(Created 2011-09-01.)

NON-LINEAR CONTROL AND SERVO SYSTEMS | FRTN05 |

**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.

*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

*Skills and abilities*

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.

**Literature**

Will be decided at the latest one month before the course start. Will be announced on the course home page: http://www.control.lth.se/course/FRTN05/