National Instruments 370755B-01 Chapter 3 Multiplicative Error Reduction, Chapter 4 Frequency-Weighted Error Reduction

Contents
Xmath Model Reduction Module vi ni.com
Onepass Algorithm.........................................................................................2-18
Multipass Algorithm ......................................................................................2-20
Discrete-Time Systems...................................................................................2-21
Impulse Response Error..................................................................................2-22
Unstable System Approximation....................................................................2-23
Related Functions............................................................................................2-23
Chapter 3
Multiplicative Error Reduction
Selecting Multiplicative Error Reduction......................................................................3-1
Multiplicative Robustness Result....................................................................3-2
bst( )...............................................................................................................................3-3
Restrictions......................................................................................................3-4
Algorithm........................................................................................................3-4
Algorithm with the Keywords right and left...................................................3-5
Securing Zero Error at DC..............................................................................3-8
Hankel Singular Values of Phase Matrix of Gr...............................................3-9
Further Error Bounds......................................................................................3-9
Reduction of Minimum Phase, Unstable G.................................................... 3-9
Imaginary Axis Zeros (Including Zeros at ∞).................................................3-10
Related Functions............................................................................................3-14
mulhank() .....................................................................................................................3-14
Restrictions......................................................................................................3-14
Algorithm........................................................................................................3-14
right and left....................................................................................................3-15
Consequences of Step 5 and Justification of Step 6........................................3-18
Error Bounds...................................................................................................3-20
Imaginary Axis Zeros (Including Zeros at ∞).................................................3-21
Related Functions............................................................................................3-24
Chapter 4
Frequency-Weighted Error Reduction
Introduction...................................................................................................................4-1
Controller Reduction.......................................................................................4-2
Controller Robustness Result..........................................................................4-2
Fractional Representations..............................................................................4-5
wtbalance() ...................................................................................................................4-10
Algorithm........................................................................................................4-12
Related Functions............................................................................................4-15
fracred() ........................................................................................................................4-15
Restrictions......................................................................................................4-15
Defining and Reducing a Controller...............................................................4-16