Nonlinear models for control of manufacturing systems

Current literature on modeling and control of manufacturing systems can roughly be divided into three groups: flow/fluid models, queueing theory, and discrete event models. Most fluid models describe linear time-invariant controllable systems without any dynamics. These models mainly focus on throughput and are not concerned with cycle time. Queuing theory deals with relationships between throughput and cycle time, but is mainly concerned with steady-state analysis. In addition, queueing models are not suitable for control theory. Discrete event models suffer from ``state-explosion''. Simple models of manufacturing systems can be studied and analyzed, but for larger problems the dimension of the state grows exponentially. In addition, most control problems studied are supervisory control problems: the avoidance of undesired states. An important class of interesting manufacturing control problems asks for proper balancing of both throughput and cycle time for a large nonlinear dynamical system that never is in steady state. None of the mentioned models is able to deal with these kind of control problems. In this paper, models are presented with are suitable for addressing this important class of interesting manufacturing control problems.