Chapter 4 ControllerSynthesis
© National Instruments Corporation 4-7 MATRIXx Xmath Robust Control Module
where
and
The weights also can be viewed as “design knobs” (for example,
[ONR84]). In this view, the weights are not directly related to specific
disturbance or performance models but rather are used as a vehicle to obtain
a closed-loop transfer matrix, Hzv, from v to z with desired properties. For
every selection of weights Win and Wout, the closed-loop system has the
following property:
But Hzv has other properties, both good and bad. To some extent, these all
can be affected by varying the weights. An effective way to provide a rapid
evaluation of performance is with the function perfplots( ), as
described in the perfplots( ) section of Chapter 3, System Evaluation. With
a few trial and error adjustments of the weights, perfplots( ) will give
a good indication of their effect on performance.
Restrictions on the Extended Plant
Not all choices of weights will result in an extended plant P=WoutGWin
that will solve Equation 4-1. The following conditions, established in
references [GD88,DGKF89], if satisfied, will result in a solution. If any
are not satisfied, an error condition occurs.
The conditions are:
•(A, B
2, C2) can be stabilized and detected
•rank(D12) = NU (number of inputs)
•rank(D21) = NY (number of outputs)
Mω() max m11 u(),m12 u()m21 u()m22 u(){}=
m11 σmax WregHyregdWdist
[]=
m12 σmax WregHyregnWnoise
[]=
m21 σmax WactHudWdist
[]=
m22 σmax WactHunWnoise
[]=
WinHzvWout ∞γ≤