Analysis of sliding modes in the frequency domain

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A frequency-domain approach to the analysis of real and ideal sliding modes (SM) in single input single output (SISO) systems with linear plants is proposed. The real SM is analysed as a superposition of fast oscillations and slow motions in a relay system. The approach is based on the notion of the locus of a perturbed relay system (LPRS). The proposed LPRS is defined as a characteristic of the response of a linear part to an unequally spaced pulse control of variable frequency in a closed-loop. Formulas for computing the LPRS are derived. It is demonstrated that beside the well know chattering phenomenon, real SM also exhibits a non-ideal disturbance rejection, which can be quantitatively assessed with the use of the proposed approach. An example of the LPRS analysis of a SM system is given.

Original languageBritish English
Pages (from-to)969-981
Number of pages13
JournalInternational Journal of Control
Issue number13
StatePublished - 10 Sep 2005


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