Abstract
A typical gas transmission system consists of multiple components, which are controlled to keep the system safe. A controller designed based on simple “If–Then Rules” cannot be guaranteed to be controllable or non-blocking, unless by formal verification. Formal verification is a difficult procedure, specifically in a gas transmission system. In this paper, a systematic method is proposed to construct the modular discrete-event model and to synthesize modular supervisors in a gas transmission system, in order to maintain the safety in the system. Two supervisors are synthesized in this paper: (1) the surge-avoidance supervisor, (2) the allowable discharge pressure supervisor. Both of them are synthesized for each compressor station through one trunk line. The constructed modular supervisors are non-conflicting.
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Appendix
Appendix
In this appendix, a quick review of TCT commands is presented [41].
DES3 = supcon(DES1, DES2).
for a controlled generator DES1, forms a trim recognizer for the supremal controllable sublanguage of the marked (“legal”) language generated by DES2 to create DES3. This structure provides a proper supervisor for DES1.
DAT3 = condat(DES1, DES2) returns control data DAT3 for the supervisor DES2 of the controlled system DES1. If DES2 represents a controllable language (with respect to DES1), as when DES2 has been previously computed with supcon, then condat will display the events that are disabled at each state of DES2. In general, condat can be used to test whether a given language DES2 is controllable: just check that the disabled events tabled by condat are themselves controllable (have odd-numbered labels).
DES3 = supreduce(DES1, DES2, DAT2) is a reduced supervisor for plant DES1 which is control-equivalent to DES2, where DES2 and control data DAT2 were previously computed using supcon and condat. Also returned is an estimated lower bound slb for the state size of a strictly state-minimal reduced supervisor. DES3 is strictly minimal if its reported state size happens to equal the slb.
DES2 = project(DES1, NULL/IMAGE EVENTS) is a generator of the projected closed and marked languages of DES1, under the natural projection specified by the listed Null or Image events.
True/False = isomorph(DES1, DES2) tests whether DES1 and DES2 are identical up to renumbering of states; if so, their state correspondence is displayed.
Screen Display = show(DES).
DES2 = Allevents(DES1/DAT1/[EVENT_LIST]) is a marked one-state DES self-looped with all the events of DES1, or else the events listed in Condat file DAT1, or else the events entered directly by the user. DES2 is called the “allevents representation” of the associated event list. It can be used as specification for the supervisory control of DES1 with respect to the sole criterion of non-blocking.
SE displays an existing DES, SA a DAT (condat) table, and SX a TXT (text) file. Tables can be browsed with page keys. The file MAKEIT.TXT keeps a record of user files as they are generated.
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Saeidi, V., Afzalian, A.A. & Gharavian, D. Discrete-Event Modeling and Supervisory Control Synthesis to Maintain the Safety in a Gas Transmission System. Arab J Sci Eng 48, 7077–7092 (2023). https://doi.org/10.1007/s13369-022-07361-9
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DOI: https://doi.org/10.1007/s13369-022-07361-9