Modelling of fuzzy discrete event dynamic systems

Discrete event dynamic systems (DEDS), are systems, which change state over time, based on current state and state transition rules. Each state is separated from its neighbour by a step rather than a continuum of infinitesimal states. This continuum in DEDS needs a representation between 0 and 1. The application of fuzzy logic in defining and modelling the DEDS is suggested as a possible solution because the nature of DEDS may be asynchronous, distributed, parallel, non-deterministic and/or stochastic. This results in the generalisation of crisp finite automata into fuzzy automata for a DEDS. In this paper, a DEDS in the form of hopper feed system is considered. The system is reformulated using state vectors and event transition matrices and is extended to fuzzy vectors and matrices. An algorithm is proposed for the final control action to be implemented using a programmable logic controller (PLC).