ComputerAided_Design_Engineering_amp_Manufactur.pdf

Note that there are two transitions, t7 and t8, in , we can pick either one as the of the new TPpath.
The tool conveys this information to the designer by popping up a new window, inside which is
displayed an arrow linking two sets of transitions: {t7, t8} and—(an empty set). Picking t7 results in the
dotted lines in Figure 8.12(c). The tool then pops up another window linking two empty sets and signaling
the completion of this step of synthesis. The set of home places now is H � {p1, p8}.
Machines 1, 2, 3, and R2 are required to start their corresponding operations. Thus, using Rules TT.2
and TT.4, generate the new paths: [t3 p12 t2], [t8 p9 t7], [t5 p11 t4], and [t6 p10 t5] (Figure 8.12(d))
where p12, p9, p11, and p10 model the availability of M1, M2, R2, and M3, respectively.
Considering the AGV1, first generate a TT-path between t4 (in � � [p4 t4]) and t3 (in �� � [t3 p4]),
i.e., [t4 p13 t3]. Then add a token to p13 using Rule TT.2. Since LEX([p4 t4], [t3 p4]) � �, add nothing,
according to Rule TT.4. LEX([t3 p4], [p4 t4]) can be any one of {[t8 p8]}, {[t7 p7 t8]}, and {[p1 t6]}. Using
either {[t8 p4} or {[t7 p7 t8]}, add the virtual PT-path from p13 to t8 as the dotted line in Figure 8.12(d). This
implies that once Machine 2 completes its processing, AGV1 delivers the part. Theoretically, one may
use {[p2 t7]} and then a PT-path [p13 t7] would be added. H � {p1, p8–p13}.
Having synthesized the partial system, i.e., the production portion from Enry 1 to Exit 1, now synthesize
the rest of the portion, from Entry 2 to Exit 2, to involve Machines 4 and 5, AGV2, and Robots 1 and 2.
For [t7 p8 t1] and [t5 p11 t4], applying Rule PP.1 leads to the two cycles [p8 t9 p14 t10 p8] and [p11 t11
p15 t12 p11]. The meanings of the added places are shown in Figure 12(e).
Consider two new PSPs: �4 � [p8 t9 p14 t10 p8] and �5 � [p11 t11 p15 t12 p11] and choose t10
from �4 and t11 from �5 to generate a new PSP, psp � [t10 p16 t13 p17 t11]. Note each of the
transitions, t10 and t11, is in a cycle that was generated using Rule PP.1. Hence, now apply Rule TT.3 to
pick up t9 from �4 and t12 from �5 and generate psp’ � [t12 p18 t14 p19 t9]. It is easily verified that
psp, psp,’ �4 , and �5 constitute a cycle. Furthermore, insert the tokens in p19 to represent the availability
of raw material from Entry 1 to fulfill Rule TT.2. H � {p1, p8–p13, p19}.
Now apply Rule TT.2 to obtain the paths: [t13 p20 t10], [t11 p21 t13], and [t14 p22 t12], which model the
availability of Machines 4, 5, and AGV2. H � {p1, p8–p13, p19–p22}. This completes the modeling process
and the final net is depicted in Figure 8.11 as a bounded, live, and reversible net if �p � H, M0 (p) � 0 and
�p � PN-H, (p) � 0; i.e., the places in the net have no tokens, except those in H.
8.7 Enhancement of Synthesis Rules
The synthesized nets, however, are limited in classes because some generations are prohibited. Recently
the author 34 has discovered new synthesis rules such that path generations previously forbidden are now
allowed without incurring logical incorrectness. For instance, a TT-path generation (e.g., PSP [t3 p4 t4]
in Figure 8.13(a)) between two exclusive transitions was forbidden (Rule TT.0); the new rule is that it
is acceptable with additional path generations (PSP [t4 p5 t3]) such that the two exclusive transitions
(t3 and t4) become synchronized and hence sequential to each other. As a result, more classes of nets
can be synthesized.
Another example is shown in Figure 8.14, 27 which models a machine/assembly shop with resource
sharing and cannot be synthesized unless we allow TT-path generations between exclusive transitions
and extend the rules to GPNs. In the sequel, we explain the model and develop the rules for both.
The Model
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The net model consists of three parts: Components I and II and the interconnecting part between them.
The system assembles two Type-1 parts and three Type-2 parts into a final product. Type-1 and Type-2
parts are processed in Workstations 1 and 2, respectively, from the corresponding raw stocks fed by Conveyors
1 and 2, respectively. Robot 1 (3) loads Type-1 (2) raw stock from Conveyor 1 (2) into Workstation
1 (2), performs some machining, and loads the finished part into the buffer. The above two subactivities
are modeled by Components I and II, respectively. Component II also models the assembly process in
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