National Instruments NI MATRIXx Xmath - Manual (Page 5)

© National Instruments Corporation v Xmath Model Reduction Module
Contents
Chapter 1
Introduction
Using This Manual.........................................................................................................1-1
Document Organization...................................................................................1-1
Bibliographic References ................................................................................1-2
Commonly Used Nomenclature ......................................................................1-2
Conventions .....................................................................................................1-2
Related Publications ........................................................................................1-3
MATRIXx Help...............................................................................................1-3
Overview........................................................................................................................1-3
Functions .........................................................................................................1-4
Nomenclature .................................................................................................1-6
Commonly Used Concepts ............................................................................................1-7
Controllability and Observability Grammians ................................................1-7
Hankel Singular Values...................................................................................1-8
Internally Balanced Realizations .....................................................................1-10
Singular Perturbation.......................................................................................1-11
Spectral Factorization ......................................................................................1-13
Low Order Controller Design Through Order Reduction .............................................1-15
Chapter 2
Additive Error Reduction
Introduction....................................................................................................................2-1
Truncation of Balanced Realizations .............................................................................2-2
Reduction Through Balanced Realization Truncation...................................................2-4
Singular Perturbation of Balanced Realization..............................................................2-5
Hankel Norm Approximation ........................................................................................2-6
balmoore( ).....................................................................................................................2-8
Related Functions ............................................................................................2-11
truncate( ) .......................................................................................................................2-11
Related Functions ............................................................................................2-11
redschur( ) ......................................................................................................................2-12
Algorithm ........................................................................................................2-12
Related Functions ............................................................................................2-14
ophank( ) ........................................................................................................................2-14
Restriction........................................................................................................2-14
Algorithm ........................................................................................................2-15
Behaviors.........................................................................................................2-15