The Power-Oriented Graphs Modeling Technique: From the Fundamental Principles to the Systematic, Step-By-Step Modeling of Complex Physical Systems

Modeling physical systems is an essential skill for engineers, since it enables to achieve a deep understanding of their dynamic behavior and, consequently, to develop effective control strategies. The first part of this paper provides a recap of the fundamental principles and properties of the Power-Oriented Graphs (POG) modeling technique, by also referring to a case study to consolidate them. The POG technique is then compared with the other two main graphical modeling techniques available in the literature, namely Bond Graph (BG) and Energetic Macroscopic Representation (EMR). The second part of this paper introduces the new Fast Modeling POG (FMPOG) procedure. The FMPOG, which operates in the POG framework, is a methodical step-by-step procedure that enables the readers to quickly derive the power-oriented graphical model of physical systems starting from their schematics. From the power-oriented graphical model, the state-space model can then be directly determined. To ensure the FMPOG procedure is easily usable by the entire community, we apply it to three examples in different energetic domains in this paper, guiding the reader step-by-step through the derivation of the physical systems models. A freely available Matlab/Simulink program is provided in a repository, allowing the users to automatically apply the FMPOG procedure to various classes of physical systems. This program allows to convert the physical systems schematics into the corresponding POG block schemes and, ultimately, into the state-space mathematical models.