Date of Award

Fall 2005

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Mechanical & Aerospace Engineering

Program/Concentration

Aerospace Engineering

Committee Director

Brett Newman

Committee Member

Chuh Mei

Committee Member

Thomas Alberts

Call Number for Print

Special Collections; LD4331.E535 P35 2005

Abstract

Evans root locus is a graphical method for analyzing or designing the stability and performance of a single channel closed-loop system. The method consists of plotting the locus of closed-loop characteristic equation roots in the complex plane as the loop gain parameter is varied over a wide range of values. Several methods for plotting the root locus graph exist and can be mainly classified into two types: analytical methods and numerical methods. The most common numerical method is based on polynomial factoring or root solving. A less common, alternative method for generating the root locus graph is based on numerical integration. The objective of this thesis is to investigate numerical integration as a method for constructing root locus diagrams and to compare it with existing methods. The differential relationship for closed-loop pole complex frequency as a function of loop gain is derived and reinterpreted as a complex number, first order state space system appropriate for numerical integration. A fourth order Runge-Kutta integration technique is considered. The loop gain domain space is decomposed into segments according to where the differential relationship exhibits discontinuities. This decomposition and integration is implemented with software and exercised with several academic and real-world test cases. Results indicate construction of root locus diagrams using a numerical integration procedure is a feasible and practical method that can be computationally implemented on a digital computer. The method provides computational efficiency and loci continuity comparable to existing methods. The method does require a set of algorithm tolerances that are problem dependent and must be tuned accordingly for successful application.

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DOI

10.25777/04xz-0a32

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