National Instruments 370757C-01 用户手册
Chapter 4
Controller Synthesis
© National Instruments Corporation
4-5
here the weighting matrices are transfer matrices, whereas in the LQG
setup they are constants.
setup they are constants.
A description of the plant in Figure 4-3 is as follows:
•
Dynamical system G
dyn
:
•
Measured variables y = y
sens
+ n:
•
Input weight W
in
:
•
Output weight W
out
:
Weight Selection
In the standard LQG formulation, the weighting functions (W
dist
, W
noise
,
W
reg
, and W
act
) are all constant matrices. In fact, if Q
reg
and Q
act
are positive
definite matrices in the LQ cost, for example,
then the following apply:
Similarly, if R
proc
and R
sens
are positive definite matrices corresponding to
the process and measurement noise intensities, then the following apply:
x·
Ax B
dist
d B
act
u
+
+
=
y
reg
C
reg
x
=
y
sens
C
sens
x
=
d
n
n
W
dist
0
0
W
noise
w
dist
w
noise
W
in
w
dist
w
noise
=
=
e
reg
e
act
W
reg
0
0
W
act
y
reg
u
W
in
y
reg
u
=
=
J
1
2
2
---
x'Q
reg
x u'Q
act
u
+
0
∞
∫
⎝
⎠
⎜
⎟
⎛
⎞
dt
=
W
reg
Q
reg
1 2
/
=
W
act
Q
act
1 2
/
=
W
dist
Q
proc
1 2
/
=
W
noise
Q
sens
1 2
/
=