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Duality of variable fractional order difference operators and its application in identification

100%

Sierociuk D. , Twardy M.

Bulletin of the Polish Academy of Sciences. Technical Sciences

2014

tom Vol. 62, nr 4

809--815

The paper presents a number of definitions of variable order difference and discusses duality among some of them. The duality is used to improve the performance of the least squares estimation when applied to variable order difference fractional systems. It turns out, that by appropriate exploitation of duality one can reduce the estimator variance when system identification is carried out.

Fractional variable order anti-windup control strategy

100%

Sierociuk D. , Malesza W.

tom Vol. 66, nr 4

427--432

In this paper, a novel anti-windup strategy is presented. It is based on using fractional variable order integrator instead of integer order one in PID controller. It is shown that among four different types of variable order derivative definitions, only one gives satisfactory results – comparable, and even slightly better than the classical back-calculation anti-windup algorithm. Results are also presented in the form of simulation plots.

Fractional Kalman filter algorithm for the states, parameters and order of fractional system estimation

100%

Sierociuk D. , Dzieliński A.

International Journal of Applied Mathematics and Computer Science

2006

tom Vol. 16, no 1

129-140

This paper presents a generalization of the Kalman filter for linear and nonlinear fractional order discrete state-space systems. Linear and nonlinear discrete fractional order state-space systems are also introduced. The simplified kalman filter for the linear case is called the fractional Kalman filter and its nonlinear extension is named the extended fractional Kalman filter. The background and motivations for using such techniques are given, and some algorithms are discussed. The paper also shows a simple numerical example of linear state estimation. Finally, as an example of nonlinear estimation, the paper discusses the possibility of using these algorithms for parameters and fractional order estimation for fractional order systems. Numerical examples of the use of these algorithms in a general nonlinear case are presented.

Identification of mobile robot kinematics using computer vision system

100%

Sierociuk D. , Czeredys M.

Przegląd Elektrotechniczny

2005

tom R. 81, nr 3

69-72

This paper presents parametric identification of caterpillar mobile robot. The data of robots position are collected by computer vision system composed of a camera mounted over the place of the robot movements and a PC computer with frame grabber. An algorithm of positioning is also described. Results of identification are simulated and compared.

Dane o pozycji robota są uzyskiwane przy pomocy komputerowego systemu wizyjnego złożonego z kamery zamontowanej ponad miejscem przemieszczania się robota i komputerem klasy PC z frame grabber'em. Algorytm tego pozycjonowania jest także opisany. Rezultaty identyfikacji są zasymulowane i porównane z rzeczywistymi.

Discrete Fractional Order Artificial Neural Network

80%

Sierociuk D. , Sarwas G. , Dzieliński A.

Acta Mechanica et Automatica

2011

tom Vol. 5, no. 2

128-132

In this paper the discrete time fractional order artificial neural network is presented. This structure is proposed for simulating the dynamics of non-linear fractional order systems. In the second part of this paper several numerical examples are shown. The final part of the paper presents the discussion on the use of fractional or integer discrete time neural network for modelling and simulating fractional order non-linear systems. The simulation results show the advantages of the proposed solution over the classical (integer) neural network approach to modelling of non-linear fractional order systems.

Some applications of fractional order calculus

80%

Dzieliński A. , Sierociuk D. , Sarwas G.

nr 4

Fractional variable order anti-windup control strategy

50%

Malesza W. , Sierociuk D.