Author
Slaheddine Najar
Other affiliations: École Normale Supérieure
Bio: Slaheddine Najar is an academic researcher from University of Gabès. The author has contributed to research in topics: Fractional calculus & System identification. The author has an hindex of 11, co-authored 34 publications receiving 355 citations. Previous affiliations of Slaheddine Najar include École Normale Supérieure.
Papers
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TL;DR: In this paper, three frequency-domain design methods are proposed to deal with robust fractional order PID controller design via numerical optimization, which achieve robustness to the variation of some parameters by maintaining the open-loop phase quasi-constant in a pre-specified frequency band.
Abstract: This paper deals with robust fractional order PID controller design via numerical optimization. Three new frequency-domain design methods are proposed. They achieve good robustness to the variation of some parameters by maintaining the open-loop phase quasi-constant in a pre-specified frequency band, i.e., maintaining the iso-damping property of the controlled system. The two first methods are extensions of the well-known Monje-Vinagre et al. method for uncertain systems. They ameliorate the numerical optimization algorithm by imposing the open-loop phase to be flat in a frequency band not only around a single frequency. The third method is an interval-based design approach that simplifies the algorithm by reducing the constraints number and offers a more large frequency band with an iso-damping property. Several numerical examples are presented to show the efficiency of each proposed method and discuss the obtained results. Also, an application to the liquid carbon monoxide level control is presented.
67 citations
TL;DR: New consistent methods for order and coefficient estimation of continuous-time systems by errors-in-variables fractional models are presented and two estimators based on Higher-Order Statistics (third-order cumulants) are developed.
Abstract: The errors-in-variables identification problem concerns dynamic systems in which input and output signals are contaminated by an additive noise. Several estimation methods have been proposed for identifying dynamic errors-in-variables rational models. This paper presents new consistent methods for order and coefficient estimation of continuous-time systems by errors-in-variables fractional models. First, differentiation orders are assumed to be known and only differential equation coefficients are estimated. Two estimators based on Higher-Order Statistics (third-order cumulants) are developed: the fractional third-order based least squares algorithm (ftocls) and the fractional third-order based iterative least squares algorithm (ftocils). Then, they are extended, using a nonlinear optimization algorithm, to estimate both the differential equation coefficients and the commensurate order. The performances of the proposed algorithms are illustrated with a numerical example.
29 citations
TL;DR: Two diagnosis methods initially developed for integer order models are here extended to handle fractional order models and the first one is the generalized dynamic parity space method and the second is the Luenberger diagnosis observer.
25 citations
01 Jan 2009
TL;DR: This paper presents a generalization of the classical discrete time Kalman filter algorithm to the case of the fractional systems and shows a simple numerical example of linear state estimation.
Abstract: This paper presents a generalization of the classical discrete time Kalman filter algorithm to the case of the fractional systems. Motivations for the use of this filter are given and the algorithm is detailed. The document also shows a simple numerical example of linear state estimation.
22 citations
TL;DR: A new method for validating existence and uniqueness of the solution of an initial value problems for fractional differential equations by an algorithm selecting a stepsize and computing a priori constant enclosure of the solutions is proposed.
22 citations
Cited by
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1,166 citations
TL;DR: This review investigates its progress since the first reported use of control systems, covering the fractional PID proposed by Podlubny in 1994, and is presenting a state-of-the-art fractionalpid controller, incorporating the latest contributions in this field.
447 citations
TL;DR: In this paper, the shifted Jacobi operational matrix (JOM) of fractional derivatives was derived and applied together with spectral tau method for numerical solution of general linear multi-term fractional differential equations (FDEs).
284 citations
TL;DR: A new formula expressing explicitly the derivatives of shifted Chebyshev polynomials of any degree and for any fractional-order in terms of shiftedChebyshevs themselves is state and prove.
243 citations
TL;DR: The proposed collocation scheme, both in temporal and spatial discretizations, is successfully extended to solve the two-dimensional TFSE, demonstrating the utility and high accuracy of the new approach over other numerical methods.
155 citations