Stability region based robust controller synthesis

• Robuste Reglersynthese auf Grundlage von stabilisierenden Parameterräumen

Schrödel, Frank; Abel, Dirk (Thesis advisor); Leonhardt, Steffen (Thesis advisor)

Aachen (2016)
Dissertation / PhD Thesis

Dissertation, Rheinisch-Westfälische Technische Hochschule Aachen, 2016

Abstract

The present work focuses on research regarding the robust controller synthesis. The method which is developed and applied in this work is based on stability region calculations for system as well as for controller parameters.This work starts with a detailed presentation viewing different approaches of the state of the art robust controller design. Following that, various expansions of these approaches are explained and in particular, a very generalcalculation method is developed based on the Lyapunov stability. The considered approaches are applicable for linear system classes (like continuous and discrete systems) as well as for nonlinear system classes which can beanalyzed by using the harmonic balance approach or simple Lyapunov functions (e.g. switching systems).The stabilizing parameter space can be calculated for a nominal system without uncertainties, while the stabilizing parameter space can be calculated under explicit consideration of parameter uncertainties. The present workoffers a detailed overview of the available tools for the robust controller analysis (like Kharitonov polynomials). Thereafter, these tools are extended in such a way that they can be combined with the parameter space approachand a robust controller synthesis approach. Consequently, a less conservative robust controller synthesis is possible.Based on the stability region calculation, several approaches for the optimal tuning of controller parameters are demonstrated. Therefore, approaches for assisted controller tuning (like performance maps) and full automatic controller tuning approaches are introduced and explained in detail. The considered approaches are explicitly using the previously calculated stability regions in order to establish a highly sophisticated and efficient controller tuning approach. Finally, the developed methods for some practical application examples are applied. It is the goal of these examples to show the usability of the developed methods and to give an idea which problem classes can be handled by using the newly established methods. Therefore, classical control engineering problems with simple parameter uncertainties are used. In Addition, more advanced problems like network systems with uncertain sampling times as well as time delays are presented.