Stability analysis of autonomously controlled production networks

In this paper we present a stability analysis of autonomously controlled production networks from mathematical and engineering points of view. Roughly speaking stability of a system means that the defined state of the system remains bounded over time. The dynamics of a production network are modelled by differential equations (macroscopic approach) and discrete event simulation (microscopic approach), respectively. Both approaches are used to perform a stability analysis. As a result of the stability analysis of the macroscopic approach we calculate parameters, which guarantee stability of the network for arbitrary inputs. These results are refined for a certain (varying) input using the microscopic approach, where we derive the smallest maximal production rates of the plants for which stability of the overall system can be guaranteed. Furthermore, the microscopic approach includes two different autonomous control methods: the queue length estimator (QLE) and the pheromone based (PHE) method. These methods allow additional autonomous decision making on the shop floor level. The approach presented in this paper is to calculate stability conditions by mathematical systems theory to guarantee stability for production networks, to identify a stability region and to refine this region by simulations.

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