Algebraic synthesis of dependable logic controllers

Mathematical Problems in Engineering

2014

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Formal methods can strongly contribute to improve dependability of controllers during design, by providing means to avoid flaws due to designers' omissions or specifications misinterpretations. This paper presents a synthesis method dedicated to logic controllers. Its goal is to obtain the control laws from specifications given in natural language by symbolic computation. The formal framework that underlies this method is the Boolean algebra ofn-variable switching functions. In this algebra, thanks to relations and theorems presented in this paper, it is possible to formally express logical controllers specifications, to automatically detect inconsistencies in specifications, and to obtain automatically the set of solutions or to choose an optimal solution according to given optimization criteria. The application of this synthesis method to an example allows illustrating its main advantages.

Section: Overview Of Our Methodsmentioning

confidence: 99%

“…To prove Step (b), it is sufficient to substitute the expression for from (21) into (18) and to use (20) as follows:…”

Section: Theorem 11 (Solution Of a Single-unknown Equation) The Boolmentioning

confidence: 99%

Design of Logic Controllers Thanks to Symbolic Computation of Simultaneously Asserted Boolean Equations

Mathematical Problems in Engineering

2014

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“…This step is performed by solving the system of equations which represents the set of consistent requirements. The mathematical results we have obtained (Theorem 2 recalled in Section 4.2), allow to find a symbolic expression of the set of solutions under the form of a parametric expression (Hietter et al (2008b)). …”

Section: Overview Of Our Methodsmentioning

confidence: 99%

Algebraic synthesis of logical controllers despite inconsistencies in specifications

IFAC Proceedings Volumes

2012

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This paper deals with the problem of consistency of the requirements which are the starting point of controller synthesis methods for Discrete Event Systems (DES). In previous papers, an algebraic synthesis method for logical systems has been proposed. This method includes a theorem allowing the proof of consistency of the set of specifications. In this paper, we show that if inconsistencies are detected, the conditions of these inconsistencies can be given to the designer. It is therefore possible for the designer to propose priority rules between the involved requirements allowing the correction of incoherent specifications. Both the mathematical and the methodological aspects of this work are presented. In an illustrative purpose, the case study of a hydraulic press is developed.

“…In a previous paper [3], we used our approach to synthesize the whole control law of a sequential system. We showed that different formalisms (such as finite states machines, logical expressions, timing diagrams, .…”

Section: Introductionmentioning

confidence: 99%

“…The choice of a control law in this space can be done by using an optimization criterion. In [3] we showed how to choose the most dependable control law.…”

Section: Introductionmentioning

confidence: 99%

Algebraic synthesis of transition conditions of a state model

Hietter

2008 9th International Workshop on Discrete Event Systems

2008

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Abstract-The synthesis method presented in this paper has been developed to automatically design logic controllers. In this paper, we show how to use this approach in the specific case where a designer must derive a particular controller from a generic model. The instantiation of the model is completely achieved by an algebraic synthesis. To illustrate the approach, the example of a water supply system is used and the generic model of the controller is given under the form of a Sequential Function Chart (SFC).