National Instruments 370757C-01 用户手册

下载
页码 71
Chapter 2
Robustness Analysis
2-12
ni.com
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.
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 
min
σ
max
DMD
1
(
) μ M
( )
D diagonal