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# Details for the Course Syllabus for Course FRTN05F valid from Autumn 2016

General
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.
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.
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
Types of Instruction
• Lectures
• Laboratory exercises
• Exercises
Examination Formats
• Written exam
• Failed, pass
Assumed Prior Knowledge
• FRT010 Automatic Control, Basic Course
Selection Criteria
Literature
• Khalil, H. K.: Nonlinear Systems. Prentice Hall, 2002. ISBN 0131227408.
Further Information
Course code
• FRTN05F