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Course information

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 2014.

Instructors:

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

Teaching assistant: Martin Andreasson mandreas@kth.se

Teaching assistant: Niklas Everitt neveritt@kth.se

Course administration such as Bilda and course homepage: Hanna Holmqvist hanna.holmqvist@ee.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). The book is available at Kårbokhandeln.

It will however be possible to follow the course 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 to the right.

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/TimePlaceContents
1 Tue 141104, 10-12 V34 Introduction: nonlinear problems and phenomena.         [pp  1-23,87-95]
2 Thu 141106, 13-15 L52 Simulation in Simulink.
3 Mon 141110, 10-12 V34 Linearisation, phase-plane analysis, equilibria, oscillations. [35-54,54-59,111-113,133-135,139]
4 Wed 141112, 15-17 Q33 Stability theory: Lyapunov methods. [pp 113-133,135-144]
5 Mon 141117, 10-12 Q34 Stability theory: input-output methods. [pp 263-275,209-210,217-219,227-229]
6 Thu 141120, 10-12 V32 Describing function analysis. [pp 280-289]
7 Tue 141125, 15-17 V34 Compensation for saturation (anti-windup) and friction.
8 Thu 141127, 13-15 M33 Compensation for back-lash and quantization.
9 Tue 141202, 10-12 Q36 High-gain design methods: linearization by high gain and sliding modes. [pp 551-563]
10 Thu 141204, 13-15 Q31 Nonlinear observers, Lyapunov design methods, and feedback linearization. [pp 469-478,505-509,589-597]
11 Mon 141208, 13-15 L52 Gain scheduling and nonlinear controllability. [pp 485-489,496-499]
12 Wed 141210, 13-15 V34 Optimal control.
13 Mon 141216, 10-12 Q33 Neural networks and fuzzy control. [pp 14-16,131-133]
14 Wed 141217, 13-15 L52 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/TimePlaceIn classSuggested
1 Wed 141105, 08-10 L51 1.1, 1.2, 1.6, 1.7 1.3, 1.4, 1.5
2 Fri 141107, 13-15 XQ23, XQ25 Computer ex 2.1-2.5
3 Tue 141111, 15-17 Q31 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 Q33 4.1, 4.2, 4.3, 4.5b, 4.7, 4.8 4.4, 4.6, 4.9, 4.10
5 Tue 141118, 10-12 Q34 Review of Lyapunov and LaSalle theorems, examples, 4.7, 4.8
6 Thu 141120, 13-15 L52 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 M33 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 V32 8.1a,c, 8.2, 8.3, 8.4, 8.7 8.1d, 8.5, 8.6
9 Wed 141203, 13-15 L52 9.2, 9.3, 9.5, 9.6 9.1, 9.4
10 Fri 141205, 10-12 XQ23, XQ25 Computer ex 10.1, 10.2, 10.3, 10.4
11 Tue 141209, 10-12 V22 11.1, 11.2, 11.6, 11.9 11.3,11.4,11.5, 11.7,11.8
12 Thu 141211, 10-12 V32 12.1, 12.2, 12.3, 12.4, 12.7 12.5, 12.6, 11.11
13 Tue 141216, 10-12 L52 13.1, 13.2, 13.3 13.4-9
14 Thu 141218, 10-12 Q31 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 preliminary and will be finalized before course start

  • 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. Be sure to sign the sign-up sheets at one of the first lectures. 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.

More Information

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