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

## 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.

## Goals

Knowledge and Understanding

For a passing grade the doctoral 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 doctoral 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 doctoral student must

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

## 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