A Computer-Aided Design Toolkit For Continuous/Discrete Systems Based On Continued Fractions

Abstract

This paper presents new algorithms (1) to generate complete mathematical symbolic expressions of continued fraction expansion coefficients in the s-domain, (2) to determine their numeric values and (3) to perform continued fraction inversion in the s-domain. A software package in PASCAL and LISP to implement these algorithms is developed. In addition, a simple z-domain inversion algorithm used in the computer implementation of bilinear s-z transformation is also included in the software package. These algorithms play an important role in the analysis and synthesis of complex electrical networks and control systems. Especially, the s-domain expansion and inversion algorithms have potential applications in model simplification and system order reductions. the paper also shows that the package, as such, serves as a comprehensive computer-aided analysis and design (CAD) toolkit for both continuous and discrete systems. the software is interactive and runs on computers equipped with a PASCAL or LISP compiler. It is noted that the iterative implementation of these methods using the new continued fraction algorithms saves considerable memory space and processing time. Numerical examples and computer data are given to demonstrate the development of the new algorithms and the usefulness of the software toolkit in the CAD design of continuous and discrete systems.