Krzysztof J. Latawiec

A Reduced Prony's Method in Power-Quality Analysis—Parameters Selection

This paper presents a new modification of the least-squares Pronys method for power-quality analysis in terms of estimation of harmonics and interharmonics in an electric power signal. The so-called reduced Pronys method can be competitive, in some specific case, to the Fourier transformation method and the classical LS Pronys method. The modification constitutes in a specific selection of a constant frequency vector in a Fourier-like manner leading to a remarkable reduction of the computational burden and enabling online real-time computations. In addition, a sampling frequency and an analysis window length can be selected to provide the numerical stability of the new algorithm.

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.

Normalized finite fractional differences

This paper presents a series of new results in finite and infinite-memory modeling of discrete-time fractional differences. The introduced normalized finite fractional difference is shown to properly approximate its fractional difference original, in particular in terms of the steady-state properties. A stability analysis is also presented and a recursive computation algorithm is offered for finite fractional differences. A thorough analysis of computational and accuracy aspects is culminated with the introduction of a perfect finite fractional difference and, in particular, a powerful adaptive finite fractional difference, whose excellent performance is illustrated in simulation examples.

A study on new right/left inverses of nonsquare polynomial matrices

A study on new right/left inverses of nonsquare polynomial matrices This paper presents several new results on the inversion of full normal rank nonsquare polynomial matrices. New analytical right/left inverses of polynomial matrices are introduced, including the so-called τ-inverses, σ-inverses and, in particular, S-inverses, the latter providing the most general tool for the design of various polynomial matrix inverses. The applicationoriented problem of selecting stable inverses is also solved. Applications in inverse-model control, in particular robust minimum variance control, are exploited, and possible applications in signal transmission/recovery in various types of MIMO channels are indicated.

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.

An application of a new matrix inverse in stabilizing state-space perfect control of nonsquare LTI MIMO systems

In this paper, a new definition of a right inverse of nonsquare parameter matrices is derived from MVC-related inverses of nonsquare polynomial matrices. The new definition is employed in a stabilizing state-space perfect control law for nonsquare LTI MIMO systems. A simulation example shows that the new inverse outperforms the classical minimum-norm right inverse.

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.

Finite approximations of a discrete-time fractional derivative

This paper presents new results in finite-memory modeling of a discrete-time fractional derivative. The introduced normalized finite fractional derivative is shown to properly approximate its fractional derivative original, in particular in terms of the steady-state properties. A stability analysis is also presented as well as a recursive computation algorithm is offered for finite fractional derivatives.

Switched-structure of linear MIMO controllers for positioning of a drillship on a sea surface

In the paper a multicontroller-based switchable control system structure is proposed to control nonlinear MIMO plants. The considered structure contains a set of linear feedback controllers operating together with an additional, statically decoupled loop of the control system. The nonlinear model of a drilling vessel in three degrees of freedom (3DOF) on the sea surface is used as a MIMO plant to be controlled. The system synthesis is carried out by linearization of the adopted nonlinear plant model at its nominal “operating points” that depend on the preset ship yaw angle and the velocity of the see current. Performance of the proposed control systems is illustrated by examples of simulation results carried out in MATLAB/Simulink using the nonlinear model of low-frequency (LF) motions of WIMPEY SEALAB drilling vessel.

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

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.