# A Program Model of Fuzzy Interpreted Petri Net to Control Discrete Event Systems
## 1 Introduction  
Although a finite state machine and a finitely recursive process can be used to model discrete event systems (DES) [1; 2], researchers began to use Petri nets (PNs). The reasons for this are the graphical representation of PNs, the possibility of parallel process control, the formal description of PNs, increasing complexity of DES, and greater expectations for the analysis and the modelling of DES [3; 4; 5]. This led to the creation of many classes of PNs [6]. Additionally, many software programs [7] that enable the analysis of various net properties were created. These tools can be applied to simulate the operations of systems based on PNs and to find their properties automatically. They usually permit the modelling of specific classes of nets. Research on the modelling, simulation, operation, and control of DES through the application of PNs can be divided into two trends. The first is related to the development of the formal methods that refer to general models. The second is also associated with the formal methods, but they refer to the specific programming languages. Amongst the papers that consider the first trend, some are related to supervisory control that can be based on structural reasoning [8], applied with the use of the hybrid net [9], and used for a system with uncontrollable and unobservable transitions [10]. Others are associated with the validation of DES, which includes: diagnosis of an asynchronous system [11]; detecting and isolating fault events [12]; fault online detection [13]; fault diagnosis with unobservable transition [14]; model checking based on user specification [15]; formal verification with the use of structural reasoning and general unary hypothesis automaton (GUHA) methods [16]. Other research concerns the application of PNs to specific problems, e.g., to model flexible manufacturing systems (FMS) [17; 18; 19; 20; 21; 22] or to modelan emergency vehicle preemption system [23]. Different models and problems related to DES can be also found in [4; 5; 6; 24; 25; 26]. The second trend refers mostly to programmable logic controllers (PLCs). For more than two decades, because of their many undeniable advantages, PLCs have become good platforms for the implementation of DES based on PNs [27]. One of the first solutions was Grafcet [28], which is currently available as the international standard IEC 60848:2013 [29]. Next, the Sequential Function Chart (SFC) was created based on Grafcet in IEC 1131-3:1992 (currently IEC 61131:2013 [30]). Many software tools of different manufacturers enable the use of Grafcet and SFC. Both nets allow the application of transitions, to which some two-state conditions can be assigned, which are usually linked to the binary sensors or the outputs of timers. Some areas of application and ways to use Grafcet and SFC are also presented in [6; 31; 32; 33]. For industrial approaches, Ladder Diagram (LD) language is more often applied than the other languages supported by the IEC 61131-3. This tendency can also be seen in methods that combine PLC programming with PNs [34; 35; 36; 37; 38; 39; 40; 41; 42; 43]. However, languages other than LD are also used. In [34], the conversion of automation PN into LD using the token passing logic methodology is described. Signal interpreted PN (SIPN), which can be implemented in LD or Instruction List (IL), is shown in [35; 36; 37]. For IL, the PLC program can be generated automatically using a computer tool for the graphical modelling of SIPN. In [38], the method to generate LD code based on control Petri net (CPN), and the specification for the creation of DES through the application of this net is presented. A summary of some solutions combining LD with PNs is presented in [39]. PNs can also be used to validate programs in LD [40] after some conversions from the LD metamodel to time Petri net. In turn, other methods that link PNs to function block diagram (FBD), IL, and LD are proposed in [41; 42; 43].