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In this paper method of impulse response approximation with orthogonal Laguerre functions is used for the approximation of bi-fractional filter (BFF). This filter is a new development in the field of non-integer order signal processing. Filter with three parameters allows advanced shaping of frequency response, especially the phase characteristic. Method of… (More)
Robust non-integer control is an emerging field in control theory. Multiple works are focused on designing controllers with flatphase and robust stability margins. In this paper design of non-integer order with robust properties is considered. This controller is designed for the model of air heating process trainer system belonging to the Department of… (More)
Paper presents a new method for implementing Oustaloup approximation of non-integer order systems in digital environment. Classical method and its limitations are presented and discussed. Method of realization is formulated and schemes for discretization are presented. Operation of method is illustrated with two examples. Work is ended with discussion of… (More)
In this paper a special case of non-integer filters - namely bi-fractional filters (BFF) - are considered. Those filters are characterised by three parameters and offer rich possibilities of frequency response shaping. This paper is a continuation of an earlier research and focuses on stable filters with eigenvalues in right complex half plane. Conditions… (More)
The immunomodulatory properties of melatonin (Mel) are generally recognized but the mechanisms of its action are not fully understood. In mammals, some of the immunomodulatory effects of Mel are mediated by opioids synthesized by immune cells under its influence. The present study was performed to examine whether Mel-induced opioids are involved in the… (More)
The goal of this paper is to compare popular methods of approximation on non-integer order systems and propose strategies of increasing their robustness to numerical errors of their coefficients. It is shown, that popular methods during discretisation lead to instability.
Control of active magnetic bearings is an important area of research. In this paper authors present the methodology of design, discretization and implementation PI<sup>λ</sup>D controller for magnetic levitation system. Implementation on the laboratory system was performed to validate the presented methodology. The presented methodology is promising… (More)
Non-integer order filters allow much greater flexibility in shaping of frequency responses than classical methods. In this paper authors present the methodology of digital filter design using non-integer order filter as a prototype. Implementation on the embedded testbed was performed to validate the presented method. Experiments with measuring of frequency… (More)
In this paper, the authors wanted to analyse the behaviour of fractional order system under relay control. There is a brief introduction to finding a solution for non-integer order systems both with zero and non-zero initial conditions. Then, the numerical approach is presented with some examples.