Bode's Sensitivity Integral Constraints: The Waterbed Effect Revisited
Bode's sensitivity integral constraints define a fundamental rule about the limitations of feedback and is referred to as the waterbed effect. We take a fresh look at this problem and reveal an elegant and fundamental result that has been seemingly masked by previous derivations. The main resul...
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext bestellen |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | |
|---|---|
| container_issue | |
| container_start_page | |
| container_title | |
| container_volume | |
| creator | Emami-Naeini, Abbas de Roover, Dick |
| description | Bode's sensitivity integral constraints define a fundamental rule about the
limitations of feedback and is referred to as the waterbed effect. We take a
fresh look at this problem and reveal an elegant and fundamental result that
has been seemingly masked by previous derivations. The main result is that the
sensitivity integral constraint is crucially related to the difference in speed
of the closed-loop system as compared to that of the open-loop system. This
makes much intuitive sense. Similar results are also derived for the
complementary sensitivity function. In that case the integral constraint is
related to the sum of the differences of the reciprocal of the transmission
zeros and the closed-loop poles of the system. Hence all performance
limitations are inherently related to the locations of the open-loop and
closed-loop poles, and the transmission zeros. A number of illustrative
examples are presented. |
| doi_str_mv | 10.48550/arxiv.1902.11302 |
| format | Article |
| fullrecord | <record><control><sourceid>arxiv_GOX</sourceid><recordid>TN_cdi_arxiv_primary_1902_11302</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>1902_11302</sourcerecordid><originalsourceid>FETCH-LOGICAL-a672-84252b923463cbe9eb55db4672559e0db887703cc31f4186b561b52b03fd8db73</originalsourceid><addsrcrecordid>eNotj71OwzAURr10QC0PwIQ3pgT_Jg4bRC1UqlSpRGKMfONrsFRSZFsRfXtCYfqGT-dIh5AbzkpltGb3Nn6HqeQNEyXnkokrsnk6ObxL9BXHFHKYQj7T7ZjxPdojbU9jytGGMacH2n0gfbMZI6Cja-9xyPSAU5gxdCuy8PaY8Pp_l6TbrLv2pdjtn7ft466wVS0Ko4QW0AipKjkANghaO1DzpXWDzIExdc3kMEjuFTcV6IrDTDDpnXFQyyW5_dNeQvqvGD5tPPe_Qf0lSP4AoP1FHQ</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Bode's Sensitivity Integral Constraints: The Waterbed Effect Revisited</title><source>arXiv.org</source><creator>Emami-Naeini, Abbas ; de Roover, Dick</creator><creatorcontrib>Emami-Naeini, Abbas ; de Roover, Dick</creatorcontrib><description>Bode's sensitivity integral constraints define a fundamental rule about the
limitations of feedback and is referred to as the waterbed effect. We take a
fresh look at this problem and reveal an elegant and fundamental result that
has been seemingly masked by previous derivations. The main result is that the
sensitivity integral constraint is crucially related to the difference in speed
of the closed-loop system as compared to that of the open-loop system. This
makes much intuitive sense. Similar results are also derived for the
complementary sensitivity function. In that case the integral constraint is
related to the sum of the differences of the reciprocal of the transmission
zeros and the closed-loop poles of the system. Hence all performance
limitations are inherently related to the locations of the open-loop and
closed-loop poles, and the transmission zeros. A number of illustrative
examples are presented.</description><identifier>DOI: 10.48550/arxiv.1902.11302</identifier><language>eng</language><subject>Computer Science - Systems and Control</subject><creationdate>2019-01</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,776,881</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/1902.11302$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.1902.11302$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Emami-Naeini, Abbas</creatorcontrib><creatorcontrib>de Roover, Dick</creatorcontrib><title>Bode's Sensitivity Integral Constraints: The Waterbed Effect Revisited</title><description>Bode's sensitivity integral constraints define a fundamental rule about the
limitations of feedback and is referred to as the waterbed effect. We take a
fresh look at this problem and reveal an elegant and fundamental result that
has been seemingly masked by previous derivations. The main result is that the
sensitivity integral constraint is crucially related to the difference in speed
of the closed-loop system as compared to that of the open-loop system. This
makes much intuitive sense. Similar results are also derived for the
complementary sensitivity function. In that case the integral constraint is
related to the sum of the differences of the reciprocal of the transmission
zeros and the closed-loop poles of the system. Hence all performance
limitations are inherently related to the locations of the open-loop and
closed-loop poles, and the transmission zeros. A number of illustrative
examples are presented.</description><subject>Computer Science - Systems and Control</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotj71OwzAURr10QC0PwIQ3pgT_Jg4bRC1UqlSpRGKMfONrsFRSZFsRfXtCYfqGT-dIh5AbzkpltGb3Nn6HqeQNEyXnkokrsnk6ObxL9BXHFHKYQj7T7ZjxPdojbU9jytGGMacH2n0gfbMZI6Cja-9xyPSAU5gxdCuy8PaY8Pp_l6TbrLv2pdjtn7ft466wVS0Ko4QW0AipKjkANghaO1DzpXWDzIExdc3kMEjuFTcV6IrDTDDpnXFQyyW5_dNeQvqvGD5tPPe_Qf0lSP4AoP1FHQ</recordid><startdate>20190109</startdate><enddate>20190109</enddate><creator>Emami-Naeini, Abbas</creator><creator>de Roover, Dick</creator><scope>AKY</scope><scope>GOX</scope></search><sort><creationdate>20190109</creationdate><title>Bode's Sensitivity Integral Constraints: The Waterbed Effect Revisited</title><author>Emami-Naeini, Abbas ; de Roover, Dick</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a672-84252b923463cbe9eb55db4672559e0db887703cc31f4186b561b52b03fd8db73</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2019</creationdate><topic>Computer Science - Systems and Control</topic><toplevel>online_resources</toplevel><creatorcontrib>Emami-Naeini, Abbas</creatorcontrib><creatorcontrib>de Roover, Dick</creatorcontrib><collection>arXiv Computer Science</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Emami-Naeini, Abbas</au><au>de Roover, Dick</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Bode's Sensitivity Integral Constraints: The Waterbed Effect Revisited</atitle><date>2019-01-09</date><risdate>2019</risdate><abstract>Bode's sensitivity integral constraints define a fundamental rule about the
limitations of feedback and is referred to as the waterbed effect. We take a
fresh look at this problem and reveal an elegant and fundamental result that
has been seemingly masked by previous derivations. The main result is that the
sensitivity integral constraint is crucially related to the difference in speed
of the closed-loop system as compared to that of the open-loop system. This
makes much intuitive sense. Similar results are also derived for the
complementary sensitivity function. In that case the integral constraint is
related to the sum of the differences of the reciprocal of the transmission
zeros and the closed-loop poles of the system. Hence all performance
limitations are inherently related to the locations of the open-loop and
closed-loop poles, and the transmission zeros. A number of illustrative
examples are presented.</abstract><doi>10.48550/arxiv.1902.11302</doi><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext_linktorsrc |
| identifier | DOI: 10.48550/arxiv.1902.11302 |
| ispartof | |
| issn | |
| language | eng |
| recordid | cdi_arxiv_primary_1902_11302 |
| source | arXiv.org |
| subjects | Computer Science - Systems and Control |
| title | Bode's Sensitivity Integral Constraints: The Waterbed Effect Revisited |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-27T16%3A24%3A23IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-arxiv_GOX&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Bode's%20Sensitivity%20Integral%20Constraints:%20The%20Waterbed%20Effect%20Revisited&rft.au=Emami-Naeini,%20Abbas&rft.date=2019-01-09&rft_id=info:doi/10.48550/arxiv.1902.11302&rft_dat=%3Carxiv_GOX%3E1902_11302%3C/arxiv_GOX%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_id=info:pmid/&rfr_iscdi=true |