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Bako L.,Ecole Des Mines de Douai | Bako L.,Laboratoire dAutomatique | Mercere G.,Laboratoire dAutomatique et dInformatique Industrielle | Lecoeuche S.,Ecole Des Mines de Douai | Lecoeuche S.,Laboratoire dAutomatique
2007 European Control Conference, ECC 2007 | Year: 2015

This paper is concerned with the identification of piecewise linear MIMO state space systems in a recursive way. The proposed method summons up benefits of recursive parameters estimation, on-line switching times detection and on-line order estimation. A structured identification scheme which applied on-line, allows to track both the extended observability matrix range space and its dimension. This method is used on-line to blindly identify switching systems and to label the different submodels. Since subspace identification methods rely on batch data block matrices, a minimum dwell time in each discrete state is necessary to achieve good performances. Simulation results comfort this point and illustrate the abilities and the benefits of the proposed approach. © 2007 EUCA.

Tenoutit M.,Laboratoire dAutomatique et dInformatique Industrielle | Maamri N.,Laboratoire dAutomatique et dInformatique Industrielle | Trigeassou J-C.,University of Bordeaux 1
IFAC Proceedings Volumes (IFAC-PapersOnline) | Year: 2011

The purpose of this paper is the synthesis of fractional PI / PID controllers ensuring robustness to the system gain variations. Based on output feedback technique, the controller is derived using Lyapunov stability condition expressed in terms of LMIs (Linear Matrix Inequalities). Time domain constraints are introduced thanks to the equality of moments between the closed-loop system and its fractional reference model. Numerical examples are given to demonstrate the proposed approach. © 2011 IFAC.

Tenoutit M.,Laboratoire dAutomatique et dInformatique Industrielle | Maamri N.,Laboratoire dAutomatique et dInformatique Industrielle | Trigeassou J.-C.,University of Bordeaux 1
International Multi-Conference on Systems, Signals and Devices, SSD'11 - Summary Proceedings | Year: 2011

The purpose of this paper is the synthesis of fractional PID controllers ensuring robustness to system gain variations. Robustness is specified by an open loop reference model derived from the CRONE template, where the fractional order allows robustness to gain variations. The tuning of the controller parameters is performed thanks to the method of moments. Numerical examples are proposed to illustrate the capabilities of this tuning technique. © 2011 IEEE.

Gabano J.D.,Laboratoire dAutomatique et dInformatique Industrielle | Poinot T.,Laboratoire dAutomatique et dInformatique Industrielle
Signal Processing | Year: 2011

Heat transfer problems in homogeneous medium obey to diffusion phenomenon. In this paper, we study heat conduction through a sphere which can be modelled with the help of fractional systems. We use models based on an original fractional integrator whose order 12 acts only over a limited spectral band. Simulations of front face thermal characterization consisting in measuring the inner surface temperature of the sphere where a random heat flux is applied are carried out. These simulations allow to validate the ability of the proposed estimation algorithms not only to rebuild the inner surface temperature but also to identify with a good accuracy the heat conductivity and diffusivity. Monte-Carlo simulations are also performed in order to provide statistical properties of the thermo-physical parameter estimates. © 2010 Elsevier B.V. All rights reserved.

Rambault L.,Laboratoire dAutomatique et dInformatique Industrielle | Al Chaera T.,Laboratoire dAutomatique et dInformatique Industrielle
Mediterranean Journal of Measurement and Control | Year: 2012

Quaternions are hypercomplex numbers which form a fourdimensional vector space over the field of real numbers. They are considered as a non-commutative extension of complex numbers. Unlike multiplication of real or complex numbers, multiplication of quaternions is not commutative. The algebra of quaternions has been extensively studied in order to determine the consequences of the non-commutativity of multiplication, and therefore to find the corresponding solutions. Nowadays, quaternions are used to describe phenomena occurring in many areas. The aim of this paper is to illustrate the use of quaternions in control theory. After defining the quaternion skew-field, the description of an nth-order Linear Time-Invariant (LTI) dynamical system with quaternionic coefficients by a transfer function or a state model is presented. Its stability is then characterized through the computation of system poles and the use of the Lyapunov theory. Consequently, real-valued conditions, based on Linear Matrix Inequalities (LMIs), for the stability of a quaternionic system by state feedback control are also derived. Moreover, some numerical examples are illustrated to help the reader get some insight on quaternionic systems. Finally, we propose to use the theory of quaternions in order to mathematically decouple a cross-coupled LTI system with real coefficients that has two inputs and two outputs. © 2012 SoftMotor Ltd.

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