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).

This paper presents an algebraic method to synthesize control laws for logical system controllers. The starting point is a set of functional and dependable requirements expressed with algebraic relations or state models. We propose to synthesize control laws by solving a Boolean equation which represents all the requirements. The mathematical results that we have obtained allow to establish the exact form of the solutions if this equation has solutions. The first step of this method is the formalization of each requirement with Boolean relations between Boolean functions. Under this formulation, the requirements can be assembled and their coherence can be analyzed. This step consists in verifying if the Boolean equation, which represents all the requirements, has solutions. The third step is the synthesis of the control laws by solving this equation. At the end of this step, a parametric formulation of all the possible solutions is given. The fourth step of the method is the choice of a particular solution. This choice is made by the designer from heuristics. This method is illustrated with an example.