scholarly journals Optimal Approximation, Simulation and Analog Realization of the Fundamental Fractional Order Transfer Function

Author(s):  
Abdelbaki Djouambi ◽  
Abdelfatah Charef ◽  
Alina Besançon

Optimal Approximation, Simulation and Analog Realization of the Fundamental Fractional Order Transfer FunctionThis 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.

2013 ◽  
Vol 2013 ◽  
pp. 1-14 ◽  
Author(s):  
Margarita Rivero ◽  
Sergei V. Rogosin ◽  
José A. Tenreiro Machado ◽  
Juan J. Trujillo

The theory and applications of fractional calculus (FC) had a considerable progress during the last years. Dynamical systems and control are one of the most active areas, and several authors focused on the stability of fractional order systems. Nevertheless, due to the multitude of efforts in a short period of time, contributions are scattered along the literature, and it becomes difficult for researchers to have a complete and systematic picture of the present day knowledge. This paper is an attempt to overcome this situation by reviewing the state of the art and putting this topic in a systematic form. While the problem is formulated with rigour, from the mathematical point of view, the exposition intends to be easy to read by the applied researchers. Different types of systems are considered, namely, linear/nonlinear, positive, with delay, distributed, and continuous/discrete. Several possible routes of future progress that emerge are also tackled.


Author(s):  
Guillermo E. Santamaria ◽  
Ine´s Tejado ◽  
Blas M. Vinagre ◽  
Concepcio´n A. Monje

The advantages and applications of modeling and control of non-integer order linear systems are well known, but the inherent complexity of practical approximations has prevented the generalized appearance in the market of simple devices capable of implementing a fractional order control on a unknown given plant in a reliable way. The purpose of this work is to make a step forward in this sense, looking for a compromise between simplicity and reliability of the system. An automatic method for tuning, design, and implementation of fractional order PIαDμ controllers is presented in this paper. The auto-tuning method is based on plant magnitude and phase measuring at a frequency of interest, obtained by the relay feedback technique. A fractional order PIαDμ controller is designed from these measurements so that specifications of phase margin and robustness to variations of the plant gain are reached. Once the fractional order PIαDμ controller transfer function is obtained, it is discretized applying Pascal Matrix Method, and approximated using continuous fraction expansion of the Tustin Operator, generalized for a general transfer function. Simulation results obtained using the described method on an a priori unknown characteristic servo are presented in this paper.


2008 ◽  
Vol 42 (6-8) ◽  
pp. 999-1014 ◽  
Author(s):  
Abdelbaki Djouambi ◽  
Abdelfatah Charef ◽  
Alina Voda-Besancon

2001 ◽  
Vol 2001 (1) ◽  
pp. 32-34 ◽  
Author(s):  
Clive Seager

Energies ◽  
2021 ◽  
Vol 14 (13) ◽  
pp. 4060
Author(s):  
Artur Kozłowski ◽  
Łukasz Bołoz

This article discusses the work that resulted in the development of two battery-powered self-propelled electric mining machines intended for operation in the conditions of a Polish copper ore mine. Currently, the global mining industry is seeing a growing interest in battery-powered electric machines, which are replacing solutions powered by internal combustion engines. The cooperation of Mine Master, Łukasiewicz Research Network—Institute of Innovative Technologies EMAG and AGH University of Science and Technology allowed carrying out a number of works that resulted in the production of two completely new machines. In order to develop the requirements and assumptions for the designed battery-powered propulsion systems, underground tests of the existing combustion machines were carried out. Based on the results of these tests, power supply systems and control algorithms were developed and verified in a virtual environment. Next, a laboratory test stand for validating power supply systems and control algorithms was developed and constructed. The tests were aimed at checking all possible situations in which the battery gets discharged as a result of the machine’s ride or operation and when it is charged from the mine’s mains or with energy recovered during braking. Simulations of undesirable situations, such as fluctuations in the supply voltage or charging power limitation, were also carried out at the test stand. Positive test results were obtained. Finally, the power supply systems along with control algorithms were implemented and tested in the produced battery-powered machines during operational trials. The power systems and control algorithms are universal enough to be implemented in two different types of machines. Both machines were specially designed to substitute diesel machines in the conditions of a Polish ore mine. They are the lowest underground battery-powered drilling and bolting rigs with onboard chargers. The machines can also be charged by external fast battery chargers.


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