The real-time behavior of the steam-boiler

Abstract

This paper presents a rigorous model of the dynamics of the physical process of the steam-boiler and of the embedding of the discrete program given in Chapter CW1 in the continuous environment. Program constants and variables are clearly distinguished from physical quantities, and it is shown, that under some conditions the program variables approximate the physical quantities. This relation between physical and program variables is, technically speaking, a coupling invariant. Hybrid and real-time aspects of the system are also considered, including several positive and negative results regarding the expected properties of the system. Some of them are impossibility results, in the sense that no (reasonable) controller program can solve some aspects of the problem properly.

This paper illustrates a simple method for combining different abstraction levels in the verification of industrial control programs. Programs are specified by their next-state relation (in first order logic) without real-time (but, if needed, using program clocks). The behavior of the environment is described by the physical laws that govern the dynamics of the process. Those two levels are bridged together by the specification of the real-time deadlines that the SW- and HW-implementation has to guarantee.

Supported in part by a BMBF grant from the German Federal Ministry of Education, Science, Research and Technology under contract number 01IS519A (project KORSYS)