Course syllabus

Olinjär reglering och servosystem
Non-Linear Control and Servo Systems

FRTN05, 7,5 credits, A (Second Cycle)

Valid for: 2013/14
Decided by: Education Board B
Date of Decision: 2013-04-10

General Information

Elective for: D4, E4, E4-ra, E4-ssr, F4, F4-ssr, M4-me, Pi4, Pi4-ssr
Language of instruction: The course will be given in English on demand


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.

Learning outcomes

Knowledge and understanding
For a passing grade the student must

Competences and skills
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.

Examination details

Grading scale: TH
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.

Code: 0108. Name: Examination.
Credits: 7,5. Grading scale: TH.
Code: 0208. Name: Laboratory Work 1.
Credits: 0. Grading scale: UG.
Code: 0308. Name: Laboratory Work 2.
Credits: 0. Grading scale: UG.
Code: 0408. Name: Laboratory Work 3.
Credits: 0. Grading scale: UG.


Required prior knowledge: FRT010 Automatic Control, Basic Course.
The number of participants is limited to: No
The course overlaps following course/s: FRT075

Reading list

Contact and other information

Course coordinator: Professor Anders Rantzer,
Course coordinator: Giacomo Como,
Course homepage: