Marian Łukaniszyn

A Comparative Analysis of Laguerre-Based Approximators to the Grünwald-Letnikov Fractional-Order Difference

This paper provides a series of new results in both steady-state accuracy and frequency-domain analyses for two Laguerre-based approximators to the Grunwald-Letnikov difference. In a comparative study, the Laguerre-based approximators are found superior to the classical Tustin- and Al-Alaoui-based approximators, which is illustrated in simulation examples.

Modeling and Identification of Fractional-Order Discrete-Time Laguerre-Based Feedback-Nonlinear Systems

This paper presents a new implementable strategy for modeling and identification of a fractional-order discrete-time block-oriented feedback-nonlinear system. Two different concepts of orthonormal basis functions (OBF) are used to model a linear dynamic part, namely ”regular” OBF and inverse IOBF. It is shown that the IOBF concept enables to separate linear and nonlinear submodels, which leads to a linear regression formulation of the parameter estimation problem, with the detrimental bilinearity effect totally eliminated. Finally, Laguerre filters are uniquely embedded in modeling of the fractional-order dynamics. Unlike for regular OBF, simulation experiments show a very good identification performance for an IOBF-structured, fractional-order Laguerre-based feedback-nonlinear model, both in terms of low prediction errors and accurate reconstruction of the actual system characteristics.

Torque characteristics of a BLDC motor with multipolar excitation

Purpose – This paper deals with magnetic field calculations and model‐based prediction of electromagnetic torque pulsations in a brushless DC (BLDC) motor.Design/methodology/approach – The impact of a Halbach‐like magnetization and a multipolar excitation of permanent magnets are analysed. The measurement results from the prototype motors are well‐compared with those obtained from the model calculations. It is shown that the cogging torque in the motor with the multipolar excitation of permanent magnets is reduced six times as compared with the conventional BLDC motor.Findings – The proposed method provides high accuracy of the analysis of coupled electromagnetic phenomena. The comparison between measured and calculated values of electromagnetic torque, cogging torque and EMF shows a very good agreement.Practical implications – Reduction of the machine cogging torque is essential for practical applications of DC motors, in particular in the robotics industry.Originality/value – This paper shows that multi...

Advances in Modelling and Control of Non-integer-Order Systems

The traditional second-order Fokker–Planck equation may not adequately describe the movement of solute in an aquifer because of large deviation from the dynamics of Brownian motion. Densities of α-stable type have been used to describe the probability distribution of these motions. The resulting governing equation of these motions is similar to the traditional Fokker–Planck equation except that the order α of the highest derivative is fractional. In this paper, a space fractional Fokker–Planck equation (SFFPE) with instantaneous source is considered. A numerical scheme for solving SFFPE is presented. Using the Riemann–Liouville and Grünwald–Letnikov definitions of fractional derivatives, the SFFPE is transformed into a system of ordinary differential equations (ODE). Then the ODE system is solved by a method of lines. Numerical results for SFFPE with a constant diffusion coefficient are evaluated for comparison with the known analytical solution. The numerical approximation of SFFPE with a time-dependent diffusion coefficient is also used to simulate Lévy motion withα-stable densities. We will show that the numerical method of SFFPE is able to more accurately model these heavy-tailed motions.

Rotor Shape Optimisation of a Switched Reluctance Motor

In the paper the method of torque pulsations reduction of a switched reluctance motor by means of rotor shape optimization is presented. The optimization procedure is constructed on a basis of a genetic algorithm. The objective function is evaluated using variations of the electromagnetic torque predicted by two-dimensional magnetostatic field analysis. To account for torque pulsations due to current switching a circuit model is used that utilizes the electromagnetic quantities predicted by the finite element analysis. To reduce the time of computations an environment for distributed computing was developed.

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

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.

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

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.

Modeling and Identification of a Fractional-Order Discrete-Time Laguerre-Hammerstein System

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

Investigation of End Winding Proximity Losses in a High-Speed PM Machine

This paper presents three- and two-dimensional finite element analyses (2D, 3D FEA) of the proximity losses in brushless AC permanent magnet motor with concentrated windings operating at high speed. The proximity effect only occurs if the examined conductor is penetrated by an external magnetic field, which is caused by adjacent conductor currents. To reduce the proximity effect several alternative winding layouts including rectangular wires are used. The calculated results of the eddy current losses within end-winding regions are significant and must be considered in the design of stator windings. 3D calculations are compared with 2D ones to show the behaviour of the eddy-current into the conductors and also compared with respect to the power loss and AC resistance. The calculations are in a good agreement with measurements on a prototype high-speed motor.

Application of a genetic algorithm for design optimisation of a passive magnetic gear

This paper analyzes an influence of selected design parameters of a passive magnetic gear on the transmitted torque density. This constitutes the basis for determination of a number of design parameters and their ranges in the optimisation process. Calculations are carried out using the two–dimensional finite element method implemented in the Matlab environment. As a result of the optimisation process, the design parameters of the magnetic gear with a much higher value of the transmitted torque are obtained.