National Instruments NI MATRIXx Xmath - Manual (Page 87)

Chapter 4 Frequency-Weighted Error Reduction
© National Instruments Corporation 4-17 Xmath Model Reduction Module
to, for example,
through, for example, balanced truncation, and then defining:
For the second rationale, consider Figure 4-5.
Figure 4-5. Internal Structure of Controller
Recognize that the controller C(s) (shown within the hazy rectangle in
Figure 4-5) can be constructed by implementing
and
and then applying an interconnection rule (connect the output of the second
transfer function matrix back to the input at point X in Figure 4-5).
E
r
s ( )
K
R
C
sI Aˆ –
( )K
E
=
C s ( ) K
R
sI Aˆ –
( )
1 –
K
E
I C + sI Aˆ –
( )
1 –
K
E
[ ]
1 –
=
K
R
sI Aˆ – K
E
C +
( )
1 –
K
E
=
K
E
P s ( )
+
-
1
s
--- K
R
+ +
C
A BK
R
–
X
+
-
K
R
sI A BK
R
+ –
( )
1 – K
E
C sI A BK
R
+ –
( ) 1 – K
E