Proportional-delayed controllers design for LTI-systems a geometric approach

J.-E. Hernández-Díez 1 C.-F. Méndez-Barrios 1 S. Mondié 2 Silviu-Iulian Niculescu 3 E.J. González-Galván 1
1 UASLP - Universidad Autonoma de San Luis Potosi [México]
2 CINVESTAV-IPN - Departamento de Control Automático
3 L2S - Laboratoire des signaux et systèmes
Abstract : This paper focuses on the design of P-δ controllers for single-input-single-output linear time-invariant systems. The basis of this work is a geometric approach allowing to partitioning the parameter space in regions with constant number of unstable roots. This methodology defines the hyper-planes separating the aforementioned regions and characterises the way in which the number of unstable roots changes when crossing such a hyper-plane. The main contribution of the paper is that it provides an explicit tool to find P-δ gains ensuring the stability of the closed-loop system. In addition, the proposed methodology allows to design a non-fragile controller with a desired exponential decay rate σ. Several numerical examples illustrate the results and a haptic experimental set-up shows the effectiveness of P-δ controllers. © 2017 Informa UK Limited, trading as Taylor and Francis Group.
Keywords : fragility proportional-delayed controllers stability Time-delay systems
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Journal articles
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https://hal-centralesupelec.archives-ouvertes.fr/hal-02281719
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Submitted on : Monday, September 9, 2019 - 2:23:27 PM
Last modification on : Wednesday, September 11, 2019 - 1:15:39 AM

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CENTRALESUPELEC | SUP_LSS | SUP_SYSTEMES | L2S | UNIV-PARIS-SACLAY

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J.-E. Hernández-Díez, C.-F. Méndez-Barrios, S. Mondié, Silviu-Iulian Niculescu, E.J. González-Galván. Proportional-delayed controllers design for LTI-systems a geometric approach. International Journal of Control, 2018, 91 (4), pp.907-925. ⟨10.1080/00207179.2017.1299943⟩. ⟨hal-02281719⟩

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