Analysis and design of classes of two-time-scale multiport models with derivative causality

Eliminating derivative causality by inserting parasitic elements produces modified systems that are two-time-scale. The computational accuracy and simulation efficiency of the solution of the modified systems are strongly influenced by the choice of the inserted parasitic element parameters. Computational accuracy can be traded off with simulation efficiency. Some important aspects of the nature and behavior of the modified two-time-scale systems have not been investigated. In addition, there is no known method that shows how to choose the values of the parasitic parameters to achieve certain desired accuracy at a highly efficient computational price. Tools based on the singular perturbation method, on physical systems modeling, and on numerical simulation are used in this research to analyze and design some classes of these two-time-scale modified systems.;Analysis revealed some important aspects of the nature and behavior of the systems under investigation. Understanding those aspects is extremely important for the general understanding of these systems. A choice for the perturbation parameter epsilon that helps to reveal the time-scale properties of the modified system is given; a suggested preferred standard singular perturbation form (PSSPF) is shown; a systematic method to transform the modified systems to the PSSPF is derived; models of the fast sub-systems are obtained and validated; and proof of stability of such a modified system is shown.;The results of the analysis efforts are used to set procedures to design the fast sub-systems. The design objective is to achieve certain desired accuracy at highly efficient computational efforts. The validated models of the fast subsystems are used in the design procedures. Examples that demonstrate the usefulness of these procedures are presented. Analysis and design work shown here include classes from both linear and nonlinear systems.