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Chapter 2 Robustness Analysis
© National Instruments Corporation 2-17 MATRIXx Xmath Robust Control Module
optscale( )
[v, vOPTD] = optscale (M, {tol})
The optscale( ) function optimally scales a matrix. An iterative
optimization (ellipsoid) algorithm which calculates upper and lower
bounds on the left side of Equation 2-5 is used. If these bounds are within
a relative accuracy you have specified
(tol), optscale( ) stops.
optscale( ) also will stop and issue a warning if the maximum number
of iterations is reached:
optscale( ) will find a μ(M) no larger than pfscale( ).
Reducibility
In some cases, the uncertain transfer functions can be divided into groups
that do not interact. This is illustrated in Figure 2-9.
Figure 2-9. Non-Interacting Uncertain Transfer Functions
As you can see, δ
3
does not affect the stability margin at all because there
is no feedback through it. The system in Figure 2-9 can be reduced to the
two separate systems shown in Figure 2-10. The stability margin of
Figure 2-9 is the minimum of the stability margins of the systems in
Figure 2-10.
200 rows(M)×
δ
2
δ
3
δ
1
δ
4