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 2012.

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

Teaching assistant: Per Hägg pehagg@kth.se Office hours: Fri 14-15

Teaching assistant: Farhad Farokhi farokhi@ee.kth.se Office hours: Wed 15-176

Course administration: Hanna Holmqvist hanna.holmqvist@ee.kth.se

STEX: Course material, homework, exams etc. 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 Mon 121022, 13-15 Q33 Introduction: nonlinear problems and phenomena. [pp 1-23,87-95] 2 Wed 121024, 13-15 Q33 Simulation in Simulink. 3 Mon 121029, 15-17 Q33 Linearisation, phase-plane analysis, equilibria, oscillations. [35-54,54-59,111-113,133-135,139] 4 Wed 121031, 10-12 Q33 Stability theory: Lyapunov methods. [pp 113-133,135-144] 5 Tue 121106, 13-15 Q33 Stability theory: input-output methods. [pp 263-275,209-210,217-219,227-229] 6 Thu 121108, 10-12 L52 Describing function analysis. [pp 280-289] 7 Tue 121113, 10-12 L52 Compensation for saturation (anti-windup) and friction. 8 Thu 121115, 13-15 Q36 Compensation for back-lash and quantization. 9 Mon 121119, 15-17 L52 High-gain design methods: linearization by high gain and sliding modes. [pp 551-563] 10 Wed 121121, 13-15 Q31 Nonlinear observers, Lyapunov design methods, and feedback linearization. [pp 469-478,505-509,589-597] 11 Mon 121126, 15-17 Q31 Gain scheduling and nonlinear controllability. [pp 485-489,496-499] 12 Wed 121128, 15-17 Q33 Optimal control. 13 Mon 121203, 13-15 Q33 Neural networks and fuzzy control. [pp 14-16,131-133] 14 Wed 121205, 10-12 Q33 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 WedTue 11210263, 08-10 L5213-15 Q33 1.1, 1.2, 1.6, 1.7 1.3, 1.4, 1.5 2 FriThu 11210285, 0813-105 XQ23, XQ25 Computer ex 2.1-2.5 3 Wed 111102, 08-10 L52Tue 121030, 13-15 Q33 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 111104, 08-10 L51Wed 121031, 13-15 Q33 4.1, 4.2, 4.3, 4.5b, 4.7, 4.8 4.4, 4.6, 4.9, 4.10 5 Wed 11211097, 08-10 L5213-15 Q33 Review of Lyapunov and LaSalle theorems, examples, 4.7, 4.8 6 Fri 1121111, 08-10 L5109, 10-12 Q33 5.4, 5.5, 5.8, 5.10, 5.11 (5.6) 5.1, 5.2, 5.3, 5.7, 5.9 7 Wed 11211164, 153-17 L525 Q31 6.1, 6.2, 6.4, 6.6, 7.1, 7.2, 7.3 6.3, .6.5, 6.8 8 Fri 1211118, 08-10 L516, 10-12 Q33 8.1a,c, 8.2, 8.3, 8.4, 8.7 8.1d, 8.5, 8.6 9 WedTue 11211230, 08-10 L5213-15 Q34 9.2, 9.3, 9.5, 9.6 9.1, 9.4 10 Fri 11211253, 108-102 XQ23, XQ25 Computer ex 10.1, 10.2, 10.3, 10.4 11 WedTue 1121130, 08-10 L5227, 13-15 Q33 11.1, 11.2, 11.6, 11.9 11.3,11.4,11.5, 11.7,11.8 12 Fri 1211202, 08-10 L5130, 10-12 Q33 12.1, 12.2, 12.3, 12.4, 12.7 12.5, 12.6, 11.11 13 Tue 11212064, 153-17 Q365 L52 13.1, 13.2, 13.3 13.4-9 14 TueWed 112121305, 103-12 L515 Q33 An old exam wil be reviewed 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 at STEX, Osquldasv. 10.

After you have submitted your homework, you will get the homework of another student to review (applies to HW1 and HW2 only). You should pick up this homework from STEX on the working day following the deadline for handing in the solution, and then have one week to perform the review. For instructions, see the Exercise compendium (or the course homepage under "Course Material").

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

Deadlines are as given below

* HW1: Nov 18 (review Nov 25)
* HW2: Nov 30 (review Dec 7)
* HW3: Dec 12
Deadlines are hard. We will not accept any delays in handing in reports or reviews.

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 will 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 10th 2012, 14-19, in E31, E32, E33, E34. 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.

* Exam registration
* Course evaluation