Справочник Пользователя для National Instruments 370757C-01
Chapter 2
Robustness Analysis
© National Instruments Corporation
2-13
of generality—so, roughly speaking, it can be solved. [SD83,SD84]
discusses this optimization problem.
discusses this optimization problem.
Notice that:
so you have the following from Equation 2-5:
This inequality is thought to be nearly an equality, so that the left side is a
good engineering approximation to the right side. No theory supports this
generally held belief, but no example is known where the left side is more
than 15% larger than the right side. Equality can be shown to hold provided
k
good engineering approximation to the right side. No theory supports this
generally held belief, but no example is known where the left side is more
than 15% larger than the right side. Equality can be shown to hold provided
k
≤ 3—for example, if there are three or fewer uncertain transfer functions
[Doy82].
Note
The approximation equation of
μ(M) (Equation 2-5) is an upper bound. This means
that the stability margin calculated using this approximation is conservative, that is, less
than the actual stability margin. This optimization problem itself can be difficult. Osborne
[Osb60] and Safonov [Saf82] provide two methods for finding good suboptimal scalings
for Equation 2-5.
than the actual stability margin. This optimization problem itself can be difficult. Osborne
[Osb60] and Safonov [Saf82] provide two methods for finding good suboptimal scalings
for Equation 2-5.
Both Osborne’s and Safonov’s Perron-Frobenius scalings usually have
been found to be close to the optimum for the optimization problem
equation. The resulting approximations,
been found to be close to the optimum for the optimization problem
equation. The resulting approximations,
are thought to be good engineering approximations to
μ.
optscale( )
provides an iterative optimization function based on the ellipsoid
algorithm.
algorithm.
σ
max
M
( )
σ DMD
1
–
(
)
=
for
D
1
=
σ
max
M
( ) μ M
( )
≥
uˆ
OS
M
( ) σ
max
D
OS
MD
OS
1
–
(
)
=
uˆ
PF
M
( ) σ
max
D
PF
MD
PF
1
–
(
)
=