Block diagram grammar and signal flow graph grammar with their applications

Abstract

A block diagram grammar and a signal flow graph grammar were previously defined as a theoretical and practical foundation for the computerized analysis and design of control systems and filters by using block diagrams and/or signal flow graphs. They are formalized on the basis of a context-sensitive graph grammar. In this research, a knowledge representation method in order to generate specific system structures such as series connections, feedback connections, and (non)recursive filters is formalized on the basis of the block diagram grammar and the signal flow graph grammar. For this purpose, we discuss the composition of the production copies of the context-sensitive graph grammar, its associativity property, and the confluence property. Then we define the composite production copies that serve as templates for generating those structures. We also describe our block diagram processing system that supports block diagram editing, parsing, system structure generation, and analysis based on the BDG. This work is the first attempt to formally represent analysis and design knowledge of control systems and filters on the basis of these grammars.