Nonlinear dynamics in distributed arrival time control of heterarchical manufacturing systems

Heterarchical control architectures with fully distributed control have been developed in order to improve responsiveness and effectiveness of manufacturing shop-floor control systems. The dynamics of these highly distributed systems have been difficult to predict particularly when control is based on heuristics. In this paper a dynamical model is developed for a single machine processing an arbitrary number of parts. The structure of the system, which requires queuing of parts when they arrive at a machine, leads to nonlinearities such as dead-zone and discontinuities. A continuous arrival time controller of the integrating type is used that results in a system that can be modeled using nonlinear differential equations that can be solved using a method due to Filippov (1960, 1988). This enables prediction of trajectories of part arrival times and derivation of closed form expressions for steady-state values. The analytical model for the dynamics is validated and the dynamic response of the system is illustrated using numerical simulation