An effective control method is developed to prevent deadlocks from occurring in a class of nets, ES3PR, where deadlocks are related to unmarked siphons. Strict minimal siphons are divided into elementary and dependent ones. For each elementary siphon, a monitor is added to ensure it sufficiently marked without generating emptiable control-induced siphons. The controllability of a dependent siphon is ensured by changing the control depth variables of its related elementary siphons, which leads to a liveness-enforcing supervisor for a plant model. Furthermore, by checking the redundancy of the additional monitors, some control-redundant monitors can be removed, which leads to a more permissive and structurally simple net supervisor. However, the resultant supervisor usually becomes a generalized net after controlling the emptiable siphons in ES3PR nets, which is difficult to conduct further analysis. Therefore, it is necessary to transform a generalized net supervisor into an ordinary one without changing its behavior properties such as liveness.
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