Non-Linear Control and Servo Systems
Olinjär reglering och servosystem

FRTN05F, 7.5 högskolepoäng

Gäller från och med: Autumn 2016
Beslutad av: Professor Thomas Johansson
Datum för fastställande: 2016-10-27

Allmänna uppgifter

Avdelning: Automatic Control
Kurstyp: Gemensam kurs, avancerad nivå och forskarnivå
Kursen ges även på avancerad nivå med kurskod: FRTN05
Undervisningsspråk: English

Syfte

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.

Mål

Kunskap och förståelse

För godkänd kurs skall doktoranden

• 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

Färdighet och förmåga

För godkänd kurs skall doktoranden

• 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

Värderingsförmåga och förhållningssätt

För godkänd kurs skall doktoranden

• 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

Kursinnehåll

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.

Kurslitteratur

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

Kursens undervisningsformer

Undervisningsformer: Föreläsningar, laborationer, övningar

Kursens examination

Examinationsform: Skriftlig tentamen
Betygsskala: Underkänd, godkänd
Examinator: Professor Anders Rantzer

Antagningsuppgifter

Förutsatta förkunskaper: FRT010 Automatic Control, Basic Course

Kurstillfällesinformation

Startdatum: 2017-10-30
Slutdatum: 2018-01-03
Kursfart: Full time

Kontaktinformation och övrigt

Kursansvarig: Anders Rantzer <anders.rantzer@control.lth.se>
Hemsida: https://www.control.lth.se/Education/EngineeringProgram/FRTN05.html