A Compositional Mathematical Model of Machines Transporting Rigid Objects

We present models of various elements of a plant that involves the transportation of lumped material. An application context is provided by a project on diagnosing disturbances in food packaging plants and, more specifically, bottling plants. While there exist models of flow of homogeneous matters, such as liquid material in a hydraulic system, based on simultaneous equations of Kirchhoff/Ohm type, in our project we need to cope with nonnegligible transportation time of objects and capture phenomena like the tailback of units (if transportation is blocked) or the propagation of gaps in the flow of units. Because the application context requires compositionality of the model, i.e. local, contextfree models of the individual transportation elements, we are also facing the problem that whether or not a single element produces an output flow (or accepts an input flow) cannot be determined solely by the model of this element, but only through modeling the interaction with the subsequent element, which may block the output (or the previous one not providing the input). This issue is addressed by modeling the potential of an existing flow distinctly from the actual occurrence of a flow, an idea which also can enhance models of continuous flow.