NON-LINEAR CONTROL AND SERVO SYSTEMS | FRT075 |

**Credits:** 4.
**Grading scale:** TH.
**Compulsory for:** M4XMK.
**Optional for:** D4, E4, F4, I3XTV, M3, N3, Pi4.
**Course coordinator:** Anders Robertsson, Anders.Robertsson@control.lth.se and Rolf Johansson, Rolf.Johansson@control.lth.se, Inst f reglerteknik.
**Prerequisites:** FRT010 Automatic Control, Basic Course or FRT110 Systems Engineering.
**Assessment:** Written examination.
**Further information:** The course is given in English on demand.
**Homepage:** http://www.control.lth.se/~kursolin.

**Aim**

The goal of the course is to learn how to recognize important non-linear control problems, to use the main analysis methods for non-linear systems and to handle some practical tools for non-linear design.

**Contents**

The course describes how non-linear systems can be treated through analysis, simulation and controller design.

*Theory:* Non-linear phenomena. Phase plane analysis. Linearisation. Simulation. Stability analysis using Lyapunov methods, circle criteria, small gain and passivity. Limit cycles. Sliding modes. A short introduction to research. Design: Simple compensation methods for saturation, friction, backlash and quantisation. Linear design methods. High gain methods and relay control. Internal model control. Gain scheduling. Tutorial on optimal control.

*Laboratory exercises:* Analysis using the describing function methodology for the pitch dynamics of the aircraft "JAS 39 Gripen" and for the study of pilot induced oscillations (PIO); Design of a swing up algorithm for an inverted pendulum; Control design with dead zone compensation for an air throttle used in car motors.

**Literature**

Slotine J J E, Li W: Applied Nonlinear Control. Prentice-Hall 1991. ISBN 0-13-040049-1.