National Instruments Xmath Interactive Control Design Module ICDM, Руководство пользователя

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Chapter 12 LQG/H-Infinity Synthesis
© National Instruments Corporation 12-11 Xmath Interactive Control Design Module
The system equations of plant, filters, and integrators are as follows:
Standard LQG (All Toggle Buttons “Off”)
In LQG synthesis mode, the controller C minimizes a weighted sum of the
steady-state actuator and output variance:
where E denotes expectation.
Integral Action
When Integral action is enabled, the controller minimizes a variation on the
LQG cost:
where
Plant ( P ):
Output filter ( F
y
):
Input filter ( F
u
):
Integrator:
x
·
p
A
p
x
p
B
p
u
act
B
p
w
p
w
x
+ + + =
y
p
C
p
x
p
w
s
w
y
+ + =
y ˜ C
y ˜
x
y ˜
w
y ˜
+ =
x
·
y ˜
A
y ˜
x
y ˜
B
y ˜
y
p
W
p
w
F
+ + =
x
·
u ˜
A
u ˜
x
u ˜
B
u ˜
u
act
+ =
u ˜ C
u ˜
x
u ˜
D
u ˜
u
act
+ =
x
·
I
y ˜ W
I
w
r
+ =
y
I
x
I
w
r
+ =
J E
t ∞ →
lim
x
T
u
T
R
xx
R
xu
R
ux
R
uu
x
T
u
T
ρ
u i ,
u
i
2
,
i 1
=
n
u
∑
+
ρ
y j ,
y
j
2
,
j 1
=
n
y
∑
+
⎝ ⎠
⎜ ⎟
⎜ ⎟
⎛ ⎞
=
J E
t
∞ →
lim
x
T
u
T
R
xx
R
xu
R
ux
R
uu
x
T
u
T
ρ
u i
,
u
i
2
i 1
=
n
u
∑
ρ
y j
,
y
j
2
y
I j
,
2
+
[ ]
j 1
=
n
y
∑
+ +
⎝ ⎠
⎜ ⎟
⎜ ⎟
⎛ ⎞
=
⎝ ⎠
⎜ ⎟
⎜ ⎟
⎛ ⎞
a
y
I j ,
t
( )
1
T
int
--------
y
j
ϒ ( ) ϒ
d
0
t
∫
=