National Instruments 370757C-01 User Manual
Chapter 2
Robustness Analysis
2-12
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You can compare this margin to that of the example in the
section; the following inputs produce Figure 2-7.
plot ([marg,margSVD],{xlog}
legend=["PF_SCALE","SVD"],
ylab="Stability Margin,dB",
xlab="Frequency, Hz."})
Figure 2-7. pfscale( ) versus svd Stability Margins
Note
The singular value approach gives results that are too conservative, suggesting that
the uncertainties can destabilize the system. Conversely, you know from the scaled singular
value calculations that the system is robustly stable.
value calculations that the system is robustly stable.
Approximation with Scaled Singular Values
In [Saf82] and [Doy82], the inequality
(2-5)
is noted. This optimization problem can be shown to be
unimodal—for D > 0, an assumption that can be made without loss
unimodal—for D > 0, an assumption that can be made without loss
min
σ
max
DMD
1
–
(
) μ M
( )
≥
D diagonal