Closed-loop real-time cooperative decision-making dynamics in heterarchical manufacturing systems

Distribution of control in heterarchical manufacturing systems creates challenges in making and modeling cooperative decisions, such as when to produce discrete parts on multiple manufacturing machines. Furthermore, the dynamics of decision-making interactions between highly autonomous entities in these systems are poorly understood and can be undependable because of the absence of a master controller or optimizer. To investigate these phenomena, a system for distributed control of the arrival time of discrete parts in multiple-machine, multiple-processing-step manufacturing systems has been developed and is described in this paper. In the system, continuous control laws replace heuristics, and part arrival times are adjusted locally using feedback of expected completion times. The reported results confirm that the dynamics of the distributed systems are favorable, with arrival times converging exponentially to theoretically predictable values regardless of whether or not a set of arrival times exists that, given the machine resources available, results in parts being completed on their due dates. In the paper, closed-form solutions are obtained for non-linear, discontinuous differential equations that describe system behavior in different dynamic regions and explain arrival time convergence and intrinsic cooperation between discrete parts in their competition for production machinery. Furthermore, the systems are shown to be responsive to real-time disturbances that can be caused by rush orders, machine failures, and changes in part processing times. These results build confidence in design, implementation, and operation of distributed control systems for manufacturing, regardless of whether they are heuristic or control-law based, even though they appear to behave in a chaotic manner due to the interactions of highly autonomous entities.