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Chapter 4
Controller Synthesis
© National Instruments Corporation
4-3
Equivalently, as a transfer matrix:
To enter the extended system, you must know the sizes of e and shown 
in Figure 4-1. The extended plant P can be constructed using the Xmath 
interconnection functions, as shown in Example 4-1. 
Building the Plant Model
The general form of the plant P is shown in Figure 4-2. 
Figure 4-2.  Construction of Plant P
The plant consists of three transfer matrices: W
in
 and W
out
, referred to as 
weights, and which can be interpreted as the system dynamics. Both P 
and G distinguish inputs and outputs into two groups of variables.
The input/output variables are organized as follows:
actuator/sensor variables
u—vector of actuator (control) signals
y—vector of sensor (measured) and other accessible signals
exogenous inputs
v—vector of commands and disturbance
w—vector of “normalized” commands and disturbances
performance outputs
z—vector of critical performance signals (regulated variables)
e—vector of “normalized” critical performance signals
P s
( )
D
11
D
12
D
21
D
22
C
1
C
2
sI A
(
)
1
B
1
B
2
[
]
+
=
w
v
z
e
u
y
Plant P
G
W
in
W
out