Towards the use of bond graphs for manufacturing control: Design of controllers

The integration of control theory methods with operations management techniques enables to treat the dynamic facet of production and supply chain problems. In this paper, we revisit a bond graph/mathematical model devoted to depict the dynamics of multi-workstation production systems, and propose closed-loop simulation models with state feedback controllers, designed according to the pole placement and LQR methods. A real case was explored and simulations with the introduction of a disturbance in the production system were carried out. The results revealed that the model can provide prescriptive capacity adjustments and can help to define appropriate reference levels for the work in process in the system. It presents a disturbance-oriented behaviour that has advantages over pure push or pull systems commonly used in Production Planning and Control (PPC). In contrast to previous publications referring to the model, where the emphasis is set on the modelling process itself, the contribution of this paper concerns the design of the controllers, an aspect that is still left open for this kind of model. This design of the controllers has some peculiarities, since the state model of the production system does not fit the standard form. The presented approach is also relevant to the readership of the operations management (OM) and operational research (OR) fields for two reasons: (1) the use of control theory in OM provides good prescriptive solutions for dynamic production environments and the quality of these solutions is directly related to the design of the controllers; (2) the models generated by the integration of control theory and optimization, in some scenarios, present advantages over purely static optimization models.