Analysis of an Industrial System
Formal Methods in System Design
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We study three simple hybrid control systems in timed $\mu$CRL \cite{Gr97}. A temperature regulation system, a bottle filling system and a railway gate control system are specified component-wise and expanded to linear process equations. Some basic properties of the systems are analysed and a few correctness requirements are proven to be satisfied. Although not designed for this purpose, timed $\mu$CRL seems to allow detailed analysis and verification of hybrid systems. The operators for parallelism and encapsulation are handled using some basic results from \cite{GvW98}. It turns out that the expansion and encapsulation of a parallel composition of processes generally leads to a considerable number of potential {\it time deadlocks\/}, which generally turn out to be harmless. Also inherent to parallelism are the multiple time dependencies between the summands of the separate components. As a consequence, expansions tend to lead to large numbers of terms. Various techniques, such as the use of invariants \cite{BG94}, have to be employed to master these complications.