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Dive into the research topics where Marek Rydel is active.

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Featured researches published by Marek Rydel.


Journal of The Franklin Institute-engineering and Applied Mathematics | 2017

Modeling of discrete-time fractional-order state space systems using the balanced truncation method

Rafal Stanislawski; Marek Rydel; Krzysztof J. Latawiec

This paper presents a new approach to approximation of linear time-invariant (LTI) discrete-time fractional-order state space SISO systems by means of the SVD-originated balanced truncation (BT) method applied to an FIR-based representation of the fractionalorder system. This specific representation of the system enables to introduce simple, analytical formulas for determination of the Cholesky factorizations of the controllability and observability Gramians, which contributes to significant improvement of the computational efficiency of the BT method. As a model reduction result for the fractional-order systems we obtain a low-order rational (integer-order) state space system. Simulation experiments show a high efficiency of the introduced methodology both in terms of the approximation accuracy of the model and low time complexity of the approximation algorithm.


Automatica | 2018

A new frequency weighted Fourier-based method for model order reduction

Marek Rydel; Rafal Stanislawski

Abstract This paper presents a new, analytically driven frequency weighted model order reduction method. The method is grounded on the Fourier-based decomposition of a high-order state space model. The method is designed for discrete-time systems, but it can be easily applied to continuous-time ones. The main advantage of the proposed algorithm is a class of quadratic time complexity as compared to the cubic one for the classical frequency weighted method, the major feature resulting from the application of analytical methods for calculation of factorizations for controllability and observability Gramians. The simulation experiment confirms the effectiveness of the proposed method both in terms of high modeling accuracy and low computational cost.


Mathematics and Computers in Simulation | 2017

Selection of reduction parameters for complex plant MIMO LTI models using the evolutionary algorithm

Marek Rydel; Włodzimierz Stanisławski

This paper discusses the optimal selection of reduction parameters for complex plant models for the Frequency Weighted and the Frequency Domain method together with the Evolutionary Algorithm. The algorithms presented here enable precise reduction of linear time invariant (LTI), multi-input and multi-output (MIMO) models and are particularly useful for models in which the individual channels differ significantly from each other and are characterized by a specific scope of adequacy for the frequency domain. A two-level reduction algorithm was introduced in order to shorten the computation time of the reduction of very high-order models. The algorithms are then applied to the reduction of the models of the BP-1150 steam boiler subsystems.


2017 Progress in Applied Electrical Engineering (PAEE) | 2017

Fractional-order modeling of electric circuits: modern empiricism vs. classical science

Krzysztof J. Latawiec; Rafal Stanislawski; Marian Lukaniszyn; Wojciech Czuczwara; Marek Rydel

In this paper, controversial views on the use of an integer- and fractional-order derivatives in the theory and practice of electric circuits are discussed. Maxwells equations are definitely useful in classical circuit analyses but empirical, fractional-order modeling is advocated in specific applications, including an exemplary supercapacitor charging circuit. Thus, both methodologies can be employed in various, application-specific modeling tasks.


international conference on methods and models in automation and robotics | 2015

Selection of the objective function of reduction parameter optimization algorithm, and its impact on the properties of reduced MIMO models

Marek Rydel; Włodzimierz Stanisławski

This article presents a range of approximation error measures for reduced mathematical MIMO models of controlled objects. These measures can be of use in evaluations of reduction quality. The impact of selection of a particular approximation error measure as the objective function of the reduction parameter optimization algorithm on the frequency characteristics of the reduced model was analyzed. Particular emphasis was given to those cases where the individual channels of a MIMO model differ significantly from one another. The results are presented on the example of a one-phase zone evaporating tubes model of a BP-1150 steam boiler.


Archive | 2015

A Comparative Analysis of Selected Integer-Order and Noninteger-Order Linear Models of Complex Dynamical Systems

Marek Rydel; Rafal Stanislawski; Włodzimierz Stanisławski; Krzysztof J. Latawiec

This paper presents a comparison of four model order reduction algorithms applied to modeling of evaporating tubes system in the BP–1150 steam boiler. The following model reduction techniques are compared: Frequency Weighted, Rational Krylov, Frequency Weighted with time delay and non-integer order transfer function with and without time delay. Optimal reduction parameters and values of f-zeros and f-poles of non-integer order transfer function are obtained using evolutionary algorithm.


Archive | 2017

Modeling of Fractional-Order Integrators and Differentiators Using Tustin-Based Approximations and Model Order Reduction Techniques

Marek Rydel; Rafal Stanislawski; Marcin Galek; Krzysztof J. Latawiec

This paper presents a set of low-order approximators/dis-cretizers of fractional order derivative and integrator. The approximations are obtained using the Frequency Weighted (FW) reduction method applied to a high order Tustin–Muir based model of fractional-order derivative and integrator. Simulation examples confirm high accuracy of the models both in frequency and time domains. This illustrates the usefulness of the introduced methodology, which can be applied to selection of a set of relatively low order discrete-time approximators of fractional-order derivative and integrator.


International Conference on Applied Physics, System Science and Computers | 2017

FFLD-Based Modeling of Fractional-Order State Space LTI MIMO Systems

Krzysztof J. Latawiec; Rafal Stanislawski; Marian Łukaniszyn; Marek Rydel; Bogusław R. Szkuta

This paper introduces a multivariable version of the Grunwald-Letnikov fractional-order difference (FD) and approximates it with a powerful combination of finite fractional difference (FFD) and finite Laguerre-based difference (FLD) to yield finite fractional/Laguerre-based difference (FFLD). The multivariable FFLD is effectively used to model fractional-order state-space LTI MIMO systems.


Conference on Non-integer Order Calculus and Its Applications | 2017

Grünwald-Letnikov-Laguerre Modeling of Discrete-Time Noncommensurate Fractional-Order State Space LTI MIMO Systems

Krzysztof J. Latawiec; Rafal Stanislawski; Marian Łukaniszyn; Marek Rydel; Bogusław R. Szkuta

In this paper, a multivariable version of the Grunwald-Letnikov noncommensurate fractional-order difference (FD) is defined and approximated with a powerful Grunwald-Letnikov-Laguerre (GLL) combination of finite fractional difference (FFD) and finite Laguerre-based difference (FLD) to obtain finite fractional/Laguerre-based difference (FFLD). The multivariable FFLD is effectively employed to model noncommensurate fractional-order state-space LTI MIMO systems.


international conference on telecommunications | 2016

Application of reduced models of non-integer order integrator to the realization of P λ AD controller

Waldemar Bauer; Marek Rydel

Finding an efficient method of implementing non-integer order controller in digital systems is a matter of ongoing research. In this paper, methods for the approximation non-integer order system in time domain are investigated. Authors present the methodology of reducing the model complexity of PIλD controller for the magnetic levitation system. Implementation on the laboratory magnetic levitation system was performed to validate the presented methodology.

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Rafal Stanislawski

Opole University of Technology

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Krzysztof J. Latawiec

Opole University of Technology

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Marcin Galek

Opole University of Technology

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Marian Lukaniszyn

Opole University of Technology

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Bogusław R. Szkuta

Opole University of Technology

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Marian Łukaniszyn

Opole University of Technology

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Wojciech Czuczwara

Opole University of Technology

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Jacek Łuniewski

Opole University of Technology

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