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

## Aim

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

• have insight in the basic differences between nonlinear and linear dynamical systems
• be able to linearise nonlinear models around stationarity points and around trajectories
• be able to analyse the influence of common nonlinearities (saturation, backlash, deadzone etc) in control loops and how these should handled from a control point of view
• understand stability analysis including Lyapunov theory, the small-gain theorem, and the circle criterion, and be able to apply it in control design
• be able to give an overview of modern directions in nonlinear control

Competences and skills
For a passing grade the student must

• be able to derive mathematical models for and simulate simple nonlinear systems
• be able to analyse limit circles both quantitatively and qualitatively
• be able to design controllers for simple nonlinear systems using model-based nonlinear control and relay feedback
• be able to solve simple optimization problems and interpret the solutions in terms of feedforward and feedback structures
• be able to practically apply control design to real nonlinear processes during laboratories
• be able to use computer tools for simulation and analysis of nonlinear systems

Judgement and approach
For a passing grade the student must

• be able to understand relations and limitations when simple models are used to describe complex dynamical systems
• be able to evaluate dominating nonlinearities and dynamics
• sbow ability for teamwork and collaboration in groups during laboratory exercises

## Contents

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

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.

Parts
Code: 0108. Name: Examination.
Code: 0208. Name: Laboratory Work 1.
Code: 0308. Name: Laboratory Work 2.
Code: 0408. Name: Laboratory Work 3.