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Root locus practical sketching rules for fractional-order systems. (English) Zbl 1293.93368

Summary: For integer-order systems, there are well-known practical rules for Root Locus (RL) sketching. Nevertheless, these rules cannot be directly applied to Fractional-Order (FO) systems. Besides, the existing literature on this topic is scarce and exclusively focused on commensurate systems, usually expressed as the ratio of two noninteger polynomials. The practical rules derived for those do not apply to other symbolic expressions, namely, to transfer functions expressed as the ratio of FO zeros and poles. However, this is an important case as it is an extension of the classical integer-order problem usually addressed by control engineers. Extending the RL practical sketching rules to such FO systems will contribute to decrease the lack of intuition about the corresponding system dynamics. This paper generalizes several RL practical sketching rules to transfer functions specified as the ratio of FO zeros and poles. The subject is presented in a didactic perspective, being the rules applied to several examples.

MSC:

93B55 Pole and zero placement problems
93C15 Control/observation systems governed by ordinary differential equations

Software:

sysdfod; DFOC; CRONE
PDFBibTeX XMLCite
Full Text: DOI

References:

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