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Technical Brief

Identification, Estimation, and Control for Linear Uncertain Systems Using Measurements of Higher-Order Derivatives

[+] Author and Article Information
Zilong Shao

CRIStAL UMR CNRS 9189,
Ecole Centrale de Lille,
Villeneuve d'Ascq 59650, France;
Non-A team,
INRIA-Lille Nord Europe,
Villeneuve d'Ascq 59650, France
e-mail: shaozilong88@gmail.com

Gang Zheng

CRIStAL UMR CNRS 9189,
Ecole Centrale de Lille,
Villeneuve d'Ascq 59650, France;
Non-A team,
INRIA-Lille Nord Europe,
Villeneuve d'Ascq 59650, France
e-mail: gang.zheng@inria.fr

Denis Efimov

CRIStAL UMR CNRS 9189,
Ecole Centrale de Lille,
Villeneuve d'Ascq 59650, France;
Non-A team,
INRIA-Lille Nord Europe,
Villeneuve d'Ascq 59650, France
e-mail: denis.efimov@inria.fr

Wilfrid Perruquetti

CRIStAL UMR CNRS 9189,
Ecole Centrale de Lille,
Villeneuve d'Ascq 59650, France;
Non-A team,
INRIA-Lille Nord Europe,
Villeneuve d'Ascq 59650, France
e-mail: wilfrid.perruquetti@inria.fr

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received March 15, 2016; final manuscript received May 31, 2017; published online August 9, 2017. Assoc. Editor: Jongeun Choi.

J. Dyn. Sys., Meas., Control 139(12), 124501 (Aug 09, 2017) (6 pages) Paper No: DS-16-1145; doi: 10.1115/1.4037007 History: Received March 15, 2016; Revised May 31, 2017

In this paper, the problem of output control for linear uncertain systems with external perturbations is studied. First, it is assumed that the output available for measurement is only the higher-order derivative of the state variable, instead of the state variable itself (for example, the acceleration for a second-order plant), and the measurement is also corrupted by noise. Then, via series of integration, an identification algorithm is proposed to identify all unknown parameters of the model and all unknown initial conditions of the state vector. Finally, two control algorithms are developed, adaptive and robust; both provide boundedness of trajectories of the system. The efficiency of the obtained solutions is demonstrated by numerical simulation.

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Figures

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Fig. 1

Time-trace of θ¯̂

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Fig. 2

Position and velocity for adaptive controller

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Fig. 3

Position and velocity for robust controller

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Fig. 4

Position behavior with periodical identification (left one with adaptive controller and right one with robust controller)

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