Less conservative conditions for robust LQR-state-derivative controller design: an LMI approach
Autor(a) principal: | |
---|---|
Data de Publicação: | 2021 |
Outros Autores: | , , , , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://dx.doi.org/10.1080/00207721.2021.1891325 http://hdl.handle.net/11449/210087 |
Resumo: | This study proposes less conservative conditions for robust linear quadratic regulator controllers using state-derivative feedback (SDF). The algebraic Ricatti equation was formulated using the SDF, and its solution was obtained by linear matrix inequalities. SDF was chosen owing to the presence of accelerometers as sensors. Since accelerometers are the main sensors in mechanical systems, the proposed technique may be used to control/attenuate their vibrations/oscillations. Moreover, to formulate the less conservative conditions, some methods in the specialised literature were used, such as, for example, slack variables by Finler's Lemma. The paper also offers necessary and sufficient conditions for an arbitrary convex combination of square real matrices A(1), A(2), ... , A(3), to be a nonsingular matrix, and thus an invertible one: A(1) must be nonsingular and all the real eigenvalues of A(1)(-1)A(2), A(1)(-1)A(3), ... , A(1)(-1)A, must be positive. This result is important in the formulation of the proposed less conservative conditions since it was assumed that a given convex combination is nonsingular. A feasibility analysis demonstrates that the proposed conditions reduce the conservatism. Thereby, it is possible to stabilise a higher number of systems and to reduce the guaranteed cost. Furthermore, a practical implementation illustrated the application of the proposed conditions. |
id |
UNSP_66edb53b725501ed89a123548a1cbb92 |
---|---|
oai_identifier_str |
oai:repositorio.unesp.br:11449/210087 |
network_acronym_str |
UNSP |
network_name_str |
Repositório Institucional da UNESP |
repository_id_str |
2946 |
spelling |
Less conservative conditions for robust LQR-state-derivative controller design: an LMI approachLinear quadratic regulator (LQR)linear matrix inequalities (LMIs)state derivative feedback (SDF)robust controlFinsler's lemmaThis study proposes less conservative conditions for robust linear quadratic regulator controllers using state-derivative feedback (SDF). The algebraic Ricatti equation was formulated using the SDF, and its solution was obtained by linear matrix inequalities. SDF was chosen owing to the presence of accelerometers as sensors. Since accelerometers are the main sensors in mechanical systems, the proposed technique may be used to control/attenuate their vibrations/oscillations. Moreover, to formulate the less conservative conditions, some methods in the specialised literature were used, such as, for example, slack variables by Finler's Lemma. The paper also offers necessary and sufficient conditions for an arbitrary convex combination of square real matrices A(1), A(2), ... , A(3), to be a nonsingular matrix, and thus an invertible one: A(1) must be nonsingular and all the real eigenvalues of A(1)(-1)A(2), A(1)(-1)A(3), ... , A(1)(-1)A, must be positive. This result is important in the formulation of the proposed less conservative conditions since it was assumed that a given convex combination is nonsingular. A feasibility analysis demonstrates that the proposed conditions reduce the conservatism. Thereby, it is possible to stabilise a higher number of systems and to reduce the guaranteed cost. Furthermore, a practical implementation illustrated the application of the proposed conditions.Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Sao Paulo State Univ UNESP, Dept Elect Engn, Sch Engn, 1370,Jose Carlos Rossi Ave, BR-15385000 Ilha Solteira, BrazilFed Technol Univ Parana UTFPR, Acad Dept Elect, Cornelio Procopio, BrazilFed Technol Univ Parana UTFPR, Dept Elect Engn, Apucarana, BrazilSao Paulo State Univ UNESP, Dept Elect Engn, Sch Engn, 1370,Jose Carlos Rossi Ave, BR-15385000 Ilha Solteira, BrazilCAPES: 001Taylor & Francis LtdUniversidade Estadual Paulista (Unesp)Fed Technol Univ Parana UTFPRBeteto, Marco Antonio Leite [UNESP]Assuncao, Edvaldo [UNESP]Teixeira, Marcelo Carvalho Minhoto [UNESP]Silva, Emerson Ravazzi Pires daBuzachero, Luiz Francisco SanchesPonte Caun, Rodrigo da2021-06-25T12:39:19Z2021-06-25T12:39:19Z2021-03-02info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article20http://dx.doi.org/10.1080/00207721.2021.1891325International Journal Of Systems Science. Abingdon: Taylor & Francis Ltd, 20 p., 2021.0020-7721http://hdl.handle.net/11449/21008710.1080/00207721.2021.1891325WOS:000624730800001Web of Sciencereponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengInternational Journal Of Systems Scienceinfo:eu-repo/semantics/openAccess2021-10-23T20:11:10Zoai:repositorio.unesp.br:11449/210087Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462021-10-23T20:11:10Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
Less conservative conditions for robust LQR-state-derivative controller design: an LMI approach |
title |
Less conservative conditions for robust LQR-state-derivative controller design: an LMI approach |
spellingShingle |
Less conservative conditions for robust LQR-state-derivative controller design: an LMI approach Beteto, Marco Antonio Leite [UNESP] Linear quadratic regulator (LQR) linear matrix inequalities (LMIs) state derivative feedback (SDF) robust control Finsler's lemma |
title_short |
Less conservative conditions for robust LQR-state-derivative controller design: an LMI approach |
title_full |
Less conservative conditions for robust LQR-state-derivative controller design: an LMI approach |
title_fullStr |
Less conservative conditions for robust LQR-state-derivative controller design: an LMI approach |
title_full_unstemmed |
Less conservative conditions for robust LQR-state-derivative controller design: an LMI approach |
title_sort |
Less conservative conditions for robust LQR-state-derivative controller design: an LMI approach |
author |
Beteto, Marco Antonio Leite [UNESP] |
author_facet |
Beteto, Marco Antonio Leite [UNESP] Assuncao, Edvaldo [UNESP] Teixeira, Marcelo Carvalho Minhoto [UNESP] Silva, Emerson Ravazzi Pires da Buzachero, Luiz Francisco Sanches Ponte Caun, Rodrigo da |
author_role |
author |
author2 |
Assuncao, Edvaldo [UNESP] Teixeira, Marcelo Carvalho Minhoto [UNESP] Silva, Emerson Ravazzi Pires da Buzachero, Luiz Francisco Sanches Ponte Caun, Rodrigo da |
author2_role |
author author author author author |
dc.contributor.none.fl_str_mv |
Universidade Estadual Paulista (Unesp) Fed Technol Univ Parana UTFPR |
dc.contributor.author.fl_str_mv |
Beteto, Marco Antonio Leite [UNESP] Assuncao, Edvaldo [UNESP] Teixeira, Marcelo Carvalho Minhoto [UNESP] Silva, Emerson Ravazzi Pires da Buzachero, Luiz Francisco Sanches Ponte Caun, Rodrigo da |
dc.subject.por.fl_str_mv |
Linear quadratic regulator (LQR) linear matrix inequalities (LMIs) state derivative feedback (SDF) robust control Finsler's lemma |
topic |
Linear quadratic regulator (LQR) linear matrix inequalities (LMIs) state derivative feedback (SDF) robust control Finsler's lemma |
description |
This study proposes less conservative conditions for robust linear quadratic regulator controllers using state-derivative feedback (SDF). The algebraic Ricatti equation was formulated using the SDF, and its solution was obtained by linear matrix inequalities. SDF was chosen owing to the presence of accelerometers as sensors. Since accelerometers are the main sensors in mechanical systems, the proposed technique may be used to control/attenuate their vibrations/oscillations. Moreover, to formulate the less conservative conditions, some methods in the specialised literature were used, such as, for example, slack variables by Finler's Lemma. The paper also offers necessary and sufficient conditions for an arbitrary convex combination of square real matrices A(1), A(2), ... , A(3), to be a nonsingular matrix, and thus an invertible one: A(1) must be nonsingular and all the real eigenvalues of A(1)(-1)A(2), A(1)(-1)A(3), ... , A(1)(-1)A, must be positive. This result is important in the formulation of the proposed less conservative conditions since it was assumed that a given convex combination is nonsingular. A feasibility analysis demonstrates that the proposed conditions reduce the conservatism. Thereby, it is possible to stabilise a higher number of systems and to reduce the guaranteed cost. Furthermore, a practical implementation illustrated the application of the proposed conditions. |
publishDate |
2021 |
dc.date.none.fl_str_mv |
2021-06-25T12:39:19Z 2021-06-25T12:39:19Z 2021-03-02 |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://dx.doi.org/10.1080/00207721.2021.1891325 International Journal Of Systems Science. Abingdon: Taylor & Francis Ltd, 20 p., 2021. 0020-7721 http://hdl.handle.net/11449/210087 10.1080/00207721.2021.1891325 WOS:000624730800001 |
url |
http://dx.doi.org/10.1080/00207721.2021.1891325 http://hdl.handle.net/11449/210087 |
identifier_str_mv |
International Journal Of Systems Science. Abingdon: Taylor & Francis Ltd, 20 p., 2021. 0020-7721 10.1080/00207721.2021.1891325 WOS:000624730800001 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
International Journal Of Systems Science |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
20 |
dc.publisher.none.fl_str_mv |
Taylor & Francis Ltd |
publisher.none.fl_str_mv |
Taylor & Francis Ltd |
dc.source.none.fl_str_mv |
Web of Science reponame:Repositório Institucional da UNESP instname:Universidade Estadual Paulista (UNESP) instacron:UNESP |
instname_str |
Universidade Estadual Paulista (UNESP) |
instacron_str |
UNESP |
institution |
UNESP |
reponame_str |
Repositório Institucional da UNESP |
collection |
Repositório Institucional da UNESP |
repository.name.fl_str_mv |
Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP) |
repository.mail.fl_str_mv |
|
_version_ |
1799964957942480896 |