Extended Place-Invariant Control in Automated Manufacturing Systems Using Petri Nets

In supervisory control of Petri nets (PNs), the place-invariant (
$P$
-invariant) control principle is the most typical and principal method to deal with the siphon control problem. Although it has a relatively narrow application, this principle is widely acknowledged due to its simplicity and efficiency. In this article, we first propose the extended
$P$
-invariant control principle in order to extend the application of
$P$
-invariants and provide a general methodology for the control of siphons. Second, three types of
$P$
-invariants, from the special to the general, are developed to implicitly or explicitly invariant control the siphons. In the most general case, the virtual
$P$
-invariants are constructed in the PNs. Third, the extended principle is further applied to the supervisor simplification. In the paradigm of the extended principle, it presents the redundancy from a structural perspective in contrast to several typical methods, and shows the significant importance of structural analysis in PNs, especially the important role of
$P$
-invariants. As a consequence, the extended
$P$
-invariant control principle can be considered as the fundamental principle of siphon control as well as its supervisor simplification.