Marian Lukaniszyn

Modeling and identification of a fractional-order discrete-time SISO Laguerre-Wiener system

This paper presents a new implementable strategy for modeling and identification of a fractional-order discrete-time nonlinear block-oriented SISO Wiener system. The concept of modeling of a linear dynamics by means of orthonormal basis functions (OBF) is employed to separate linear and nonlinear submodels, which enables a linear regression formulation of the parameter estimation problem. Finally, discrete-time Laguerre filters are uniquely embedded in modeling of the fractional-order dynamics, eliminating the disastrous bilinearity issue. Simulation experiments show a very good identification performance for a fractional-order Laguerre-based Wiener model, both in terms of low prediction errors and accurate reconstruction of the actual system characteristics.

A new form of a σ-inverse for nonsquare polynomial matrices

This paper presents a new simple form of a polynomial matrix σ-inverse introduced as a result of research works on minimum variance control (MVC) for LTI MIMO nonsquare systems. A new approach to construction of a σ-inverse of a nonsquare polynomial matrix can result in e.g. pole-free design of MVC, which is provided by specially selected degrees of freedom of the σ-inverse. A simulation example in the Matlab® environment illustrates theoretical achievements of the paper.

The steady-state error issue in Laguerre-based modeling of the GL fractional difference

This paper presents new results in the reduction of a steady-state error in modeling of the Grünwald-Letnikov (GL) discrete-time fractional difference by means of discrete-time Laguerre filters. A discussion of various approximation criteria contributes to the steady-state accuracy problem. The paper is culminated with the presentation of finite fractional/Laguerre-based difference (FFLD), whose excellent approximation performance including very low steady-state error is illustrated in simulation examples.

Adaptive finite fractional difference with a time-varying forgetting factor

Normalized finite fractional differences are considered as an approximation to the Grunwald-Letnikov fractional difference. In particular, adaptive finite fractional difference (AFFD) is recalled and effectively modified by the introduction of a time-varying forgetting factor. The modified AFFD is shown in simulations to provide an excellent approximation performance, both in terms of the modeling accuracy and robustness.

Time-domain approximations to the Grünwald-Letnikov difference with application to modeling of fractional-order state space systems

This paper presents a general, modified framework for various time-domain approximations to the Grünwald-Letnikov fractional difference, namely finite fractional and Laguerre-based differences. The approximations are applied in the modeling problem for linear fractional-order state space systems, with two different implementation schemes presented.

Constrained minimum variance control of nonsquare LTI MIMO systems

Constrained minimum variance control is offered for nonsquare LTI MIMO systems. A constrained control design takes advantage of the so-called control zeros. The new control strategy is compared with familiar generalized minimum variance control and possible application areas of the two are discussed.

Modeling and identification of fractional first-order systems with Laguerre-Grünwald-Letnikov fractional-order differences

This paper introduces a method for modeling and identification of a simple dynamical system described by fractional-order differential equation. The Grünwald-Letnikov fractional-order derivative is approximated by a discrete-time Laguerre-based model, giving rise to a new discrete-time integerorder equation modeling the considered system. An application example involves a supercapacitor charging circuit. High accuracy of parametric identification for the circuit model, under moderate computational effort, is achieved on a real-life experimental data.

Influence of an end-winding size on proximity losses in a high-speed PM synchronous motor

This paper deals with AC winding loss including proximity loss investigation in a high-speed permanent magnet (PM) machine for traction applications. The research is focused on the end-winding effects that have not been widely reported in the literature. The calculated results confirm that the end-winding copper loss can significantly affect the eddy-current loss within copper and it must be taken into account to provide reasonable prediction of total losses. A three-dimensional (3D) finite element analysis (FEA) is employed to evaluate and identify the end-winding contribution into the overall winding power loss generated. To explain how much the power loss may change due to dimensions and size of end-winding, the parameterized 3D FE models are investigated. In this study, the results clearly demonstrate that the size of end-winding has influence on the winding resistance and, consequently, the power loss in the AC operation. The theoretical prediction of the losses within the armature of the high-speed permanent magnet synchronous machine (PMSM) is validated experimentally on a segmented stator.

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

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.

Pole-free GMVC and LQR designs for nonsquare LTI MIMO systems

This paper presents (structurally stable) pole-free control designs for (a deterministic version of) generalized minimum variance control and linear quadratic regulation for nonsquare LTI MIMO systems. For both discrete-time control strategies, two alternative approaches are offered, the numerical one related with limiting control solutions as control weighting matrices tend to the zero ones and the other produced by analytically-derived perfect controls, for which it is possible to put the weighting matrices directly to the zero ones. In the latter case, the solutions are identical with that for minimum variance control, in which case the pole-free designs must account for the so-called control zeros, being the extension of transmission zeros for nonsquare LTI MIMO systems. Simulation examples illustrate the theoretical achievements of the paper.