An Improved Algorithm based on Shannon-Happ Formula for Calculating Transfer Function from Signal Flow Graph and Its Visualization

TL;DR

This paper introduces an enhanced algorithm based on the Shannon-Happ formula for calculating transfer functions from Signal Flow Graphs, incorporating symbolic variables, efficiency improvements, and visualization tools.

Contribution

It presents a novel, more efficient algorithm for transfer function calculation from SFGs that includes symbolic variables and visualization capabilities.

Findings

Improved algorithm reduces computation time for transfer functions.

Inclusion of symbolic variables allows modeling of nonlinear items.

Visualization tools enhance understanding of system performance.

Abstract

A new method based on Shannon-Happ formula to calculate transfer function from Signal Flow Graph (SFG) is presented. The algorithm provides an explicit approach to get the transfer function in a format with both numerical and symbolic expressions. The adoption of the symbolic variable in SFG, which could represent the nonlinear item or the independent sub-system, is achieved by variable separation approach. An investigation is given for the solutions of several special conditions of SFG. To improve the efficiency of the algorithm, a new technique combined with Johnson method for generating the combinations of the non-touching loops is developed. It uses the previous combinations in lower order to get the ones in higher order. There is an introduction about the visualization of SFG and the subroutines for system performance analysis in the software, AVANT.