Michael Görges

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.

Modelling and Analysis of Autonomously Controlled Production Networks

Abstract To cope with increasing internal and external dynamics of production networks, a decentralized and flexible autonomous control approach seems to be promising. This paper presents a dynamic model of a production network with geographically dispersed facilities and fixed transport schedules. It investigates the influence of local autonomous control methods on integrated production and transport processes and shows that the application of autonomous control may improve the handling of internal and external dynamics.

Local Input-to-State Stability of Production Networks

In this paper, we analyze a given production network in view of stability, which means boundedness of the state of the network over time. From a mathematical point of view we model the network by differential equations. With help of local input-to-state stability (LISS) Lyapunov functions and a small gain condition we check, if the network is stable. This results in the derivation of conditions for the production rates for which stability of the production network is guaranteed.

Autonome Produktionssteuerung bei zentraler Produktionsplanung

Kurzfassung Globale Trends wie die zunehmende Produktindividualisierung führen zusammen mit einer gestiegenen Marktvolatilität zu komplexen und dynamischen Produktionsabläufen, mit denen die Produktionsplanung und -steuerung (PPS) heute konfrontiert ist. Autonome Steuerungsmethoden ermöglichen in diesem Kontext eine hohe Reaktionsfähigkeit auf dynamische Einflüsse. Der vorliegende Beitrag stellt die Potenziale, Zusammenhänge und Handlungsfelder dar, um die Vorteile von autonomer Produktionssteuerung mit denen zentraler Produktionsplanung zu verbinden.

Autonomous Decision Policies for Networks of Production Systems

Modern production and logistic systems are facing increasing market dynamics: customers demand highly individualized goods, the adherence to due dates becomes critical and stipulated delivery times are decreasing. Particularly logistic networks, e.g. production networks or supply chains, are strongly affected by this trend. On the other hand, production networks have to deal with inherent internal dynamics, which are caused by e.g. machine breakdowns or rush orders. The concept of autonomous control, coming from the theory of self-organization, offers decentralized autonomous decision policies (ADPs), which enable logistic objects to make and execute decision on their own. Due to this kind of decision making, autonomous control aims at a distributed coping with dynamic complexity and, at the same time, at an improvement of the logistic performance. This contribution addresses the concept of autonomous control and the underlying autonomous decision policies as a novel concept for the control of the material flows in networks of coupled production facilities. Moreover, it shows different concepts of modeling and analysis of autonomously controlled networks. To achieve this goal, a dual approach including both, mathematical methods as well as simulation models, is presented. Subsequently, the possibilities to analyze the dynamic behavior of the autonomous logistic system are discussed, i.e., the system’s stability and its logistic performance. Finally, this contribution presents an exemplary case of a production network to demonstrate the practicability of the approach of modeling and analysis of autonomous control for production networks.

Stability Analysis Scheme for Autonomously Controlled Production Networks with Transportations

In this paper, we present a scheme for the stability analysis of autonomously controlled production networks with transportations. We model production networks by differential equations and discrete event simulation models (DES) from a mathematical and engineering point of view, where transportation times are considered in the models as time delays. Lyapunov functions as a tool to check the stability of networks are used to calculate stability regions. Then, this region is refined using the detailed DES. This approach provides a scheme to determine stability regions of networks with less time consumption in contrast to a pure simulation approach. In presence of time delays, new challenges in the analysis occur, which is pointed out in this paper.

Potentials and Limitations of Autonomously Controlled Production Systems

The application of autonomous control to production logistic systems has already shown promising results. Especially, in highly dynamic situations autonomous control outperforms conventional production planning and control methods. However, the implementation of autonomous control to production systems seems to be unsuitable to some situations. It appears that classical planning methods perform best in well-defined situations with less dynamics. This contribution addresses the potentials and the limitations of autonomous control compared to centralized planning and controll algorithms. Therefore, scenarios of the flexible flow shop problem with varying degrees of complexity and dynamics are used for evaluating autonomous control methods. The results are compared to classical scheduling algorithms for the flexible flow shop scheduling, in order to identify limitations and potentials of autonomous control.

Logistic Systems with Multiple Autonomous Control Strategies

Production planning and control (PPC) systems have to cope with rising complexity and dynamics that arise from a higher demand for individualized goods, short delivery times, a strict adherence to due dates and internal unexpected events, e.g. machine breakdowns or rush orders. Conventional production planning and control methods cannot handle unpredictable events and disturbances in a satisfactory manner because in practice the complexity of centralized architectures tends to grow rapidly with size, resulting in rapid deterioration of fault tolerance, adaptability and flexibility [8]. One approach to overcome these difficulties is to develop decentralized systems with autonomous control methods to reduce the complexity that has to be taken into account for rendering decisions [13].