Syllabus academic year 2009/2010
(Created 2009-08-11.)

Higher education credits: 7,5. Grading scale: TH. Level: A (Second level). Language of instruction: The course will be given in English on demand. FRTN05 overlap following cours/es: FRT075, FRT075, FRT075 och FRT075. Optional for: D4, E4, E4ra, F4, F4rs, I4, M4, M4me, N4, Pi4, Pi4sbs. Course coordinator: Dr. Anders Robertsson, och Professor Rolf Johansson,, Inst f reglerteknik. Prerequisites: FRT010 Automatic Control, Basic Course or FRT110 Systems Engineering. The course might be cancelled if the numer of applicants is less than 10. Assessment: Written exam (5 hours), three laboratory exercises. In case of less than 5 registered students, the second and third exams may be given in oral form. Home page:

The aim of the course is to the learn to recognize nonlinear control problems, to master the most important analysis techniques for nonlinear systems, and the learn how to use practical tools for nonlinear control design.

Knowledge and understanding
For a passing grade the student must

Skills and abilities
For a passing grade the student must

Judgement and approach
For a passing grade the student must

The course describes how non-linear systems can be treated through analysis, simulation and controller design.

Laboratory exercises: Analysis using the describing function and control design with
dead-zone compensation for an air throttle used in car motors;
Energy-based design of a swing-up algorithm for an inverted pendulum;
Trajectory generation using optimal control for the pendulum-on-a-cart process.

Lectures: Non-linear phenomena. Mathematical modelling of nonlinear systems, Stationary points, Linearisation around stationary points and trajectories, Phase plane analysis. Stability analysis using Lyapunov methods, circle criterion, small-gain and passivity. Computer tools for simulation and analysis, Effects of saturation, backlash and dead-zones in control loops, Descring functions for analysis of limit cycles, High-gain methods and relay feedback, Optimal control, Nonlinear synthesis and design.

Will be decided at the latest one month before the course start. Will be announced on the course home page: