Image Processing Reference
In-Depth Information
9.2 PROCESS CONTROL MODELS—A GENERAL CONTROL VIEW
The compact characterization of a printer, described in Chapter 10, as an analytical
MIMO system is very important for applications, and is something quite innovative
at the time this topic was written. However, this is not enough for control. For typical
control applications, we need a representation of the system in the form of a vector
differential equation in continuous time
x
¼
g
(
x
(
t
)
, u
(
t
)
, t
)
(
9
:
1
a)
y
¼
h
(
x
(
t
)
, u
(
t
)
, t
)
or the discrete time version
x
(
k
þ
) ¼
g
(
x
(
k
)
, u
(
k
)
, k
)
1
(
9
:
1
b)
y
(
k
) ¼
h
(
x
(
k
)
, u
(
k
)
, k
)
where
x is the system state
u is the input actuator
y is the output quantity
t and k represent continuous and discrete-time instants, respectively
In fact, we are especially interested in the linear version of the system given by
x
¼
A
(
t
)
x
þ
B
(
t
)
u
y
¼
C
(
t
)
x
þ
D
(
t
)
u
(
:
a)
9
2
or
x
(
k
þ
) ¼
A
(
k
)
x
(
k
) þ
B
(
k
)
u
(
k
)
y
(
k
) ¼
C
(
k
)
x
(
k
) þ
D
(
k
)
u
(
k
)
1
(
9
:
2
b)
If we can express the system in this form, there are well established results available
in the literature for the control of such systems using state or output feedback control.
If the linear system is also time invariant (i.e., when the matrices A, B, C, and D are
constant), then simple design techniques are readily available for powerful control-
lers and there are simple criteria for controllability and observability. This version
can be written in continuous time as
x
¼
Ax
þ
Bu
y
¼
Cx
þ
Du
(
9
:
3
a)
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