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Xmath
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Chapter 6
Tutorial
Xmath Model Reduction Module
6-8
ni.com
Generate Figure 6 -5:
tvec=0:(140/99):140;
compare(syscl,sysclr,tvec,{type=7})
f5=plot({keep,legend=["original","reduced"]})
Figure 6-5.
Step Response with redschur
Contents
Main
Page
Important Information
Warranty
Copyright
Trademarks
Patents
Conventions
Contents
Chapter 1 Introduction
Chapter 2 Additive Error Reduction
Chapter 3 Multiplicative Error Reduction
Chapter 4 Frequency-Weighted Error Reduction
Page
Introduction
Using This Manual
Document Organization
Bibliographic References
Commonly Used Nomenclature
Conventions
Related Publications
MATRIXx Help
Overview
Functions
Page
Nomenclature
Commonly Used Concepts
Controllability and Observability Grammians
Hankel Singular Values
Page
Internally Balanced Realizations
Singular Perturbation
Page
Spectral Factorization
Page
Low Order Controller Design Through Order Reduction
Page
Additive Error Reduction
Introduction
Truncation of Balanced Realizations
Page
Reduction Through Balanced Realization Truncation
Singular Perturbation of Balanced Realization
Hankel Norm Approximation
Page
balmoore( )
Page
Page
truncate( )
redschur( )
Page
ophank( )
Restriction
Behaviors
Page
Page
Onepass Algorithm
Page
Multipass Algorithm
Discrete-Time Systems
Impulse Response Error
Unstable System Approximation
Multiplicative Error Reduction
Selecting Multiplicative Error Reduction
CG
Multiplicative Robustness Result
bst( )
Page
Algorithm with the Keywords right and left
Page
Page
Securing Zero Error at DC
Hankel Singular Values of Phase Matrix of Gr
Further Error Bounds
Reduction of Minimum Phase, Unstable G
Imaginary Axis Zeros (Including Zeros at )
G
G
s() Gs() valuesvalues
-a
a b
s() Gs() valuesvalues
Page
Page
mulhank( )
right and left
Page
Page
Consequences of Step 5 and Justification of Step 6
Page
Error Bounds
Imaginary Axis Zeros (Including Zeros at )
Page
Page
Page
Frequency-Weighted Error Reduction
Introduction
Controller Reduction
Controller Robustness Result
Page
Page
Fractional Representations
e d
--- n d
---Cs()
Page
Page
KrsI A KEC+()
Ps()
B
K
+ -
K
+()
+Ps()I
s()
Cs() P
K
+
wtbalance( )
Page
Page
Page
Page
fracred( )
Defining and Reducing a Controller
Page
Page
Page
Additional Background
Page
Utilities
hankelsv( )
stable( )
Page
compare( )
Tutorial
Plant and Full-Order Controller
40 dB/decade Frequency (rad/sec)
Loop Gain (dB)
0.3 0.07 40 dB/decade
Page
Page
Controller Reduction
Page
Page
Page
ophank( )
Page
Page
wtbalance
Page
Page
Page
Page
Generate Figure 6 -13 :
Page
Page
fracred
Page
Page
Page
A
Bibliography
Page
Page
Page
Page
B
Technical Support and Professional Services
Index
Symbols
A
B
C
G
H
I
K
L