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Friction generated limit cycles

Henrik Olsson, Karl Johan Åström

Open publisher page 14 citations

Abstract

This paper presents techniques that admit an exact analysis of limit cycles caused by friction. Necessary conditions for limit cycle oscillations are given as well as conditions for local stability of the limit cycles. There are two types of limit cycles, one where motion sticks for a time interval and another where the velocity is zero only at single time instants. The results are applied to an example with a resonant servo. Comparisons with describing function analysis are also made.

About this research paper

What this paper is about

This paper presents techniques that admit an exact analysis of limit cycles caused by friction. Necessary conditions for limit cycle oscillations are given as well as conditions for local stability of the limit cycles. There are two types of limit cycles, one where motion sticks for a time interval and another where the velocity is zero only at single time instants. The results are applied to an example with a resonant servo. Comparisons with describing function analysis are also made.

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OpenAlex reports 14 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

This paper presents techniques that admit an exact analysis of limit cycles caused by friction. Necessary conditions for limit cycle oscillations are given as well as conditions for local stability of the limit cycles. There are two types of limit cycles, one where motion sticks for a time interval and another where the velocity is zero only at single time instants. The results are applied to an example with a resonant servo. Comparisons with describing function analysis are also made.

Key concepts: Limit (mathematics), Limit cycle, Describing function, Control theory (sociology), Interval (graph theory), Stability (learning theory), Zero (linguistics), Function (biology)

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