National Instruments Xmath Interactive Control Design Module ICDM - Manual (Page 74)

Chapter 8 H-Infinity Synthesis
© National Instruments Corporation 8-5 Xmath Interactive Control Design Module
If either of these singular values is equal to or exceeds
γ, the γ-entropy is
defined to be +
∞.
In other words, the
γ-entropy is finite only for
, and rapidly
increases to +
∞ as
becomes close to
γ, where the H∞-norm is
defined as:
Refer to Chapters 5 and 12 of Linear Controller Design, Boyd and Barratt,
Prentice-Hall 1991, for some interpretations of the
γ-entropy.
Therefore, the controller designed will always satisfy . For this
reason,
γ is sometimes called the H∞ performance level. For γ, which is too
small, there may be no controller that can achieve the required performance
level.
For large
γ, the γ-entropy of H is very nearly the same as the LQG cost with
the same parameters (
ρ and ν), so the H∞ controller will be nearly the same
as the LQG controller with the same values of ρ and ν.
Output Weight Editing
When Weight Zero Edit is enabled, the user can graphically edit the
output weight transfer function W. The weighting transfer function is
given by:
Its denominator is fixed and equal to the numerator of the plant transfer
function; its numerator can be manipulated by the user.
The lower left plot shows the poles and zeros of the weight transfer
function W. When Weight Zero Edit is enabled, the user can grab and
drag the zeros shown, or Add/Delete/Edit zeros using the push buttons.
The lower right plot shows the magnitude of the weight transfer function.
When it is flat and equal to 0 dB for all frequencies, you have W = 1; that
is, standard (unweighted) design.
H
∞
γ <
H
∞
H
∞
max σ
1
H j ω ( ) ( )
=
0 ω ∞ ≤ ≤
H
∞
γ <
W s ( )
n
w
s ( )
n
p
s ( )
------------ =