National Instruments 370757C-01 用户手册
Chapter 4
Controller Synthesis
4-2
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The function
hinfcontr( )
can be used to find an optimal H
∞
controller
K that is arbitrarily close to solving:
(4-2)
The
hinfcontr( )
function description in the
section
describes how the optimum can be found manually by decreasing
γ until
an error condition occurs, or conversely by increasing
γ until the error
condition is fixed.
The particular restrictions, required by the 2-Riccati solutions and
summarized in the
summarized in the
section are
those imposed in [GD88,DGKF89].
Extended Transfer Matrix
Referring to Figure 4-1, plant P specifies two groupings of vector inputs
and outputs. Such systems or transfer matrices are referred to as extended
transfer matrices or systems. To enter these in Xmath requires a
modification of your existing system representation. The standard system
has the form y = G(s)u and can be described either in state-space form:
and outputs. Such systems or transfer matrices are referred to as extended
transfer matrices or systems. To enter these in Xmath requires a
modification of your existing system representation. The standard system
has the form y = G(s)u and can be described either in state-space form:
or as a transfer matrix:
G(s) can be described in Xmath using the state-space system object:
G = system(A,B,C,D)
There is, however, insufficient information in this form to distinguish
the input/output groupings in the extended system P in Figure 4-1.
The state-space form of P is:
the input/output groupings in the extended system P in Figure 4-1.
The state-space form of P is:
K
min H
ew ∞
γ
≤
γ
opt
=
x'
Ax Bu
+
=
y
Ax Du
+
=
G s
( )
D C sI A
–
(
)
1
–
B
+
=
x·
Ax B
1
w B
2
u
+
+
=
e
C
1
x D
11
w D
12
u
+
+
=
y
C
2
x D
21
w D
22
u
+
+
=