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Research Papers

Derivative-Based Sampled Data Control for Continuous Linear Parameter Varying System With Unknown Parameters

[+] Author and Article Information
Sonia Maalej

Laboratory CRIStAL,
UMR CNRS 9189,
Université de Lille 1,
BP 48,
Villeneuve d'Ascq 59651, France;
Laboratory Non-A,
INRIA,
Villers-lès-Nancy 54600, France
e-mail: sonia.maalej@gmail.com

Alexandre Kruszewski

Centrale Lille,
UMR 9189-CRISTAL,
Centre de Recherche en Informatique,
Signal et Automatique de Lille,
Lille F-59000, France
e-mail: alexandre.kruszewski@ec-lille.fr

Lotfi Belkoura

Laboratory Non-A,
INRIA,
Villers-lès-Nancy 54600, France;
Cité Scientifique,
Lille F-59000, France

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT,AND CONTROL. Manuscript received June 1, 2017; final manuscript received February 15, 2019; published online April 3, 2019. Assoc. Editor: Jongeun Choi.

J. Dyn. Sys., Meas., Control 141(8), 081013 (Apr 03, 2019) (8 pages) Paper No: DS-17-1288; doi: 10.1115/1.4042947 History: Received June 01, 2017; Revised February 15, 2019

This paper deals with the robust stabilization of a class of linear parameter varying (LPV) systems in the sampled data control case. Instead of using a state observer or searching for a dynamic output feedback, the considered controller is based on output derivatives estimation. This allows the stabilization of the plant with very large parameter variations or uncertainties. The proof of stability is based on the polytopic representation of the closed-loop under Lyapunov conditions and system transformations. The result is a control structure with only one parameter tuned via very simple conditions. Finally, the effectiveness of the proposed method is verified via a numerical example of a second-order LPV system.

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Figures

Grahic Jump Location
Fig. 1

Robust data sampled controller

Grahic Jump Location
Fig. 3

Stability set of the closed-loop (19) for τx = 0.01, α = 1, Kx=[10−4 2.2×10−2], and different delays hx

Grahic Jump Location
Fig. 4

Stability set of the second-order system (19) with τ = 0.01 and K=[10−4 2.2×10−2] for different approximation of the input gain α and a time-delay h=(τ/5)

Grahic Jump Location
Fig. 5

Response of the system states

Grahic Jump Location
Fig. 6

States estimation errors

Tables

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