Environmental Engineering Reference
In-Depth Information
U
i
U
i
U
i
+ 1
U
i
+ 1
U
i
+ 2
U
i
+ 2
F
g,
2
F
g,
2
F
g,
1
F
g,
1
q
i,
2
q
i,
2
F
g,
3
F
g,
3
F
s,
3
F
s,
3
q
i,
1
q
i,
1
F
s,
2
F
s,
2
q
i,
3
q
i,
3
Figure 3.26
Basic forces for the agents
static constant,
x
is the position of the agent and
x
p
is the ending point of the
predecessor.
The second force, the gravitational force, tries to pull the agent up.
Up
in
the virtual model represents beginning of time in the real world, as shown in
Figure 3.26. The gravitational force is given by
F
g
mg
,where
m
is the mass
of the agent and
g
the gravitational acceleration. With the mass of all agents being
the same,
F
g
=
k
g
,where
k
g
is a static constant force vector. This gravitational
force is only applied to an agent when it is floating freely. If the agent is in
contact with another, in the direction pulled by the force, the counterforce from
the contact will cancel out the gravity. The total force is denoted
F
t
:
F
t
=
F
g
With only these two simple forces, a set of agents can be added that can align
themselves and thereby make a valid schedule of how to be processed by the
system. See Figure 3.26, where
U
i
+
1
is the next bath the
q
i
bar has to visit, the
F
s
are the spring forces between these agents, and the
F
g
are the gravitational
forces between these agents.
The spring force serves to compact the plan of an agent group in order to
minimize the total processing time of a bar, whereas the gravity force works to
compact the entire plan for all bars in order to maximize utilization of all baths.
=
F
s
+
12.3.2 Organizations
To make the interaction between the agents more flexible, six social laws are
introduced:
Law 1
If there is a certain amount of free space around the agent, increase size to
T
current
=
T
min
+
X(T
max
−
T
min
)
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