Course Syllabus for

Non-Linear Control and Servo Systems
Olinjär reglering och servosystem

FRTN05F, 7.5 credits

Valid from: Autumn 2016
Decided by: Professor Thomas Johansson
Date of establishment: 2016-10-27

General Information

Division: Automatic Control
Course type: Course given jointly for second and third cycle
The course is also given at second-cycle level with course code: FRTN05
Teaching language: English


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 doctoral student must

Competences and Skills

For a passing grade the doctoral student must

Judgement and Approach

For a passing grade the doctoral student must

Course Contents

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. 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.

Course Literature

Khalil, H. K.: Nonlinear Systems. Prentice Hall, 2002. ISBN 0131227408.

Instruction Details

Types of instruction: Lectures, laboratory exercises, exercises

Examination Details

Examination format: Written exam
Grading scale: Failed, pass

Admission Details

Assumed prior knowledge: FRT010 Automatic Control, Basic Course

Course Occasion Information

Contact and Other Information

Course coordinator: Anders Rantzer <>
Web page:

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