Information Technology Reference
In-Depth Information
A common case is a guard sensor that distinguishes between a nite set of
mutually exclusive plant modes
P
1
;:::;
P
n
and ensures transition to correspond-
ing continuation phases
1
;:::;
n
. If the set of modes do not cover the plant
state, it is convenient to specify that the sensor will remain enabled until one of
the modes occur. The commitments of a guard sensor in phase
are:
Progress:
When
P
i
holds for
in phase
, the phase is left.
V
i
=1
d
P
i
^ e
−! d : e
Selection:
The phase
will under
P
i
move to
i
only.
V
i
=1
d:e
P
i
e−!d_
i
e
Stability:
The default mode
P
0
=
V
i
=1
:
;
d ^
P
i
freezes the
phase.
P
0
e−!de
d:e
;
d ^
In general, consistency is not preserved if sensor commitments on the same
phase
are combined, because one sensor may want to be stable while another
may decide to progress. One shall therefore avoid introducing more than one
sensor in an elementary phase. If more are needed, decomposition of the phase
is generally required.
3.2
Actuators
An actuator is characterized by its ability to move the plant to a state determined
by the controller. It is thus the dual of a sensor. We shall start with a description
of a general actuator that transmits a value from the controller state to the plant
state:
Consider controller phases
x
and a state assertion
P
(
x
) over the plant state
which both are dependent on a rigid variable
x
.An
P
(
x
) actuator with reaction
time
and enabled in phases
x
is given by:
Progress:
When the phase
x
has held for
, the plant state
P
(
x
) is established.
8
x
d
x
e
−! d
P
(
x
)
e
Framing:
If the
x
phase is reentered and
P
(
x
) still holds, it continues to hold.
8
x
d:
x
e
;
d
x
^
P
(
x
)
e−!d
P
(
x
)
e
The framing property species that the actuator avoids unnecessary tran-
sients in the plant state. It will ultimately reduce to an assumption about time
bounded stability of a plant state. The unbounded framing can be rened to
bounded framing (a bounded invariance) (
d:
x
e
;
d
x
^
P
(
x
)
e^`
)
−! d
P
(
x
)
e
and synchronization
.
Actuator commitments over the same phase combine when they control dis-
joint plant states.
d
x
e
−! d
P
(
x
)
e
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