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Chapter 3 Building System Connections
© National Instruments Corporation 3-13 Xmath Control Design Module
The single system resulting from the feedback combination of Sys1 and
Sys2 has u
1
as its input, y
1
as its output, and a state vector consisting of the
appended states of
Sys1 and Sys2. Using these five equations to find the
state-space dynamics of the complete system results in the overall system
description.
This algorithm assumes that the closed-loop system is well constructed
(the (I + D
2
D
1
) and (I + D
1
D
2
) terms must be invertible). This condition
ensures that the output system
Sys will be proper.
y
1
ID
1
D
2
+()
1–
C
1
D
1
ID
2
D
1
+()
1–
C
2
–
x
1
x
2
= +
x
·
x
·
1
x
·
2
= •
x
1
x
2
B
1
ID
2
D
1
+()
1–
B
2
ID
1
D
2
+()
1–
D
1
u
1
+
=
A
1
B
1
ID
2
D
1
+()
1–
D
2
C
1
– B–
1
ID
2
D
1
+()
1–
C
2
B
2
ID
1
D
2
+()
1–
C
1
A
2
B
2
ID
1
D
2
+()
1–
D
1
C
2
–
•
D
1
ID
2
D
1
+()
1–
u
1