｜自動化製造系統裡浮標守恆裴氏圖的時域分解

摘要：本文提出時域分解法來將自動化製造系統的浮標守恆裴氏圖分解出歐氏記號圖。依據理論分析結果，控制製造設備的資訊流可用浮標守恆裴氏圖來表達。又可設計即時偵查法則以便在偵測到不正常的資訊流行為時來提供警訊。相對於歐氏記號圖可透過擬陣理論來推導出偵查法則，直接從浮標守恆裴氏圖設計出偵查法則是非常困難的。另一個解決此設計問題的方法是在時域裡將浮標守恆裴氏圖分解成歐氏記號圖。在此情況下，偵查法則可由歐氏記號圖推導出並合成之。這種新解法可以大量降低偵查法則的設計複雜度。本文將詳細地說明時域分解法的分解三步驟。特別是透過Prolog語言將此套裝軟體開發出來並使得分解過程可以自動化。

Abstract: Temporal decomposition method is proposed for generating Eulerian marked graphs from token-conserved Petri net in automated manufacturing system. According to its theoretic analysis, information flow used for controlling manufacturing devices is well represented by token-conserved Petri net. Also real-time monitor rules are designed for offering alert messages in case of detecting the abnormal behavior of information flow. However, it is difficult to design monitor rules directly from a token-conserved Petri net if compared with Eulerian marked graphs which monitor rules can be easily derived using matroid theory. An alternative approach to the design problem is to decompose the given token-conserved Petri net into different Eulerian marked graphs in temporal domain. Then the monitor rules are directly derived and synthesized from each Eulerian marked graph. This new approach reduces the design complexity of monitor rules dramatically. In this paper, the underlying principle of temporal decomposition method is described in three steps. Moreover, a software package based on Prolog language is implemented to make the decomposition process automatically.

關鍵詞：自動化製造系統、浮標守恆裴氏圖、歐氏記號圖、時域分解法、偵查法則

Keywords：Automated Manufacturing System, Token-Conserved Petri Net, Eulerian Marked Graph, Temporal Decomposition Method, Monitor Rule

前言
自動化製造系統（Automated Manufacturing System）裡的生產設備通常是透過資訊流來指揮，而資訊流是透過可程式控制器（Programmable Logic Controller, PLC）[3, 13]與偵查器（Monitor）[2, 3]來掌握。其中可程式控制器協調生產設備的互動，而偵查器由偵查法則（Monitor Rule）[2, 4, 5]組成並用來偵查可程式控制器是否正常運作。為了能正確的描述可程式控制器與偵查器的行為，兩者皆需要建立數學模式。

本文將說明自動化製造系統的資訊流可用浮標守恆裴氏圖（Token-Conserved Petri Net）來表達，但其偵查法則的設計則非常複雜。如果資訊流可用歐氏記號圖（Eulerian Marked Graph）[1, 2, 5]來表達，則其偵查法則的設計可透過擬陣理論（Matroid Theory）[4, 5, 12]來進行。在先前的時域研究[5]裡，發現浮標守恆裴氏圖可以分解成歐氏記號圖。本文將提出時域分解法（Temporal Decomposition Method）來將浮標守恆裴氏圖用三步驟方式來分解出歐氏記號圖。在此情況下，浮標守恆裴氏圖的偵查法則設計將變得更容易進行。

為了更詳細地說明時域分解法的內容，底下先針對浮標守恆裴氏圖與歐氏記號圖的數學性質說明之。接著再說明時域分解法的內容，即可透過可用轉移點集合（Available Transition Set）計算、可觸發轉移點集合（Enable Transition Set）計算、及產生歐氏記號圖三大步驟來進行。這裡可用轉移點集合與可觸發轉移點集合皆可用Prolog程式[7]來直接計算。接著舉兩個自動化製造系統的案例來說明時域分解法的應用：即工件加工系統[5]與液體加熱系統[5]。這裡工件加工系統的浮標守恆裴氏圖可分解出3張的歐氏記號圖，而液體加熱系統的浮標守恆裴氏圖可分解出2張的歐氏記號圖。接著再以工件加工系統為例說明偵查法則的設計。最後則是結論。