 13-15 5.4, 5.5, 5.8, 5.10, 5.11 (5.6) 5.1, 5.2, 5.3, 5.7, 5.9 7 Wed 141126, 13-15 6.1, 6.2, 6.4, 6.6, 7.1, 7.2, 7.3 6.3, .6.5, 6.8 8 Fri 141128, 13-15 8.1a,c, 8.2, 8.3, 8.4, 8.7 8.1d, 8.5, 8.6 9 Wed 141203, 13-15 9.2, 9.3, 9.5, 9.6 9.1, 9.4 10 Fri 141205, 10-12 Computer ex 10.1, 10.2, 10.3, 10.4 11 Tue 141209, 10-12 11.1, 11.2, 11.6, 11.9 11.3,11.4,11.5, 11.7,11.8 12 Thu 141211, 10-12 12.1, 12.2, 12.3, 12.4, 12.7 12.5, 12.6, 11.11 13 Tue 141216, 10-12 13.1, 13.2, 13.3 13.4-9 14 Thu 141218, 10-12 An old exam wil be reviewed We will have three Q&A sessions on the following dates, in XQ23. Nov 13, 15-17 Nov 27, 15-17 Dec 11, 15-17 Homework There are three compulsory homework assignments, all given in the Excercise compendium (HW1-3)

The homework solutions need to be well motivated and clearly written. Instructions are given in the Exercise compendium. Under "Course Material" you will find a template for the reports.

The solutions should be handed in through BILDA (available from early november)

You are expected to do the homeworks in groups of two (more than two students per group will not be accepted)

Deadlines are

* HW1: Nov 19
* HW2: Dec 3
* HW3: Dec 17
Deadlines are hard. We will not accept any delays in handing in reports or reviews. A score of at least 80% is required for pass. If you receive between 50% and 80% in the first attempt, you will be given a chance to hand in a revised version.

Computer Accounts Computer accounts will only be created for students formally registered for the course. Only after your registration is recorded in Ladok by the course administration an account be will created.

Software Matlab and Simulink are extensively used in the course. To draw phase planes with Matlab, use the programs DFIELD and PPLANE developed at Rice University, see the link below (note the Java version, which you can run through your web browser). See also the built-in Matlab command dee (differential equation editor).

You may also need the typesetting language TeX/LaTeX to write your reports. Instructions on how to install this are given in the exercise compendium.

math.rice.edu/~dfield

Exam The exam takes place on January 19th 2015, 08-13, in V21, V33, V35. It is a regular written exam with five problems. You may bring the lecture notes from this course, a mathematics handbook, and the course book from the basic control course (EL1000 or EL1110). No other material is allowed (nonlinear textbook, exercises, calculators etc.).

The problems of the exams roughly follow the style of the examples found in the course material.

You need to sign up for the exam at least two weeks in advance, using "My Pages" (eller "Mina sidor")

www.kth.se/student/studok?l=en_UK (English)

www.kth.se/student/studok/anmalan-till-tentamen-via-mina-sidor-1.56216 (svenska)

Course Evaluation At the end of the course, please fill in the course evaluation which can be found in Bilda.

More Information For more information, please contact the instructors or see the Study Handbook.

* Exam registration