A method for modelling and simulation of fractional systems

Poinot, Thierry; Trigeassou, Jean‐Claude

doi:10.1016/s0165-1684(03)00185-3

Cited by 107 publications

(45 citation statements)

References 9 publications

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“…In the following two examples, a direct method for discretization is used [40]. Also, simulations have been adopted here with the Rieman-Liouville definition as the proved stability results do not depend on the chosen definition.…”

Section: Simulations Resultsmentioning

confidence: 99%

Stabilization of fractional order systems using a finite number of state feedback laws

2010

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In this paper, the stabilization of linear timeinvariant systems with fractional derivatives using a limited number of available state feedback gains, none of which is individually capable of system stabilization, is studied. In order to solve this problem in fractional order systems, the linear matrix inequality (LMI) approach has been used for fractional order systems. A shadow integer order system for each fractional order system is defined, which has a behavior similar to the fractional order system only from the stabilization point of view. This facilitates the use of Lyapunov function and convex analysis in systems with fractional order 1 < q < 2. To this end, an extremumseeking method is used for obtaining Lyapunov function and defining a suitable sliding sector in order to enable switching between available control gains for system stabilization. Consequently, using the LMI approach in fractional order systems, necessary and sufficient conditions are provided for stabilization of systems with fractional order 1 < q < 2 using a limited number of available state feedback gains which lead to variable structure control.

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Section: Simulations Resultsmentioning

confidence: 99%

Stabilization of fractional order systems using a finite number of state feedback laws

2010

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“…Rational or fractional black-box model can also be first identified and then the physical parameters be deduced from the parameters of the black-box model (see, for instance, Aoun, Malti, Levron, & Oustaloup, 2004;Gabano & Poinot, 2001;Point & Trigeassou, 2003;Point, Trigeassou, & Lin, 2002). However, these approaches require models with many parameters that are implicitly coupled to the physical ones.…”

Section: Introductionmentioning

confidence: 99%

Estimating parameters with pre-specified accuracies in distributed parameter systems using optimal experiment design

Potters

Bombois

Mansoori

et al. 2016

International Journal of Control

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Estimation of physical parameters in dynamical systems driven by linear partial differential equations is an important problem. In this paper, we introduce the least costly experiment design framework for these systems. It enables parameter estimation with an accuracy that is specified by the experimenter prior to the identification experiment, while at the same time minimising the cost of the experiment. We show how to adapt the classical framework for these systems and take into account scaling and stability issues. We also introduce a progressive subdivision algorithm that further generalises the experiment design framework in the sense that it returns the lowest cost by finding the optimal input signal, and optimal sensor and actuator locations. Our methodology is then applied to a relevant problem in heat transfer studies: estimation of conductivity and diffusivity parameters in front-face experiments. We find good correspondence between numerical and theoretical results.

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“…Fractional-order system identification is a basic issue of application of fractional calculus [53][54][55][56][57][58]. Several researchers have reported their work on identifying the fractional-order model in the time-domain and frequency-domain.…”

Section: Introductionmentioning

confidence: 99%

Genetic Algorithm-Based Identification of Fractional-Order Systems

Zhou

Cao

Chen

2013

Entropy

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Abstract:Fractional calculus has become an increasingly popular tool for modeling the complex behaviors of physical systems from diverse domains. One of the key issues to apply fractional calculus to engineering problems is to achieve the parameter identification of fractional-order systems. A time-domain identification algorithm based on a genetic algorithm (GA) is proposed in this paper. The multi-variable parameter identification is converted into a parameter optimization by applying GA to the identification of fractional-order systems. To evaluate the identification accuracy and stability, the time-domain output error considering the condition variation is designed as the fitness function for parameter optimization. The identification process is established under various noise levels and excitation levels. The effects of external excitation and the noise level on the identification accuracy are analyzed in detail. The simulation results show that the proposed method could identify the parameters of both commensurate rate and non-commensurate rate fractional-order systems from the data with noise. It is also observed that excitation signal is an important factor influencing the identification accuracy of fractional-order systems.

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A method for modelling and simulation of fractional systems

Cited by 107 publications

References 9 publications

Stabilization of fractional order systems using a finite number of state feedback laws

Stabilization of fractional order systems using a finite number of state feedback laws

Estimating parameters with pre-specified accuracies in distributed parameter systems using optimal experiment design

Genetic Algorithm-Based Identification of Fractional-Order Systems

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