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# Course memo Autumn 2021-1

## Course presentation

Nonlinear Control treats the analysis and synthesis of nonlinear control systems. 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.

Headings denoted with an asterisk ( * ) is retrieved from the course syllabus version Autumn 2021

## Content and learning outcomes

### Course contents

The course treats control theory for nonlinear dynamic systems:

• analysis of input-output stability by means of e.g. the small gain theorem and the circle criterion
• analysis of stability of equilibrium points through linearization and Lyapunov methods
• analysis of stability for passive systems
• design and analysis of feedback control for nonlinear systems through linearization, feedback linearization and Lyapunov based methods
• design and analysis of high gain feedback, e.g. sliding mode control
• observers for nonlinear systems
• setpoint regulation control and setpoint tracking
• simulation of nonlinear dynamic models.

### Intended learning outcomes

After passing the course, the student shall be able to

• formulate theory and definitions of important concepts in nonlinear control systems
• apply theory and methods within nonlinear control.

### Detailed plan

Learning activities Content Preparations
Lectures (2 per week) Introduction to new concepts and theory. Read corresponding material in lecture notes and course book.
Exercises (2 per week) Solution of problems. Have a look at exercises before the sessions, and review the necessary theory.
Homeworks (4 in total) Solve problems in MATLAB in groups of 2. Write report. Review necessary theory and solve earlier exercises.
Math help session (3 in total) Get help in solving homework assignments. Try to solve the homework assignments first.
Written exam Solve 5 problems independently. Review all course material.

## Preparations before course start

### Literature

The course is mainly based on the textbook Khalil, H. K., Nonlinear Control, (Global edition, 2015, Pearson Education Ltd, ISBN 978-1-292-06050-7).

Lecture notes, exercises, and homeworks are found in digital form in Canvas.

### Software

You will need to be able to run MATLAB on your computer for this course. (MATLAB Online is also included in the KTH MATLAB license.)

Please inform the course coordinator if you have special needs not related to the written exam, and show your certificate from Funka.

• Support measures under code R (i.e. adjustments related to space, time, and physical circumstances, e.g. longer writing time) are always granted.
• Support measures under code P (pedagogical measures) may be granted or rejected by the examiner after you have applied for this in accordance with KTH rules. Support measures under code P are usually always granted for courses given at EECS.

## Examination and completion

A, B, C, D, E, FX, F

### Examination

• INLA - Homework, 2.5 credits, Grading scale: P, F
• INLB - Home work, 2.5 credits, Grading scale: P, F
• TENT - Written exam, 2.5 credits, Grading scale: A, B, C, D, E, FX, F

Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.

The examiner may apply another examination format when re-examining individual students.

The course is divided into four modules. Each module is examined by a homework assignment (Homework 1-4), and one exam problem.

#### Homework (INLA)

INLA consists of Homework 1 and 2. These are problems that should be solved in MATLAB in groups of 2, and submitted on the due date.

To get a pass grade (P) on INLA, you need 5/10 points on each of Homework 1 and 2. For each of the homeworks assignments, if you get  8/10 points, you will get one bonus point on the corresponding exam problem. The bonus points are only counted for the first original exam, not for any later re-exams.

#### Homework (INLB )

INLB consists of Homework 3 and 4. These are problems that should be solved in MATLAB in groups of 2, and submitted on the due date.

To get a pass grade (P) on INLB, you need 5/10 points on each of Homework 1 and 2. For each of the homework assignments, if you get  8/10 points, you will get one bonus point on the corresponding exam problem. The bonus points are only counted for the first original exam, not for any later re-exams.

#### Written exam (TENT)

The exam will have 5 problems: one per module and one additional more advanced problem. The written exam is solved individually.

Including the bonus points, the final exam will decide the final grade (which also requires pass grade on INLA and INLB). There are five problems with max 10 points per problem.

Grade Fx: 21 points or more, and 5 points or more on three out of problems 1-4.

Grade E: 23 points or more, and 5 points or more on each of problems 1-4.

Grade D: 28 points or more, and 5 points or more on each of problems 1-4.

Grade C: 33 points or more, and 5 points or more on each of problems 1-4.

Grade B: 38 points or more, and 5 points or more on each of problems 1-4.

Grade A: 43 points or more, and 5 points or more on each of problems 1-4.

Formulate and apply theory within nonlinear control

E: to solve basic problems

D: to solve advanced problems within some part of the course

C: to solve advanced problems within several parts of the course

B: to solve advanced problems with all parts of the course or to solve problems combining several parts of the course

A: to solve advanced problems within all parts of the course and to solve problems combining several parts of the course.

### Opportunity to complete the requirements via supplementary examination

Students with Fx on the written exam should contact the examiner for an opportunity for supplementary examination to grade to E.

Students with F on some homework assignements will be given the chance to resubmit again after the written exam if, and only if, the written exam is passed. The same chance is given after the re-exam.

### Reporting of exam results

Homework assignments are submitted and corrected in Canvas.

The result on the writen exam is reported directly via LADOK.

### Ethical approach

• All members of a group are responsible for the group's work.
• In any assessment, every student shall honestly disclose any help received and sources used.
• In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.

## Further information

No information inserted

### Offered By

EECS/Intelligent Systems

English

### Course offering

Autumn 2021-1 (Start date 01/11/2021, English)