Computationally Improved Optimal Control Methodology for Linear Programming Problems of Flexible Manufacturing Systems
Deadlock prevention policies are used to solve the deadlock problems of FMSs. It is well known that the theory of regions is the efficient method for obtaining optimal (i.e., maximally permissive) controllers. All legal and live maximal behaviors of Petri net models can be preserved by using marking...
Saved in:
| Main Authors: | , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
|
| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/294835 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849683686630359040 |
|---|---|
| author | Yen-Liang Pan Yi-Sheng Huang Yi-Shun Weng Weimin Wu MuDer Jeng |
| author_facet | Yen-Liang Pan Yi-Sheng Huang Yi-Shun Weng Weimin Wu MuDer Jeng |
| author_sort | Yen-Liang Pan |
| collection | DOAJ |
| description | Deadlock prevention policies are used to solve the deadlock problems of FMSs. It is well known that the theory of regions is the efficient method for obtaining optimal (i.e., maximally permissive) controllers. All legal and live maximal behaviors of Petri net models can be preserved by using marking/transition-separation instances (MTSIs) or event-state-separation-problem (ESSP) methods. However, they encountered great difficulties in solving all sets of inequalities that is an extremely time consuming problem. Moreover, the number of linear programming problems (LPPs) of legal markings is also exponential with net size when a plant net grows exponentially. This paper proposes a novel methodology to reduce the number of MTSIs/ESSPs and LPPs. In this paper, we used the well-known reduction approach Murata (1989) to simply the construct of system such that the problem of LPPs can then be reduced. Additionally, critical ones of crucial marking/transition-separation instances (COCMTSI) are developed and used in our deadlock prevention policy that allows designers to employ few MTSIs to deal with deadlocks. Experimental results indicate that the computational cost can be reduced. To our knowledge, this deadlock prevention policy is the most efficient policy to obtain maximal permissive behavior of Petri net models than past approaches. |
| format | Article |
| id | doaj-art-cedf75639b2f4cbdac5c0eef7bf5446a |
| institution | DOAJ |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-cedf75639b2f4cbdac5c0eef7bf5446a2025-08-20T03:23:43ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/294835294835Computationally Improved Optimal Control Methodology for Linear Programming Problems of Flexible Manufacturing SystemsYen-Liang Pan0Yi-Sheng Huang1Yi-Shun Weng2Weimin Wu3MuDer Jeng4Department of Avionic Engineering, Air Force Academy, TaiwanDepartment of Electronic Engineering, National Ilan University, TaiwanDepartment of Electronic Engineering, Army Academy, TaiwanState Key Laboratory of Industrial Control Technology and Institute of Cyber-Systems and Control, Zhejiang University, Hangzhou 310027, ChinaDepartment of Electronic Engineering, National Taiwan Ocean University, TaiwanDeadlock prevention policies are used to solve the deadlock problems of FMSs. It is well known that the theory of regions is the efficient method for obtaining optimal (i.e., maximally permissive) controllers. All legal and live maximal behaviors of Petri net models can be preserved by using marking/transition-separation instances (MTSIs) or event-state-separation-problem (ESSP) methods. However, they encountered great difficulties in solving all sets of inequalities that is an extremely time consuming problem. Moreover, the number of linear programming problems (LPPs) of legal markings is also exponential with net size when a plant net grows exponentially. This paper proposes a novel methodology to reduce the number of MTSIs/ESSPs and LPPs. In this paper, we used the well-known reduction approach Murata (1989) to simply the construct of system such that the problem of LPPs can then be reduced. Additionally, critical ones of crucial marking/transition-separation instances (COCMTSI) are developed and used in our deadlock prevention policy that allows designers to employ few MTSIs to deal with deadlocks. Experimental results indicate that the computational cost can be reduced. To our knowledge, this deadlock prevention policy is the most efficient policy to obtain maximal permissive behavior of Petri net models than past approaches.http://dx.doi.org/10.1155/2013/294835 |
| spellingShingle | Yen-Liang Pan Yi-Sheng Huang Yi-Shun Weng Weimin Wu MuDer Jeng Computationally Improved Optimal Control Methodology for Linear Programming Problems of Flexible Manufacturing Systems Journal of Applied Mathematics |
| title | Computationally Improved Optimal Control Methodology for Linear Programming Problems of Flexible Manufacturing Systems |
| title_full | Computationally Improved Optimal Control Methodology for Linear Programming Problems of Flexible Manufacturing Systems |
| title_fullStr | Computationally Improved Optimal Control Methodology for Linear Programming Problems of Flexible Manufacturing Systems |
| title_full_unstemmed | Computationally Improved Optimal Control Methodology for Linear Programming Problems of Flexible Manufacturing Systems |
| title_short | Computationally Improved Optimal Control Methodology for Linear Programming Problems of Flexible Manufacturing Systems |
| title_sort | computationally improved optimal control methodology for linear programming problems of flexible manufacturing systems |
| url | http://dx.doi.org/10.1155/2013/294835 |
| work_keys_str_mv | AT yenliangpan computationallyimprovedoptimalcontrolmethodologyforlinearprogrammingproblemsofflexiblemanufacturingsystems AT yishenghuang computationallyimprovedoptimalcontrolmethodologyforlinearprogrammingproblemsofflexiblemanufacturingsystems AT yishunweng computationallyimprovedoptimalcontrolmethodologyforlinearprogrammingproblemsofflexiblemanufacturingsystems AT weiminwu computationallyimprovedoptimalcontrolmethodologyforlinearprogrammingproblemsofflexiblemanufacturingsystems AT muderjeng computationallyimprovedoptimalcontrolmethodologyforlinearprogrammingproblemsofflexiblemanufacturingsystems |