  Our objective is to design a controlled system with a simple method for
discrete event systems based on Petri nets. It is possible to construct the
Petri net model of a system and the specification separately. By synchronous
composition of both models, the desired functioning closed loop model is
deduced. Often uncontrollable transitions lead to forbidden states. The problem
of forbidden states is solved using linear constraints. A set of linear
constraints allows forbidding the reachability of these states. Generally, the
number of these so-called forbidden states and consequently the number of
constraints are large and lead to a great number of control places. A
systematic method to reduce the size and the number of constraints for safe
Petri Nets is given. By using a method based on the Petri nets invariants,
maximal permissive controllers are determined. The size of the controller is
close to the size of the specified model, and it can be implemented on a PLC in
a structural way.
