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Chapter 2 Robustness Analysis
© National Instruments Corporation 2-19 MATRIXx Xmath Robust Control Module
Using this relation and any of the previously discussed approximations for
μ(
.
), you can compute an approximation to wcgain( ). Because the
approximations to μ(
.
) are upper bounds, the resulting approximations to
wcgain( ) also are upper bounds. For speed purposes, wcgain( ) uses
Perron-Frobenius scaling to calculate the approximation of μ.
wcgain( )
gamma = wcgain(H, gammin, gammax, gam0)
The wcgain( ) function estimates the largest possible magnitude from
a given input of the system to a given output, when the other inputs are
connected to the other outputs through uncertain transfer functions
bounded by one.
For a discussion of
wcgain( ) syntax, refer to the Xmath Help. This is a
low-level function that calculates the worst-case gain at a single frequency,
where the magnitude bounds are normalized to one as follows:
Because it is a lower level function, there is no syntax checking. This
function is called by the
wcbode( ) function.
l
1
… l
k
1===