Improvement of Suboptimal Siphon- and FBM-Based Control Model of a Well-Known ${\rm S}^{3}{\rm PR}$

Chao, Daniel Yuh

doi:10.1109/tase.2010.2088120

Cited by 60 publications

(49 citation statements)

References 25 publications

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“…If one lumps these monitors into a single one, fewer control places and arcs can be employed. However, the modified (called controller) region [V] ([V] plus V forms a P-invariant [17]) is larger (than that of marked operation places) and affects the uncontrolled model more; hence it reaches fewer states. The MTSI method considers all FBM while the CMTSI considers only a few equivalently lumping several FBM into the critical one.…”

Section: Intuitive Explanationmentioning

confidence: 99%

“…3) cannot be emptied based on the theory in [17]. Siphon S 8 ¼ p 7 ; p 11 ; p 12 ; p 17 ; p 19 ; V S2 ; V S3 f g (see Table 1 in [17]) is synthesized from the core subnet obtained by adding TP-handle H TP1 [t 11 p 17 t 10 p 19 t 7 V S3 ] with resource place r=p 19 upon c 3 . S 8 is emptiable as explained below.…”

Section: Theorymentioning

confidence: 99%

“…2 Benchmark 2 from [5] respectively. Now, M p 17 f p 17 ; p 19 ; V S4 ; V S3 g (see Table 1 in [17]) is synthesized from the core subnet obtained by adding TP-handle H TP2 [t 11 p 17 t 10 p 19 t 7 V S3 ] with resource place r=p 19 upon c 3 . S 10 S 10 ½ ¼ p 2 ; p 3 ; p 4 ; p 5 ; p 6 ; p 9 ; p 10 Þ f g ð Þ is emptiable for a similar reason.…”

Section: Theorymentioning

confidence: 99%

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Comments on “enhancement of an efficient liveness-enforcing supervisor for flexible manufacture systems”

Chao¹

2011

Int J Adv Manuf Technol

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Region theory can synthesize maximally permissive supervisors by solving a set of inequalities based on the marking/transition-separation instances (MTSIs). It is infeasible to solve these inequalities for either a sizable net or a small net with a sizable initial marking. Huang et al. [1] propose novel crucial MTSIs to reduce the number of MTSIs. Experimental results show that the proposed control policy is the most efficient algorithm among the closely related approaches. One example shows that it not only reaches all live states but also employs fewer control arcs than that by Li et al. Huang et al. offer no hints on why it employs fewer control arcs. This paper develops theory to explain the physics behind.

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Section: Intuitive Explanationmentioning

confidence: 99%

Section: Theorymentioning

confidence: 99%

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Comments on “enhancement of an efficient liveness-enforcing supervisor for flexible manufacture systems”

Chao¹

2011

Int J Adv Manuf Technol

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“…PETRI nets (PN) have been used for modeling and analyzing concurrent systems [1][2][3][4][5][6][7][8][9].The net behavior depends not only on the graphical structure, but also on the initial marking of the net. Therefore they cannot be determined by static analysis such as dependency analysis; rather, they can be obtained with reachability analysis [11][12][13][14][15][16].…”

Section: Introductionmentioning

confidence: 99%

Closed form formula construction to enumerate control related states of Bottom Left k-net S<sup>3</sup>PR system (with a Bottom Left side non-sharing resource place) of Petri nets

Chao¹,

Yu²

2015

2015 IEEE 12th International Conference on Networking, Sensing and Control

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Earlier, Chao pioneered the very first closed-form solution of the number of reachable and other states for marked graphs (MG) and k-th order system which is the simplest class of S 3 PR (Systems of Simple Sequential Processes with Resources). This paper progresses one step further on enumerating reachable (forbidden, live, and deadlock) states for Bottom Left k-net systems (one non-sharing resource place in the Bottom position of the right-side process, below denoted as Bottom-Left-k-net) with a formula depending on parameter k for a subclass of nets with k sharing resources.

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“…To resolve this problem, deadlock prevention (by adding monitors to problematic siphons) has been quite a popular research [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. Siphon is a structure object in a Petri net.…”

Section: Introductionmentioning

confidence: 99%

Optimal control policy for a well-known S<sup>3</sup>PR

Chao

Chen

2010

IECON 2010 - 36th Annual Conference on IEEE Industrial Electronics Society

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It has been a hot research topic to compare the effectiveness of new control policies by testing against a wellknown S 3 PR model. So far, only the control policy by Piroddi et al. may reach the optimal number of states among all approaches for a well-known benchmark using a siphon-based approach. The resulting model is a generalized Petri net since some control arcs are weighted, which complicates the system. The only improvement that can be made is to reduce the number of control arcs (by 3), and the number of weighted control arcs (by 9) as we report in this paper. Also the token count is reduced. This is achieved by replacing two monitors with weighted arcs by two new monitors without weighted arcs. INA (Integrated Net Analyzer) analysis indicates that the resulting controlled model is live and reaches the same 21581 states by Piroddi et al. We develop a formal theory for explaining the cause of state losses and providing the foundation for the above improvement model.

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Improvement of Suboptimal Siphon- and FBM-Based Control Model of a Well-Known ${\rm S}^{3}{\rm PR}$

Cited by 60 publications

References 25 publications

Comments on “enhancement of an efficient liveness-enforcing supervisor for flexible manufacture systems”

Comments on “enhancement of an efficient liveness-enforcing supervisor for flexible manufacture systems”

Closed form formula construction to enumerate control related states of Bottom Left k-net S<sup>3</sup>PR system (with a Bottom Left side non-sharing resource place) of Petri nets

Optimal control policy for a well-known S<sup>3</sup>PR

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