Residues in Partial Fraction Decomposition Applied to Pole Sensitivity Analysis and Root Locus Construction

TL;DR

This paper introduces a novel interpretation of residues in partial fraction decomposition to analyze pole sensitivity and proposes an efficient root locus construction algorithm, improving computational performance in control systems analysis.

Contribution

It offers a new residue interpretation for pole sensitivity analysis and presents a faster root locus algorithm with equivalent results to existing methods.

Findings

The new algorithm reduces execution time compared to MATLAB's built-in function.

Residue interpretation enhances understanding of pole variations under parameter changes.

The method maintains accuracy while improving computational efficiency.

Abstract

The applications of the partial fraction decomposition in control and systems engineering are several. In this letter, we propose a new interpretation of residues in the partial fraction decomposition, which is employed for the following purposes: to address the pole sensitivity problem, namely to study the speed of variation of the system poles when the control parameter changes and when the system is subject to parameters variations, as well as to propose a new algorithm for the construction of the root locus. The new algorithm is proven to be more efficient in terms of execution time than the dedicated MATLAB function, while providing the same output results.