National Instruments NI MATRIXx Xmath - Manual (Page 6)

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 G
r ................................................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