A PD-type state-dependent Riccati equation with iterative learning augmentation for mechanical systems
This work proposes a novel proportional-derivative (PD)-type state-dependent Riccati equation (SDRE) approach with iterative learning control (ILC) augmentation. On the one hand, the PD-type control gains could adopt many useful available criteria and tools of conventional PD controllers. On the oth...
| Autores: | , , , |
|---|---|
| Tipo de recurso: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2022 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/136033 |
| Acceso en línea: | https://hdl.handle.net/11441/136033 https://doi.org/10.1109/JAS.2022.105533 |
| Access Level: | acceso abierto |
| Palabra clave: | Closed-loop PD-type SDDRE SDRE Iterative Learning Control (ILC) Symmetric |
| id |
ES_7b0a0fe38341f0022c2cd26fbc1ff9a8 |
|---|---|
| oai_identifier_str |
oai:idus.us.es:11441/136033 |
| network_acronym_str |
ES |
| network_name_str |
España |
| repository_id_str |
|
| spelling |
A PD-type state-dependent Riccati equation with iterative learning augmentation for mechanical systemsNekoo, Saeed RafeeAcosta Rodríguez, José ÁngelHeredia Benot, GuillermoOllero Baturone, AníbalClosed-loopPD-typeSDDRESDREIterative Learning Control (ILC)SymmetricThis work proposes a novel proportional-derivative (PD)-type state-dependent Riccati equation (SDRE) approach with iterative learning control (ILC) augmentation. On the one hand, the PD-type control gains could adopt many useful available criteria and tools of conventional PD controllers. On the other hand, the SDRE adds nonlinear and optimality characteristics to the controller, i.e., increasing the stability margins. These advantages with the ILC correction part deliver a precise control law with the capability of error reduction by learning. The SDRE provides a symmetric-positive-definite distributed nonlinear suboptimal gain K(x) for the control input law u = −R−1(x)BT(x)K(x)x. The sub-blocks of the overall gain R−1(x)BT(x)K(x), are not necessarily symmetric positive definite. A new design is proposed to transform the optimal gain into two symmetric-positive-definite gains like PD-type controllers as u = − KSP(x)e-KSD(x)e. The new form allows us to analytically prove the stability of the proposed learning-based controller for mechanical systems; and presents guaranteed uniform boundedness in finite-time between learning loops. The symmetric PD-type controller is also developed for the state-dependent differential Riccati equation (SDDRE) to manipulate the final time. The SDDRE expresses a differential equation with a final boundary condition, which imposes a constraint on time that could be used for finite-time control. So, the availability of PD-type finite-time control is an asset for enhancing the conventional classical linear controllers with this tool. The learning rules benefit from the gradient descent method for both regulation and tracking cases. One of the advantages of this approach is a guaranteed-stability even from the first loop of learning. A mechanical manipulator, as an illustrative example, was simulated for both regulation and tracking problems. Successful experimental validation was done to show the capability of the system in practice by the implementation of the proposed method on a variable-pitch rotor benchmark. IEEEInstitute of Electrical and Electronics Engineers Inc.Ingeniería de Sistemas y AutomáticaTEP151: Robótica, Visión y Control2022info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersionapplication/pdfapplication/pdfhttps://hdl.handle.net/11441/136033https://doi.org/10.1109/JAS.2022.105533reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésIEEE/CAA Journal of Automatica Sinica, 9 (8), p. 1499-1511https://ieeexplore.ieee.org/document/9774982info:eu-repo/semantics/openAccessoai:idus.us.es:11441/1360332026-06-17T12:51:07Z |
| dc.title.none.fl_str_mv |
A PD-type state-dependent Riccati equation with iterative learning augmentation for mechanical systems |
| title |
A PD-type state-dependent Riccati equation with iterative learning augmentation for mechanical systems |
| spellingShingle |
A PD-type state-dependent Riccati equation with iterative learning augmentation for mechanical systems Nekoo, Saeed Rafee Closed-loop PD-type SDDRE SDRE Iterative Learning Control (ILC) Symmetric |
| title_short |
A PD-type state-dependent Riccati equation with iterative learning augmentation for mechanical systems |
| title_full |
A PD-type state-dependent Riccati equation with iterative learning augmentation for mechanical systems |
| title_fullStr |
A PD-type state-dependent Riccati equation with iterative learning augmentation for mechanical systems |
| title_full_unstemmed |
A PD-type state-dependent Riccati equation with iterative learning augmentation for mechanical systems |
| title_sort |
A PD-type state-dependent Riccati equation with iterative learning augmentation for mechanical systems |
| dc.creator.none.fl_str_mv |
Nekoo, Saeed Rafee Acosta Rodríguez, José Ángel Heredia Benot, Guillermo Ollero Baturone, Aníbal |
| author |
Nekoo, Saeed Rafee |
| author_facet |
Nekoo, Saeed Rafee Acosta Rodríguez, José Ángel Heredia Benot, Guillermo Ollero Baturone, Aníbal |
| author_role |
author |
| author2 |
Acosta Rodríguez, José Ángel Heredia Benot, Guillermo Ollero Baturone, Aníbal |
| author2_role |
author author author |
| dc.contributor.none.fl_str_mv |
Ingeniería de Sistemas y Automática TEP151: Robótica, Visión y Control |
| dc.subject.none.fl_str_mv |
Closed-loop PD-type SDDRE SDRE Iterative Learning Control (ILC) Symmetric |
| topic |
Closed-loop PD-type SDDRE SDRE Iterative Learning Control (ILC) Symmetric |
| description |
This work proposes a novel proportional-derivative (PD)-type state-dependent Riccati equation (SDRE) approach with iterative learning control (ILC) augmentation. On the one hand, the PD-type control gains could adopt many useful available criteria and tools of conventional PD controllers. On the other hand, the SDRE adds nonlinear and optimality characteristics to the controller, i.e., increasing the stability margins. These advantages with the ILC correction part deliver a precise control law with the capability of error reduction by learning. The SDRE provides a symmetric-positive-definite distributed nonlinear suboptimal gain K(x) for the control input law u = −R−1(x)BT(x)K(x)x. The sub-blocks of the overall gain R−1(x)BT(x)K(x), are not necessarily symmetric positive definite. A new design is proposed to transform the optimal gain into two symmetric-positive-definite gains like PD-type controllers as u = − KSP(x)e-KSD(x)e. The new form allows us to analytically prove the stability of the proposed learning-based controller for mechanical systems; and presents guaranteed uniform boundedness in finite-time between learning loops. The symmetric PD-type controller is also developed for the state-dependent differential Riccati equation (SDDRE) to manipulate the final time. The SDDRE expresses a differential equation with a final boundary condition, which imposes a constraint on time that could be used for finite-time control. So, the availability of PD-type finite-time control is an asset for enhancing the conventional classical linear controllers with this tool. The learning rules benefit from the gradient descent method for both regulation and tracking cases. One of the advantages of this approach is a guaranteed-stability even from the first loop of learning. A mechanical manipulator, as an illustrative example, was simulated for both regulation and tracking problems. Successful experimental validation was done to show the capability of the system in practice by the implementation of the proposed method on a variable-pitch rotor benchmark. IEEE |
| publishDate |
2022 |
| dc.date.none.fl_str_mv |
2022 |
| dc.type.none.fl_str_mv |
info:eu-repo/semantics/article info:eu-repo/semantics/acceptedVersion |
| format |
article |
| status_str |
acceptedVersion |
| dc.identifier.none.fl_str_mv |
https://hdl.handle.net/11441/136033 https://doi.org/10.1109/JAS.2022.105533 |
| url |
https://hdl.handle.net/11441/136033 https://doi.org/10.1109/JAS.2022.105533 |
| dc.language.none.fl_str_mv |
Inglés |
| language_invalid_str_mv |
Inglés |
| dc.relation.none.fl_str_mv |
IEEE/CAA Journal of Automatica Sinica, 9 (8), p. 1499-1511 https://ieeexplore.ieee.org/document/9774982 |
| dc.rights.none.fl_str_mv |
info:eu-repo/semantics/openAccess |
| eu_rights_str_mv |
openAccess |
| dc.format.none.fl_str_mv |
application/pdf application/pdf |
| dc.publisher.none.fl_str_mv |
Institute of Electrical and Electronics Engineers Inc. |
| publisher.none.fl_str_mv |
Institute of Electrical and Electronics Engineers Inc. |
| dc.source.none.fl_str_mv |
reponame:idUS. Depósito de Investigación de la Universidad de Sevilla instname:Universidad de Sevilla (US) |
| instname_str |
Universidad de Sevilla (US) |
| reponame_str |
idUS. Depósito de Investigación de la Universidad de Sevilla |
| collection |
idUS. Depósito de Investigación de la Universidad de Sevilla |
| repository.name.fl_str_mv |
|
| repository.mail.fl_str_mv |
|
| _version_ |
1869411484689235968 |
| score |
15.300719 |