Abstract
Deadlock prevention policy is widely used to design the liveness-enforcing supervisors because of its advantage that deadlocks are considered and solved in design and planning stages for flexible manufacturing systems modeled with Petri nets. However, how to evaluate the implementation cost of these liveness-enforcing supervisors is not done in the existing literature. This article proposes an algorithm to evaluate the implementation cost performance of different liveness-enforcing supervisors designed by deadlock prevention policy. By designing a multiple objective linear programming problem associated with two parameters (denoted as f1 and f2) to characterize the corresponding implementation costs for the added control places and the related input and out transitions and control arcs, the proposed algorithm first obtains the variable regions of f1 and f2 And then a satisfactory level coefficient (denoted as [Formula: see text]) concentrating on the optimal compromise solutions of f1 and f2 (denoted as f1* and f2*) is solved by a linear programming problem. As a result, the implementation cost performance of the corresponding liveness-enforcing supervisor can be indicated conveniently on the basis of the values of [Formula: see text], f1*, and f2*. The practical potential of the proposed algorithm is demonstrated via a theoretical analysis and several widely used examples from the existing literature.
Highlights
On the basis of analyzing the evolving behavior characterization of a livenessenforcing supervisor,[1,2,39] its implementation cost performance (ICP) involves several factors associated with the added control place (CP) and the related input and output transitions, including their number and their initial markings for CPs, firing times (occurrences) for input and output transitions (jtinput, Vkj and jtoutput, Vkj), and the number and weight values for input and output control arcs
A novel algorithm to evaluate the implementation cost performance (ICP) of the liveness-enforcing supervisors constructed by siphon-based method (SBM) or reachability graph-based method (RGBM) is developed in section ‘‘An iterative ICP evaluating algorithm,’’ which indicates how about the ICP of a liveness-enforcing supervisor is in terms of the values of l, f1Ã, and f2Ã
The ICP comparison of different liveness-enforcing supervisors constructed by SBM or RGBM presented in Ezpeleta et al.[4,5,11,17,19], and[13] is carried out by Algorithm 1
Summary
On the basis of analyzing the evolving behavior characterization of a livenessenforcing supervisor,[1,2,39] its ICP involves several factors associated with the added CPs and the related input and output transitions, including their number and their initial markings for CPs, firing times (occurrences) for input and output transitions (jtinput, Vkj and jtoutput, Vkj), and the number and weight values for input and output control arcs.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
