Central H-Infinity Controller - National Instruments Xmath Interactive Control Design Module ICDM User Manual

Chapter 8 H-Infinity Synthesis
r=0

Central H-Infinity Controller

Xmath Interactive Control Design Module
u
C(s)
w
1
Figure 8-2. Block Diagram Showing the Basic Setup for H-Infinity Synthesis
Figure 8-2 shows a block diagram with the basic setup for H synthesis
where closed-loop transfer matrix H relates the two exogenous inputs w
and w to the two outputs z
2
The design is based on H, the closed-loop transfer matrix relating the noises
w and w to the signals z
1 2
The entries of the closed-loop transfer matrix can be interpreted as the
(normalized) transfer functions from the process and sensor noises to
the actuator and output, respectively.
The singular values of H are shown in the top left plot of the H Synthesis
window.
The controller C is chosen to minimize the -entropy of the closed-loop
transfer matrix H, given by:
2
I H
----
=
where and are the singular values of H(j ).
1 2
y
P(s)
and z .
1 2
and z . H is given by the following equation:
1 2
1
PC
–
H
---------------- -
=
1 PC
+
PW
⎛
1
∫
⎜
log
----------------------------------- -
2
⎝
1
– ( )
1
0
8-4
z
1
z
2
W(s)
w
2
C
–
PCW
–
⎞
1
⎟
log
+ ----------------------------------- -
2
⎠
1
– ( )
2
1
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