Micro-chaos in digital control
Summary In this paper we analyze a model for the effect of digital control on one-dimensional, linearly unstable dynamical systems. Our goal is to explain the existence of small, irregular oscillations that are frequently observed near the desired equilibrium. We derive a one-dimensional map that ca...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Haller, G. [verfasserIn] |
|---|
| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
1996 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer-Verlag New York Inc. 1996 |
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| Übergeordnetes Werk: |
Enthalten in: Journal of nonlinear science - Springer-Verlag, 1991, 6(1996), 5 vom: Sept., Seite 415-448 |
|---|---|
| Übergeordnetes Werk: |
volume:6 ; year:1996 ; number:5 ; month:09 ; pages:415-448 |
| Links: |
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| DOI / URN: |
10.1007/BF02440161 |
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| Katalog-ID: |
OLC2057903729 |
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| 520 | |a Summary In this paper we analyze a model for the effect of digital control on one-dimensional, linearly unstable dynamical systems. Our goal is to explain the existence of small, irregular oscillations that are frequently observed near the desired equilibrium. We derive a one-dimensional map that captures exactly the dynamics of the continuous system. Using thismicro-chaos map, we prove the existence of a hyperbolic strange attractor for a large set of parameter values. We also construct an “instability chart” on the parameter plane to describe how the size and structure of the chaotic attractor changes as the parameters are varied. The applications of our results include the stick-and-slip motion of machine tools and other mechanical problems with locally negative dissipation. | ||
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10.1007/BF02440161 doi (DE-627)OLC2057903729 (DE-He213)BF02440161-p DE-627 ger DE-627 rakwb eng 530 510 VZ 11 ssgn Haller, G. verfasserin aut Micro-chaos in digital control 1996 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag New York Inc. 1996 Summary In this paper we analyze a model for the effect of digital control on one-dimensional, linearly unstable dynamical systems. Our goal is to explain the existence of small, irregular oscillations that are frequently observed near the desired equilibrium. We derive a one-dimensional map that captures exactly the dynamics of the continuous system. Using thismicro-chaos map, we prove the existence of a hyperbolic strange attractor for a large set of parameter values. We also construct an “instability chart” on the parameter plane to describe how the size and structure of the chaotic attractor changes as the parameters are varied. The applications of our results include the stick-and-slip motion of machine tools and other mechanical problems with locally negative dissipation. Chaotic Attractor Topological Entropy Parameter Plane Parameter Domain Digital Control Stépán, G. aut Enthalten in Journal of nonlinear science Springer-Verlag, 1991 6(1996), 5 vom: Sept., Seite 415-448 (DE-627)130975990 (DE-600)1072984-7 (DE-576)025193295 0938-8974 nnns volume:6 year:1996 number:5 month:09 pages:415-448 https://doi.org/10.1007/BF02440161 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-CHE SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_40 GBV_ILN_70 GBV_ILN_2006 GBV_ILN_2010 GBV_ILN_2018 GBV_ILN_2057 GBV_ILN_2088 GBV_ILN_2409 GBV_ILN_4012 GBV_ILN_4036 GBV_ILN_4277 GBV_ILN_4310 GBV_ILN_4323 AR 6 1996 5 09 415-448 |
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10.1007/BF02440161 doi (DE-627)OLC2057903729 (DE-He213)BF02440161-p DE-627 ger DE-627 rakwb eng 530 510 VZ 11 ssgn Haller, G. verfasserin aut Micro-chaos in digital control 1996 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag New York Inc. 1996 Summary In this paper we analyze a model for the effect of digital control on one-dimensional, linearly unstable dynamical systems. Our goal is to explain the existence of small, irregular oscillations that are frequently observed near the desired equilibrium. We derive a one-dimensional map that captures exactly the dynamics of the continuous system. Using thismicro-chaos map, we prove the existence of a hyperbolic strange attractor for a large set of parameter values. We also construct an “instability chart” on the parameter plane to describe how the size and structure of the chaotic attractor changes as the parameters are varied. The applications of our results include the stick-and-slip motion of machine tools and other mechanical problems with locally negative dissipation. Chaotic Attractor Topological Entropy Parameter Plane Parameter Domain Digital Control Stépán, G. aut Enthalten in Journal of nonlinear science Springer-Verlag, 1991 6(1996), 5 vom: Sept., Seite 415-448 (DE-627)130975990 (DE-600)1072984-7 (DE-576)025193295 0938-8974 nnns volume:6 year:1996 number:5 month:09 pages:415-448 https://doi.org/10.1007/BF02440161 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-CHE SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_40 GBV_ILN_70 GBV_ILN_2006 GBV_ILN_2010 GBV_ILN_2018 GBV_ILN_2057 GBV_ILN_2088 GBV_ILN_2409 GBV_ILN_4012 GBV_ILN_4036 GBV_ILN_4277 GBV_ILN_4310 GBV_ILN_4323 AR 6 1996 5 09 415-448 |
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10.1007/BF02440161 doi (DE-627)OLC2057903729 (DE-He213)BF02440161-p DE-627 ger DE-627 rakwb eng 530 510 VZ 11 ssgn Haller, G. verfasserin aut Micro-chaos in digital control 1996 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag New York Inc. 1996 Summary In this paper we analyze a model for the effect of digital control on one-dimensional, linearly unstable dynamical systems. Our goal is to explain the existence of small, irregular oscillations that are frequently observed near the desired equilibrium. We derive a one-dimensional map that captures exactly the dynamics of the continuous system. Using thismicro-chaos map, we prove the existence of a hyperbolic strange attractor for a large set of parameter values. We also construct an “instability chart” on the parameter plane to describe how the size and structure of the chaotic attractor changes as the parameters are varied. The applications of our results include the stick-and-slip motion of machine tools and other mechanical problems with locally negative dissipation. Chaotic Attractor Topological Entropy Parameter Plane Parameter Domain Digital Control Stépán, G. aut Enthalten in Journal of nonlinear science Springer-Verlag, 1991 6(1996), 5 vom: Sept., Seite 415-448 (DE-627)130975990 (DE-600)1072984-7 (DE-576)025193295 0938-8974 nnns volume:6 year:1996 number:5 month:09 pages:415-448 https://doi.org/10.1007/BF02440161 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-CHE SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_40 GBV_ILN_70 GBV_ILN_2006 GBV_ILN_2010 GBV_ILN_2018 GBV_ILN_2057 GBV_ILN_2088 GBV_ILN_2409 GBV_ILN_4012 GBV_ILN_4036 GBV_ILN_4277 GBV_ILN_4310 GBV_ILN_4323 AR 6 1996 5 09 415-448 |
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10.1007/BF02440161 doi (DE-627)OLC2057903729 (DE-He213)BF02440161-p DE-627 ger DE-627 rakwb eng 530 510 VZ 11 ssgn Haller, G. verfasserin aut Micro-chaos in digital control 1996 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag New York Inc. 1996 Summary In this paper we analyze a model for the effect of digital control on one-dimensional, linearly unstable dynamical systems. Our goal is to explain the existence of small, irregular oscillations that are frequently observed near the desired equilibrium. We derive a one-dimensional map that captures exactly the dynamics of the continuous system. Using thismicro-chaos map, we prove the existence of a hyperbolic strange attractor for a large set of parameter values. We also construct an “instability chart” on the parameter plane to describe how the size and structure of the chaotic attractor changes as the parameters are varied. The applications of our results include the stick-and-slip motion of machine tools and other mechanical problems with locally negative dissipation. Chaotic Attractor Topological Entropy Parameter Plane Parameter Domain Digital Control Stépán, G. aut Enthalten in Journal of nonlinear science Springer-Verlag, 1991 6(1996), 5 vom: Sept., Seite 415-448 (DE-627)130975990 (DE-600)1072984-7 (DE-576)025193295 0938-8974 nnns volume:6 year:1996 number:5 month:09 pages:415-448 https://doi.org/10.1007/BF02440161 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-CHE SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_40 GBV_ILN_70 GBV_ILN_2006 GBV_ILN_2010 GBV_ILN_2018 GBV_ILN_2057 GBV_ILN_2088 GBV_ILN_2409 GBV_ILN_4012 GBV_ILN_4036 GBV_ILN_4277 GBV_ILN_4310 GBV_ILN_4323 AR 6 1996 5 09 415-448 |
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Summary In this paper we analyze a model for the effect of digital control on one-dimensional, linearly unstable dynamical systems. Our goal is to explain the existence of small, irregular oscillations that are frequently observed near the desired equilibrium. We derive a one-dimensional map that captures exactly the dynamics of the continuous system. Using thismicro-chaos map, we prove the existence of a hyperbolic strange attractor for a large set of parameter values. We also construct an “instability chart” on the parameter plane to describe how the size and structure of the chaotic attractor changes as the parameters are varied. The applications of our results include the stick-and-slip motion of machine tools and other mechanical problems with locally negative dissipation. © Springer-Verlag New York Inc. 1996 |
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Summary In this paper we analyze a model for the effect of digital control on one-dimensional, linearly unstable dynamical systems. Our goal is to explain the existence of small, irregular oscillations that are frequently observed near the desired equilibrium. We derive a one-dimensional map that captures exactly the dynamics of the continuous system. Using thismicro-chaos map, we prove the existence of a hyperbolic strange attractor for a large set of parameter values. We also construct an “instability chart” on the parameter plane to describe how the size and structure of the chaotic attractor changes as the parameters are varied. The applications of our results include the stick-and-slip motion of machine tools and other mechanical problems with locally negative dissipation. © Springer-Verlag New York Inc. 1996 |
| abstract_unstemmed |
Summary In this paper we analyze a model for the effect of digital control on one-dimensional, linearly unstable dynamical systems. Our goal is to explain the existence of small, irregular oscillations that are frequently observed near the desired equilibrium. We derive a one-dimensional map that captures exactly the dynamics of the continuous system. Using thismicro-chaos map, we prove the existence of a hyperbolic strange attractor for a large set of parameter values. We also construct an “instability chart” on the parameter plane to describe how the size and structure of the chaotic attractor changes as the parameters are varied. The applications of our results include the stick-and-slip motion of machine tools and other mechanical problems with locally negative dissipation. © Springer-Verlag New York Inc. 1996 |
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Micro-chaos in digital control |
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