Modelling and Control of Production Systems based on Nonlinear Dynamics Theory B. Scholz-Reiter (2), M. Freitag, A. Schmieder Department of Planning and Control of Production Systems, University of Bremen, Bremen, Germany Abstract Today's highly dynamic market with its rapid changing demand requires highly dynamic order processing in very flexible production systems. Most conventional production planning and control methods do not support such fast-moving activities. A dynamical approach is introduced for modelling and control of production systems. It was developed from concepts of the Nonlinear Dynamics Theory. Manufacturing processes as well as planning and control mechanisms are seen as one unit toward the establishment of a dynamical system. The dynamical approach includes an analysis of the dynamic behaviour of the production system as well as the control of the manufacturing process by a continuous adjustment because of changes or disturbances in the environment or in the production system itself. Keywords: Production, Control, Nonlinear Dynamics 1 INTRODUCTION The development of Nonlinear Dynamics Theory and its applications in different fields enables us to understand and describe the dynamics of complex production systems where linear approaches fail or are too far from reality [1]. But complex dynamic behaviour can occur even in relatively simple production systems. Beaumariage and Kempf have shown the sensitive dependence of throughput times on the initial conditions and scheduling rules in a re-entrant production system model [2]. The origin of this unstable behaviour is not obvious. Beaumariage and Kempf suggest chaotic dynamics as being the reason. To understand such complex dynamic behaviour of a production system, an intrinsic deterministic model is necessary, into which stochastic influences can be incorporated later on. Bartholdi, Bunimovich and Eisenstein have shown, that deterministic models can describe the dynamics of production systems appropriately. They described a sewing production line whose dynamic behaviour was exclusively driven by deterministic rules [3][4]. Understanding the production dynamics is therefore the motivation for modelling and control of production systems using Nonlinear Dynamics Theory. Classical production planning and control systems (PPC systems) are based on concepts that do not consider the production system as a dynamical 1 system. Usually, heuristic approaches are preferred in order to simulate the production process and its scheduling and control. But optimisation methods do not provide the controller with good results if there are some changes during the optimisation period [5][6]. In the context of today’s highly dynamic market with its rapid changes in demand, modern PPC systems have to deal increasingly with flexibility and variety. This paper presents a dynamical approach for modelling and control of production systems based on Nonlinear 1 The use of “dynamical” rather than the simple adjective “dynamic” has become conventional in the Nonlinear Dynamics community. Dynamics Theory, which incorporates the modelling of the dynamical aspects of the production systems in interaction with the control system that includes the functional aspects of PPC. 2 PRODUCTION MODELS AND PPC CONCEPTS The usual models of production systems are derived from classical optimisation tasks studied in Operations Research [7]. The model for the production system itself therefore consists of different optimisation problems. There is no interaction of these particular theories. This could be developed in a meta-theory, but in general, the results will be hard to interpret [8]. Known concepts for production planning and control are normally founded on models for parts of the overall PPC job that solve local problems like the job shop scheduling [8]. Such optimisation models - solved by exact algorithms or heuristic approaches - are often not satisfying even at a low level of complexity [9]. Nevertheless, numerous PPC systems are based on these PPC concepts. Such a PPC system is designed to find optimal solutions for specific PPC problems. The most important optimisation goals are total costs, throughput time, capacity utilization, inventory costs and delivery reliability. Thereby, strategies for different objectives can lead to contrary results, e.g. maximal capacity utilization and minimal throughput times. Most recent PPC systems work in line with the successive planning concept consisting of successive planning steps. It is widely used but also criticised because it lacks the interaction between the planning steps [8]. Several approaches try to overcome the difficulties resulting from this planning and control scheme [8][10]. They deal with local rules instead of global planning, event-oriented planning instead of planning periods or individual PPC modules in the context of decentralisation of control [10]. But they extend the possibilities of traditional PPC systems towards faster adaptation to changes in the environment of a production system.