Abstract
A new approach to constructing reliable discrete PLC-programs with timers-programming based on specification and verification-is proposed. Timers are modelled in a discrete way. For the specification of the program behavior we use the linear-time temporal logic LTL. Programming is carried out in the ST-language according to an LTL-specification. A new approach to programming PLC is shown by an example. The proposed programming approach provides an ability of a correctness analysis of PLC-programs using the model checking method. The programming requires fulfillment of the following two conditions: (1) the value of each variable should be changed not more than once per one full PLC-program implementation (per one full working cycle of PLC); (2) the value of each variable should only be changed in one place of a PLC-program. Under the proposed approach the change of the value of each program variable is described by a pair of LTL-formulas. The first LTL-formula describes situations that increase the value of the corresponding variable, the second LTL-formula specifies conditions leading to a decrease of the variable value. The LTL-formulas (used for specification of the corresponding variable behavior) are constructive in the sense that they construct the PLC-program, which satisfies temporal properties expressed by these formulas. Thus, the programming of PLC is reduced to the construction of LTL-specification of the behavior of each program variable.
Highlights
Применение программируемых логических контроллеров (ПЛК) в системах управления сложными производственными процессами предъявляет строгие требования корректности к программам ПЛК
The proposed programming approach provides an ability of a correctness analysis of PLC-programs using the model checking method
Under the proposed approach the change of the value of each program variable is described by a pair of LTL-formulas
Summary
Задача проверки модели (Model Checking) состоит в определении выполнимости для конечной модели программы, которая задается системой переходов (структурой Крипке), свойства, выраженного формулой темпоральной логики. Формула логики LTL описывает свойство одного пути структуры Крипке, выходящего из некоторого выделенного текущего состояния. Формально отношение выполнимости |= формулы φ логики LTL для некоторого пути π структуры Крипке S над P индуктивно определяется следующим образом:. Π |= φ ∧ ψ ⇐⇒ π |= φ и π |= ψ; π |= X φ ⇐⇒ π1 |= φ; π |= ψ U φ ⇐⇒ ∃j 0, что πj |= φ и при этом для всех i, 0 i < j, πi |= ψ. Структура Крипке удовлетворяет формуле (свойству) φ логики LTL, если φ выполняется для всех путей, выходящих из начального состояния s0
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