# FRTN05 - Nonlinear Control and Servo Systems

## Olinjär reglering och servosystem, 7.5 hp

Syllabus | Schedule |

#### News

- 27/1 - The corrected exams will be shown on
**Monday 3 February 12:30-13:00**in Automatic Control's seminar room, 2112B. - 24/1 - The exam is now corrected, and the results will soon be reported into Ladok. The adjusted grade limits are: ≥10 points => grade 3, ≥16.5 points => grade 4 and ≥21.5 points => grade 5.
- 22/1 - Suggested solutions for the latest (January 2020) exam are now available here.
- 26/11 - Note that Exercise 10 has been moved to Friday December 6 at 10:15-12:00. Moreover, Exercise 10,12 and 13 have switched room to Lab A & B on the ground floor. Also note that problem 7.26 has been changed, so you will need to re-download the exercise booklet for that problem.
- 25/11 - sign up for lab 3 is open.
- It is now possible to sign up for lab 1 and lab 2!

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In real life, most control systems are nonlinear in one way or the other (nonlinear dynamics, actuation saturations, sensor nonlinearities, etc). While a controller designed for linear systems may continue to work well in many nonlinear systems, this is not always the case. In some situations, nonlinear effects must be taken into account in order to get acceptable performance. In the course Nonlinear Control and Servo Systems (FRTN05) we study common nonlinearities and how to handle those, treat different analysis methods and learn how to do control synthesis for nonlinear systems, both in theory and practice.

### Lecturer

Anders Rantzer, (course responsible) M-building (fifth floor, room 5143) 046 - 222 87 83

### Teaching Assistants

Martin Heyden, M-building (second floor) 046 - 222 4287

Christian Rosdahl, M-building (second floor) 046 - 222 8795

### Literature

Recommended textbook is

- Glad, T., and Ljung,L., "Reglerteori: Flervariabla och olinjära metoder" (2003, Studentlitteratur, Lund, ISBN 9-14-403003-7) or the English translation "Control Theory: Multivariable and Nonlinear Methods", 2000, Taylor & Francis Ltd, ISBN 0-74-840878-9. Chapter 11-16,18. This book covers MPC and Optimal control which are not covered in the other text book. The first part of this book (Ch. 1-10) covers linear control theory and is useful for the course Multivariable Control - (FRTN10 Flervariabel reglering)

An alternative reference is

- Khalil, H. K., Nonlinear Systems (3rd ed., 2002, Prentice Hall, ISBN 0-13-122740-8). This is a good textbook on nonlinear control systems, at a bit more advanced level than the course.

Handouts: Lecture notes and extra material will be handed out and posted on this website.

### Lectures and Exercises

Lectures on Mondays are held at 13.15-15.00, other days at 08.15-10.00. Lectures are held in **M:E.**

The exercises are held Tuesdays and Thursdays 15:15-17:00 in the Automatic Control seminar room M:2112B on the second floor in the M-building, except for 19/11, 21/11 and 5/12, when it is held in **lab A** and **lab B** of the Automatic Control Department, first floor of the M-building. See Exercise schedule and problem set.

Monday 4/11: L1: Introduction. Typical nonlinear problems and phenomena. Models. (2019)

Wednesday 6/11: L2: Linearization. Stability. Controllability. Simulation. (2019)

Friday 8/11: L3: Phase-plane analysis. Classification of singular points. Stability of periodic solutions. (2019)

Monday 11/11: L4: Lyapunov methods. (2019)

Wednesday 13/11 L5: Stability theory. Small gain theorem. Circle criteria. Passivity. (2019)

Friday 15/11: L6: Describing function analysis. (2019)

Wedesday 20/11: L7: Saturation and antiwindup. Friction. (2019)

Friday 22/11: L8: Compensation for backlash and quantization. (2019)

Reading material on: antiwindup and friction

Monday 25/11: L9: Lyapunov-based design and sliding modes. (2019)

Wednesday 27/11: L10: Optimal control: The Maximum Principle, examples. (2019)

Lab1: Deadzone-compensation for an air throttle in a car.

Monday 2/12:L11: Optimal control (cont'd). (2019)

D. Liberzon, Calculus of variations and optimal control theory: A Coincise Introduction, Princeton University Press, 2012.

Wednesday 4/12: L12: Dynamic programming. (2019)

Lab2 : Pendulum swing-up

No lectures this week

Lab 3: Optimal control of pendulum an a cart.

Monday 16/12: L13: Internal model control. Model predictive control. Nonlinear observers. Gain scheduling. (2019)

Wednesday 18/12: L14: Course summary. (2019)

### Exercises and Solutions

Exercise schedule and problem set

### Laboratories

Lab1: Deadzone-compensation for an air throttle in a car (nonlinear compensation and describing function analysis

Lab2: Pendulum swing-up

Lab3: Pendulum on a cart

### Software

Matlab and Simulink are extensively used in the course, and can be obtained from here using your StiL/Lucat-account.

Graphical user interfaces called **pplane** and **dfield** for phase-plane analysis have been developed at Rice University, http://math.rice.edu/, and are available for academic use.

For MATLAB 2017a, use the following versions: pplane9.m and dfield9.m.

For MATLAB 2014b-2016b, use the following versions: pplane8.m and dfield8.m.

If you have a newer version of Matlab you can instead use the Java version available on https://math.rice.edu/~dfield/dfpp.html

### Old Exams

March 7, 2012

April 5, 2013

Mar 12, 2014

Jan 13, 2016