Robust control of a cable from a hyperbolic partial differential equation model

Lucie Baudouin 1 Aude Rondepierre 2, 3 Simon Neild 4
1 LAAS-MAC - Équipe Méthodes et Algorithmes en Commande
LAAS - Laboratoire d'analyse et d'architecture des systèmes
2 IMT - Institut de Mathématiques de Toulouse UMR5219
3 LAAS - Laboratoire d'analyse et d'architecture des systèmes
4 Department of Mechanical and Aerospace Engineering [Glasgow]
Abstract : This paper presents a detailed study of the robust control of a cable’s vibrations, with emphasis on considering a model of infinite dimension. Indeed, using a partial differential equation model of the vibrations of an inclined cable with sag, we are interested in studying the application of H∞-robust feedback control to this infinite dimensional system. The approach relies on Riccati equations to stabilize the system under measurement feedback when it is subjected to external disturbances. Henceforth, our study focuses on the construction of a standard linear infinite dimensional state space description of the cable under consideration before writing its approximation of finite dimension and studying the H∞ feedback control of vibrations with partial observation of the state in both cases. The closed loop system is numerically simulated to illustrate the effectiveness of the resulting control law.
Keywords : partial differential equations Cable model robust control state-space model measurement feedback
Document type :
Journal articles
Complete list of metadatas

Cited literature [26 references]  Display  Hide  Download
https://hal.archives-ouvertes.fr/hal-01096851
Contributor : Lucie Baudouin <>
Submitted on : Monday, January 22, 2018 - 6:23:13 PM
Last modification on : Friday, January 10, 2020 - 9:10:08 PM
Long-term archiving on: Thursday, May 24, 2018 - 9:17:42 AM

File

BriefCable_final.pdf
Files produced by the author(s)

Identifiers

Collections

CNRS | INSMI | TDS-MACS | IMT | UNIV-TLSE2 | INSA-TOULOUSE | LAAS-DECISION-ET-OPTIMISATION | LAAS-MAC | LAAS | INSA-GROUPE | UNIV-TLSE3 | UT1-CAPITOLE

Citation

Lucie Baudouin, Aude Rondepierre, Simon Neild. Robust control of a cable from a hyperbolic partial differential equation model. IEEE Transactions on Control Systems Technology, Institute of Electrical and Electronics Engineers, 2019, 27 (3), pp.1343-1351. ⟨10.1109/TCST.2018.2797938⟩. ⟨hal-01096851v2⟩

Export

BibTeX TEI DC DCterms EndNote

Share

Metrics

Record views

351

Files downloads

520

Contact

Informations

CCSD