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 u1 as its input, y1 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+D2D1) and (I+D1D2) terms must be invertible). This condition
ensures that the output system Sys will be proper.
y1ID
1D2
+()
1–C1D1ID
2D1
+()
1–C2
–
x1
x2
=+
x
·x
·1
x
·2
=•
x1
x2
B1ID
2D1
+()
1–
B2ID
1D2
+()
1–D1
u1
+
=A1B1ID
2D1
+()
1–D2C1
–B–1ID
2D1
+()
1–C2
B2ID
1D2
+()
1–C1A2B2ID
1D2
+()
1–D1C2
–
•
D1ID
2D1
+()
1–u1