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Nonlinear Control and Servo Systems

FRTN05, Olinjär reglering och servosystem

Syllabus 2012   CEQ   Exam Schedule

In reality are all practical control systems nonlinear in one aspect or the other (nonlinear dynamics in e.g., robotics, actuation saturations, sensor nonlinearities etc). Despite this fact, control based on linear system may work fine in many cases, whereas in other situations you have to take the nonlinear effects into accounts to get a stable control system. Moreover, the performance and robustness may be significantly improved by considering the nonlinear aspects of the system. In the course Nonlinear Control and Servo Systems (FRTN05) we study ordinary nonlinearities and how to handle those, treat different analysis methods and learn how to do control synthesis for nonlinear systems, in both theory and practise. Brief course information (in Swedish) is available. This is an extended version, 7.5 hp, of the old course FRT075 which was offered until 2007.

News

Results for the April 5th, 2013 exam session. Solutions. Contact Olof Sörnmo if you wish to have a look at your exam.

Results for the March 13th, 2013 exam session. Solutions. The exams will be shown on Tuesday, March 19 between 12:00-12:30 in Lab C.

  • Exam on Wednesday March 13th, 2013, 8:00-13:00, M:L 1-2
  • The Exercise sessions are held in Lab B, M-building, ground floor
     

Lecturer

Giacomo Como, M-building (fifth floor, room 5143) 046-222 8783

Teaching assistants 

Anders Mannesson, M-building (second floor, room 2112C, room with round window next to the elevator), 046-222 1570
Olof Sörnmo, M-building (second floor, room 2156, the first room on the left in the corridor on the second floor.), 046-222 9745

 

Literature

Recommended textbooks are either of
  • Glad, T., and Ljung,L., "Reglerteori, flervariabla och olinjära metoder" (2003, Studentlitteratur, Lund, ISBN 9-14-403003-7) or the English translation "Control Theory", 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 books. The first part of this book (Ch. 1-10) covers linear control theory and is a good extra for the course Multivariable Control - (FRTN10 Flervariabel reglering)
  • Khalil, H. K., Nonlinear Systems (3rd ed., 2002, Prentice Hall, ISBN 0-13-122740-8). This book is a very good text book on nonlinear control systems, but a bit more advanced.

Handouts: Lecture notes and extra material will be handed out.

Lectures and Exercises

Lecture Mondays 13.15-15.00 and Wednesdays 8.15-10.00, M:E, except the last lecture March 4 in M:D.
Extra Lecture Thursday Jan 24, 10.15-12.00, M:E

Exercises are held Tuesdays and Wednesdays 15.15-17.00 in Reglerteknik-Lab B on the ground floor, south-west end of the M-building. See Exercise schedule and problem set.

The lecture slides will be handed out during the lectures. Below you find last year's versions to be replaced when the lecture is given (indicated by red or green bullet).

 Jan 21: L1: Introduction. Typical nonlinear problems and phenomena. Models.(Full format)
 Jan 23: L2: Simulation in Simulink. Linearization. Stability (Full format)
Jan 24: L3: Phase-plane analysis. Classification of singular points. Stability of periodic solutions. (Full format)

 Jan 28: L4: Lyapunov methods. (Full format)
 Jan 30: L5: Stability theory. Small gain theorem. Circle criteria. Passivity. (Full format)

 Feb 4: L6: Describing function analysis. (Full format)
 Feb 6: L7: Saturation and antiwindup. Friction. (Full format)

 Feb 11: L8: Compensation for back-lash and Quantization. (Full format)
 Lab1: Deadzone-compensation for an air throttle in a car (describing function analysis) (Sign-up starts Jan 28)
 Feb 13: L9: Exact linearization and Lyapunov-based design (Full format)
 Feb 18: L10: Optimal control: The Maximum principle, examples. (Full format)
 Lab2 : Pendulum swing-up (Sign-up starts Febuary 4)
 Feb 20: L11: Optimal control (cont'd). (Full format)

 Feb 25: L12: High-gain design design methods --- Sliding modes. (Full format)
 Lab 3: Optimal control of pendulum an a cart. (Sign-up starts February 11)
 Feb 27: L13: Internal model control. Model predictive control. Nonlinear observers. Gain scheduling. (Full format)

 Mar 4: L14: Course summary. Questions. (Full format)

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) (Sign-up starts January 28)
 Lab2: Pendulum swing-up (Sign-up starts February 4)
 Lab3: Pendulum on a cart. (Sign-up starts February 11)

Software

Matlab and Simulink are extensively used in the course. Graphical user interfaces called pplane and dfield for phase-plane analysis in Matlab are available for educational purposes from http://math.rice.edu/~dfield/. Matlab is available for home computers. Put the file in your working directory, start Matlab and type "pplane6" or "pplane7" depending on your Matlab version (6.5 or 7). An alternative tool is pptool.m.

Old Exams (from FRT075)

March 7, 2006
April 21, 2006
May 28, 2008
August 26, 2008
June 1, 2009
May 28, 2010