National Instruments NI MATRIXx Xmath - Manual (Page 97)

Chapter 6 Tutorial
Xmath Model Reduction Module 6-2 ni.com
A minimal realization in modal coordinates is C(sI – A) –1 B where:
The specifications seek high loop gain at low frequencies (for performance)
and low loop gain at high frequencies (to guarantee stability in the presence
of unstructured uncertainty). More specifically, the loop gain has to lie
outside the shaded region shown in Figure 6-1.
Figure 6-1. Loop Gain Constraints
A diag 0 1
0 0
0.015 – 0.765
0.765 – 0.015 –
0.028 – 1.410
1.410 – 0.028 –
0.04 – 1.85
1.85 – 0.04 –
, , ,
⎩ ⎭
⎨ ⎬
⎧ ⎫
=
B
0.026
0.251 –
0.033
0.886
–
4.017 –
0.145
3.604
0.280
=
C ′
0.996 –
0.105 –
0.261
0.009
0.001 –
0.043 –
0.002
0.026 –
=
40 dB/decade
Frequency (rad/sec) Loop Gain (
d
B)
0.3
0.07
40 dB/decade