混杂生产过程的混杂Petri网建模及分析技术研究
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摘要
混杂系统是由连续变量动态系统与离散事件动态系统相互混杂、相互作用而形成的统一动态系统。近些年来,人们在混杂系统理论与工程应用方面的研究取得了一系列成果,然而如何有效的描述和分析混杂系统仍然是混杂系统中最困难、同时也是最富创造性的活动。混杂生产过程是一类重要的混杂系统,本文以一类混杂生产过程为背景,对混杂生产过程的混杂Petri网模型构建、模型分析技术及混杂生产过程的优化与调度等进行了研究和探索,课题的研究得到了国家自然科学基金和广西科学基金的资助。论文主要的研究结果包括:(1)建立了一种新的连续Petri网模型------区间速率连续Petri网模型,并对迁移的使能和引发语义、模型行为演变、模型有效冲突判定及消解、模型可达稳态等问题进行了研究。(2)给出了混杂Petri网一个通用的模型行为演变方法。该方法采用了基于线性规划方法的混杂Petri网瞬时引发速率求解方法。分析了改变不变行为状态事件之间的相互作用及其对模型行为演变正确性的影响,提出了改变不变行为状态事件的判定方法。(3)给出了基于模型行为演变图的混杂Petri网可达性分析方法。分析结果表明了所提出方法的正确性和有效性。该方法不仅适用于R.David和H.Alla定义的混杂Petri网模型,而且适用于一阶混杂Petri网和区间速率连续Petri网等其它混杂Petri网模型。(4)给出了间歇过程在复杂中间存储策略包括无限存储策略、有限存储策略、无中间存储策略和混杂存储策略下p-时间Petri网模型的描述方法,进而给出了基于可行调度集和修正分枝界定的间歇过程最短生产时间的最优调度算法。该算法利用一间歇过程最短生产时间不大于另一间歇过程最短生产时间的条件有效地限制了对解空间的搜索,进而改善了算法的计算性能。(5)定义了广义混杂Petri网模型从而克服了一阶混杂Petri网模型的语义问题,提出了相应的使能和引发语义,并给出了模型行为分析的有效方法。基于所提出的模型,给出了混杂系统建模与优化的实例。(6)讨论了一种混杂生产过程——糖产品压榨系统的混杂Petri网建模及生产调度问题,给出了糖产品压榨系统的生产调度算法。实例表明了所提出方法的有效性。(7)提出了一类流体随机Petri网转换成一阶混杂Petri网的形式化描述方法,并对其转换的正确性进行了证明,实例分析表明了流体随机Petri网转换成一阶混杂Petri网的必要性。
Hybrid systems are composed of discrete event dynamic systems and continuous time dynamic systems, which interact with each other. The hybrid system theory, proposed on the demand of the economic development, is the result of the development of computer science and control theory. As a typical hybrid system, hybrid batch/continuous processes are one of the most impotant processing modes in the process industries. The behaviors of this kind of process can no longer be considered as either continuous or discrete, and therefore pose a difficult problem with regards to formulation and solution algorithm. Modeling and analysis of hybrid batch/continuous processes using hybrid petri nets model was developed in this paper. This work was supported by the National Natural Science Foundation of China (grant No.60243002), and the Natural Science Foundation of GuangXi (grant No. GuiKeQing 0640032). This paper makes following contributions:(1) On the view that the dynamics of time Petri nets can also be approximated continuously, a general continuous Petri nets (CPNs) formalism----Interval speed CPNs) was considered. The problem of behavior analysis and effective conflict for interval speed continuous Petri nets (ICPNs) was developed, and the necessary and sufficient condition for a steady state to be reachable was presented. (2) As the traditional algorithm for the dynamic evolution of Hybrid Petri Nets may not be used for many HPNs models, a new algorithm to construct evolution graph for HPNs was developed. Through case study, the effectiveness of the developed algorithm was illustrated. (3) The decidability of marking rechability for hybrid Petri nets was discussed. The necessary and sufficient condition for a marking to be reachable was presented. Also, an algorithm that decides whether a given marking is reachable or not was introduced through the evolution graph of HPNs. (4) A p-time Petri nets-based formulation approach for batch plants with complicated intermediate storage policies (such as: unlimited intermediate storage, no intermediate storage, finite intermediate storage, and mixed intermediate storage) was presented, then an algorithm for short-term scheduling of batch plants based on a feasible schedule set and a modified branch & bound is developed. In this method, the condition that the minimal makespan of one batch no greater than the minimal makespan of the other batch was presented, thereby the explicit enumeration of search was avoided so that the algorithm performance was improved. Through case study, the effectiveness of the proposed approach and algorithm are illustrated. (5) A new type of hybrid Petri nets model called general hybrid Petri nets (GHPNs) is defined. The enabling and firing semantics of transitions of the GHPNs is discussed, and the net dynamic behavior is also developed. As an example of application, we show how the proposed formalism can be applied to modeling and optimization of a flexible manufacturing system. (6) Motivated by the need of the effective scheduling and control of operations in sugar milling, hybrid time Petri nets(HTPNs) which allows the formulation of variable cycle time and variable flow rate in sugar milling systems was considered. Through analysis of HTPNs model, an effective scheduling algorithm for sugar milling systems was developed. (7) To analyze Fluid Stochastic Petri nets(FSPN) model by First-Order Hybrid Petri Nets(FOHPN) model, the formal conversion from Fluid Stochastic Petri nets to First-Order Hybrid Petri Nets was presented. Also, the effectiveness of the proposed conversion was proofed.
Through case study, the necessity of the conversion is illustrated.
Hybrid systems are composed of discrete event dynamic systems and continuous time dynamic systems, which interact with each other. The hybrid system theory, proposed on the demand of the economic development, is the result of the development of computer science and control theory. As a typical hybrid system, hybrid batch/continuous processes are one of the most impotant processing modes in the process industries. The behaviors of this kind of process can no longer be considered as either continuous or discrete, and therefore pose a difficult problem with regards to formulation and solution algorithm. Modeling and analysis of hybrid batch/continuous processes using hybrid petri nets model was developed in this paper. This work was supported by the National Natural Science Foundation of China (grant No.60243002), and the Natural Science Foundation of GuangXi (grant No. GuiKeQing 0640032). This paper makes following contributions:(1) On the view that the dynamics of time Petri nets can also be approximated continuously, a general continuous Petri nets (CPNs) formalism----Interval speed CPNs) was considered. The problem of behavior analysis and effective conflict for interval speed continuous Petri nets (ICPNs) was developed, and the necessary and sufficient condition for a steady state to be reachable was presented. (2) As the traditional algorithm for the dynamic evolution of Hybrid Petri Nets may not be used for many HPNs models, a new algorithm to construct evolution graph for HPNs was developed. Through case study, the effectiveness of the developed algorithm was illustrated. (3) The decidability of marking rechability for hybrid Petri nets was discussed. The necessary and sufficient condition for a marking to be reachable was presented. Also, an algorithm that decides whether a given marking is reachable or not was introduced through the evolution graph of HPNs. (4) A p-time Petri nets-based formulation approach for batch plants with complicated intermediate storage policies (such as: unlimited intermediate storage, no intermediate storage, finite intermediate storage, and mixed intermediate storage) was presented, then an algorithm for short-term scheduling of batch plants based on a feasible schedule set and a modified branch & bound is developed. In this method, the condition that the minimal makespan of one batch no greater than the minimal makespan of the other batch was presented, thereby the explicit enumeration of search was avoided so that the algorithm performance was improved. Through case study, the effectiveness of the proposed approach and algorithm are illustrated. (5) A new type of hybrid Petri nets model called general hybrid Petri nets (GHPNs) is defined. The enabling and firing semantics of transitions of the GHPNs is discussed, and the net dynamic behavior is also developed. As an example of application, we show how the proposed formalism can be applied to modeling and optimization of a flexible manufacturing system. (6) Motivated by the need of the effective scheduling and control of operations in sugar milling, hybrid time Petri nets(HTPNs) which allows the formulation of variable cycle time and variable flow rate in sugar milling systems was considered. Through analysis of HTPNs model, an effective scheduling algorithm for sugar milling systems was developed. (7) To analyze Fluid Stochastic Petri nets(FSPN) model by First-Order Hybrid Petri Nets(FOHPN) model, the formal conversion from Fluid Stochastic Petri nets to First-Order Hybrid Petri Nets was presented. Also, the effectiveness of the proposed conversion was proofed.
Through case study, the necessity of the conversion is illustrated.
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