Abstract
This paper highlights algebraic and mathematical properties in symmetry with Petri nets in order to control automated systems such as flexible workshops, which represent one of the most important examples in industry and for discrete event systems in general. This project deals with the problem of forbidden state transition by using a new application of the theory of regions for supervisory control. In the literature, most control synthesis methods suffer greatly from a cumbersome calculation burden of the Petri net supervisor given the complex exploration of the state graph. Our new methodology lightens the computational load of the Petri net supervisor by choosing specific regions on the reachability graph, on which the control is calculated offline using CPLEX. The determined controller is activated online if the process enters the chosen region, and deactivated otherwise. All our experiments were applied in a flexible workshop implemented in our research laboratory, which was used to engrave selected models on glass blocks of different colors.
Highlights
IntroductionDiscrete event systems (DESs) represent dynamic systems in which the reachability graph is discrete
Unlike continuous systems, discrete event systems (DESs) represent dynamic systems in which the reachability graph is discrete
We addressed the design of a PN controller for forbidden transitions/states presented as general mutual exclusion constraints (GMECs)
Summary
Discrete event systems (DESs) represent dynamic systems in which the reachability graph is discrete. The time use of these kinds of systems does not interest us, because only the occurrence of events matters in our case studies. The appearance of a single event causes the generation of a new state. If there is no occurrence of an event, the system remains unchanged (i.e., there is no state change). An event can correspond to the transmission of a message in a communication network, to the occurrence of a disturbance in a transport network, or to the arrival of a part in a production cell. PNs fit perfectly into the description of certain types of DESs. An automaton is nothing other than a marking graph generated from a Petri net
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