Information Technology Reference
In-Depth Information
⎧
⎨
v
2
max
u
+
S−
v
2
max
u
max
2
v
max
u
max
if
S
≥
max
v
max
t
b
=
2
S
u
max
(40)
⎩
if
S<
v
2
max
u
max
The different minimal-time profiles for carrying out the task with respect to
v
v
max
max
t
t
t
t
0
t
t
0
1
2
b
2
()
b
()
a
Fig. 6.
Different minimal-time depending on distance S. (a):
S<
v
2
max
u
max
v
2
max
u
max
,(
b
):
S ≥
.
distance
S
can be seen in Fig. 6. The minimal-time depends on the relationship
between
S
and
v
2
max
u
max
(which is obtained based on the optimal control action).
t
b
is the ending time and the distance
S
is used as the integration over [0
,t
b
].
In summary, the minimal-time required to do task
τ
i,j
can be obtained by
Pontryagin's necessary conditions. This minimal-time is given by
t
b
above. It is
the lower bound on the time required for doing a task by a piece of equipment.
This bound is sent to the higher level as
s
min
i,j
for scheduling the tasks.
3.3 Control Architecture Summary
The control problem for three pieces of equipment is decomposed into three
steps. First once the lower-level controller receives the request from the higher
level for the time required for doing a task, the lower bound of the transport
time is obtained by the lower-level controller by solving a minimal-time control
problem. Then the supervisory controller determines the operation time of each
piece of equipment. The scheduling problem is formulated by the supervisory
controller as a linear programming problem and solved recursively. The operation
time allowed for carrying out a task by a piece of equipment is then sent from
the supervisory controller to lower-level control of each piece of equipment. The
pieces of equipment subsequently carry out the task, possibly also taking into
account energy saving objectives. The complete procedure of the hierarchical
control structure is as follows:
-
the higher level requests the time required for doing a particular task;
-
minimal time control of QC, AGV and ASC at the lower level is calculated
locally;
