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© National Instruments Corporation v MATRIXx Xmath Robust Control Module
Contents
Chapter 1
Introduction
Using This Manual.........................................................................................................1-1
Document Organization...................................................................................1-1
Bibliographic References ................................................................................1-2
Commonly-Used Nomenclature......................................................................1-2
Related Publications ........................................................................................1-2
MATRIXx Help...............................................................................................1-3
Overview........................................................................................................................1-3
Chapter 2
Robustness Analysis
Modeling Uncertain Systems.........................................................................................2-1
Stability Margin (smargin).............................................................................................2-3
smargin( ).........................................................................................................2-4
Worst-Case Performance Degradation (wcbode) ..........................................................2-8
wcbode( ).........................................................................................................2-9
Advanced Topics ...........................................................................................................2-10
Stability Margin...............................................................................................2-10
Stability Margin and Structured Singular
Values (µ) .......................2-10
Stability Margin Bounds Using Singular Values ..............................2-11
Approximation with Scaled Singular Values....................................2-12
ssv( ) ................................................................................................................2-15
osscale( )..........................................................................................................2-16
pfscale( ) ..........................................................................................................2-16
optscale( ) ........................................................................................................2-17
Reducibility....................................................................................................................2-17
Worst-Case Performance Degradation (wcgain) ...........................................................2-18
Conversion to a Stability Margin Problem......................................................2-18
wcgain( )..........................................................................................................2-19