Analysis of the Robust Performance of Large-Scale Linear Systems using a Hierarchical Approach

Analysis of the Robust Performance of Large-Scale Linear Systems using a Hierarchical Approach: PLL Network Application

Boersma, Sjoerd

Korniienko, A. (mentor)
Bombois, X. (mentor)

Mechanical, Maritime and Materials Engineering

Delft Center for Systems and Control

Systems and Control

2014-09-10

Large-scale systems have become more important in the last years and will probably continue to do so due to the increasing complexity of nowadays problems. One example of such a system is a clock distribution network consisting of several phase locked loop systems deployed in an array. It is possible to obtain a (nominal) linear model describing the dynamical behaviour of a phase locked loop system around an operating point and to design a controller such that desired performance is achieved for this model and the overall linear model of the large-scale system. Although the phase locked loop systems are produced on an industrial scale, they will never be exactly equivalent. These dispersions can be captured by including uncertainty blocks in the model which results in a set of models describing the large-scale system. It is interesting to check if after including uncertainty in the model, certain performance can still be ensured. Analysing performance for such a set of mathematical models is called analysis of the robust performance. A method to perform robust performance analysis called μ-analysis or the direct approach exists though is relatively time consuming. Since the time computation is significant and crucial when applying the direct approach, it is interesting to study another method which can decrease the computation effort. M. Dinh, A. Korniienko and G. Scorletti have, after an idea of M.G. Safonov, developed a frequency dependent method to perform robust performance analysis on a linear large-scale system in several steps which can reduce the computation time needed though can give more conservative results with respect to the direct method. This new method is called the hierarchical approach. In this thesis we will explain the hierarchical approach and compare the robust performance analysis results obtained with the direct approach and with the hierarchical approach. We will also illustrate that the latter approach contains a trade-off between computation time and conservatism. We then introduce the two contributions of this thesis. First, an additional mathematical tool will be presented which can be used in the hierarchical approach to reduce the conservatism in the results. Then we will introduce a method which allows us to perform analysis of the robust performance not only for one specific frequency but also for a range around this frequency.

http://resolver.tudelft.nl/uuid:9fa2aecf-b62c-45f3-94ca-c9b300c11b50

Student theses

master thesis

(c) 2014 Boersma, Sjoerd