Deadlocked Prevention Method for Flexible Manufacturing Systems Using the Theory of Regions and Reduction Technology

The theory of regions has been recognized as the powerful method of deadlock prevention policy for obtaining maximally permissive controllers. All legal and live maximal behavior of Petri net models can be preserved by using marking/transition-separation instances or event-state-separation-problem methods. However, they encountered great difficulties in solving all sets of inequalities that is an extremely time consuming problem. Additionally, the number of linear programming problems of legal markings is also exponential with net size when a plant net grows exponentially. This work proposes a novel methodology to reduce the above contributions. In this paper, the reachability condition equations in the theory of region can be reduced under the reduction approach. The problem of the issue can then be reduced. Moreover, a crucial marking/transition-separation instances is developed in our deadlock prevention policy that allows designers to employ few marking/transition-separation instances to deal with deadlocks. The advantage of the proposed policy is that a maximally permissive controller can be obtained with drastically reduced computation.