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1
Content available New perspectives of analog and digital simulations of fractional order systems
Charef A., Charef M., Djouambi A., Voda A.
Archives of Control Sciences
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2017
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Vol. 27, no. 1
91--118
EN
In the recent decades, fractional order systems have been found to be useful in many areas of physics and engineering. Hence, their efficient and accurate analog and digital simulations and numerical calculations have become very important especially in the fields of fractional control, fractional signal processing and fractional system identification. In this article, new analog and digital simulations and numerical calculations perspectives of fractional systems are considered. The main feature of this work is the introduction of an adjustable fractional order structure of the fractional integrator to facilitate and improve the simulations of the fractional order systems as well as the numerical resolution of the linear fractional order differential equations. First, the basic ideas of the proposed adjustable fractional order structure of the fractional integrator are presented. Then, the analog and digital simulations techniques of the fractional order systems and the numerical resolution of the linear fractional order differential equation are exposed. Illustrative examples of each step of this work are presented to show the effectiveness and the efficiency of the proposed fractional order systems analog and digital simulations and implementations techniques
2
Content available remote Robust fractional adaptive control based on the strictly positive realness condition
Ladaci S., Charef A., Loiseau J. J.
International Journal of Applied Mathematics and Computer Science
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2009
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Vol. 19, no 1
69-76
EN
This paper presents a new approach to robust adaptive control, using fractional order systems as parallel feedforward in the adaptation loop. The problem is that adaptive control systems may diverge when confronted with finite sensor and actuator dynamics, or with parasitic disturbances. One of the classical robust adaptive control solutions to these problems makes use of parallel feedforward and simplified adaptive controllers based on the concept of positive realness. The proposed control scheme is based on the Almost Strictly Positive Realness (ASPR) property of the plant. We show that this condition implies also robust stability in the case of fractional order controllers. An application to Model Reference Adaptive Control (MRAC) with a fractional order adaptation rule is provided with an implementable algorithm. A simulation example of a SISO robust adaptive control system illustrates the advantages of the proposed method in the presence of disturbances and noise.
3
Content available remote Optimal approximation, simulation and analog realization of the fundamental fractional order transfer function
Djouambi A., Charef A., Besançon A. V.
International Journal of Applied Mathematics and Computer Science
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2007
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Vol. 17, no 4
455-462
EN
This paper provides an optimal approximation of the fundamental linear fractional order transfer function using a distribution of the relaxation time function. Simple methods, useful in systems and control theories, which can be used to approximate the irrational transfer function of a class of fractional systems for a given frequency band by a rational function are presented. The optimal parameters of the approximated model are obtained by minimizing simultaneously the gain and the phase error between the irrational transfer function and its rational approximation. A simple analog circuit which can serve as a fundamental analog fractional system is obtained. Illustrative examples are presented to show the quality and usefulness of the approximation method.
4
Content available remote Stabilising solutions to a class of nonlinear optimal state tracking problems using radial basis function networks
Ahmida Z., Charef A., Becerra V. M.
International Journal of Applied Mathematics and Computer Science
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2005
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Vol. 15, no 3
369-381
EN
A controller architecture for nonlinear systems described by Gaussian RBF neural networks is proposed. The controller is a stabilising solution to a class of nonlinear optimal state tracking problems and consists of a combination of a state feedback stabilising regulator and a feedforward neuro-controller. The state feedback stabilising regulator is computed online by transforming the tracking problem into a more manageable regulation one, which is solved within the framework of a nonlinear predictive control strategy with guaranteed stability. The feedforward neuro-controller has been designed using the concept of inverse mapping. The proposed control scheme is demonstrated on a simulated single-link robotic manipulator.
5
Content available remote The use of trace elements and fossil fluids for the mining prospection in diapir zone (North Tunisia)
Charef A.
Biuletyn Państwowego Instytutu Geologicznego
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2001
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nr 396
29-30
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