Open AccessA Gallery of Root Locus of Fractional Systems
Author(s) -
J. A. Tenreiro Machado
Publication year - 2013
Publication title -
volume 4: 18th design for manufacturing and the life cycle conference; 2013 asme/ieee international conference on mechatronic and embedded systems and applications
Language(s) - English
Resource type - Conference proceedings
DOI - 10.1115/detc2013-12470
Subject(s) - tacking , root locus , fractional order system , mathematics , stability (learning theory) , fractional calculus , economic shortage , computer science , integer (computer science) , transfer function , mathematical optimization , control system , engineering , machine learning , mechanical engineering , electrical engineering , linguistics , philosophy , government (linguistics) , programming language
The root locus (RL) is a classical tool for the stability analysis of integer order linear systems, but its application in the fractional counterpart poses some difficulties. Therefore, researchers have mainly preferred to adopt frequency based methods. Nevertheless, recently the RL was considered for the stability analysis of fractional systems. One first method is by tacking advantage of commensurable expressions that occur when truncating fractional orders up to a finite precision. The second method consists of searching the complex plane for solutions of the characteristic equation using a numerical procedure. The resulting charts are insightful about the characteristics of the closed-loop system that outperform the frequency response methods. Given the limited know how in this particular topic and the shortage of literature, this study explores several types of fractional-order transfer functions and presents the corresponding RL.© 2013 ASME
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