Petri nets are a useful mathematical formalism for specification of manufacturing systems, supported by various analysis and verification methods. The progress made in automating control systems and the widespread use of Industry 4.0 pose a number of challenges to their application, starting from the education at university level and ending with modelling of real case studies. The paper aims to present and analyse the most relevant challenges and opportunities related to the use of Petri nets as a modelling technique of manufacturing systems. The review of the literature is primarily based on the years 2019–2020 to reflect the current state of the art. The newest approaches to deadlock prevention and recovering, but also other important analysis problems and difficulties in modelling real industrial processes are discussed. Trends for the future are also identified.

This paper shows a novel prototyping technique for concurrent control systems described by interpreted Petri nets. The technique is based on the decomposition of an interpreted Petri net into concurrent sequential automata. In general, minimum decomposition requires runtime that is exponential in the number of Petri net places. We show that in many cases, including the real-life ones, the minimum decomposition problem can be solved in polynomial time. The proposed method allows implementing a concurrent control system using minimal number of sequential components, which requires polynomial time and can be applied to most of the considered cases. The presented concept is illustrated by a real-life industrial example of a beverage production and distribution machine implemented in a field programmable gate array.

In this paper, we study selected aspects of determinism in the control part of a cyber-physical system (CPS) that is specified by a Petri net-based model. In particular, the control interpreted Petri nets (CIPNs) are applied, which are an extension of the ordinary Petri nets, supplemented by signals (related to sensors and actuators) that permit communication with the environment. The notions of weak and strong determinism in a system described by a CIPN are introduced in the paper. The proposed concepts are supported by formal definitions and theorems. Moreover, a novel modelling methodology for a deterministic system specified by a CIPN is proposed. The presented solutions are illustrated by a case study example of a real-life cyber-physical system. Finally, the results of experimental verification of the proposed determinism-based techniques are demonstrated and discussed.

In the article we present a new algorithm of Petri net decomposition into State Machine Components (SMCs). The idea bases on the application of the comparability graph theory. The comparability graphs are classified as a subclass of the perfect graphs and have unique properties. If a graph belongs to the comparability class, many problems (like graph coloring, maximal clique problem) can be solved in polynomial time. Therefore, if the sequentiality graph of a Petri net belongs to comparability class, the whole decomposition process turns to be polynomial. The preliminary experiments have demonstrated the effectiveness of the proposed idea. Over 90% of concurrency and sequentiality graphs of tested benchmarks belong to the comparability class. The efficiency is even higher if the Petri net class is reduced to the EFC (Extended Free-Choice).