User manual

Chapter 3 Building System Connections
Xmath Control Design Module 3-10 ni.com
2
C
-1.5 1.5
D
0
X0
0
0
Algorithm
For the feedback system shown in Example 3-3, you can write the
following system equations:
Combining these equations with the equation for the positive feedback
input term:
and multiplying by the input and output gains M and N, you obtain the
following state-space equations describing the entire system between input
u and output y. If you do not specify any values for the gain matrices,
K defaults to zero (no feedback) and M and N default to appropriately-sized
identity matrices (unity gain on the input and output).
This algorithm assumes that the closed-loop system is well posed to ensure
that
Sys will be proper. The (I – KD
1
) term must be invertible, and a
warning appears if the condition estimate of the term (refer to
rcond) is
less than
eps.
x
·
A
1
xB
1
u
1
+= y
1
C
1
xD
1
u
1
+=
u
1
Ky
1
Mu+=
x
·
A
1
B
1
IKD
1
–()
1–
KC
1
+()xB
1
IKD
1
–()
1–
Mu+=
yNIKD
1
–()
1–
C
1
xND
1
IKD
1
–()
1–
Mu+=