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Pozycja Open Access Comparison of frequency domain methods for discrete-time, linear time-varying system with invariant eigenvalues(International Society for Advanced Research, 2007-10) Orlowski, Przemyslaw; Institute of Control Engineering Szczecin University of TechnologyThe main aim of this paper is to compare and evaluate frequency methods applicable for discrete-time (DT) linear time-varying (LTV) systems, in particular: two-dimensional (time, frequency) transfer function (2D-TF), timeaveraged 2D-TF and approximated Bode diagrams calculated using SVD-DFT approach and power spectral density (PSD) properties. The main evaluation criteria is possible applicability to feedback system stability analysis. The paper begins from short theoretical background of frequency methods applicable for LTV systems. Further properties of these methods are compared and discussed on the basis of particular case of parameter controlled switching DT LTV system.Pozycja Open Access An extension of Nyquist feedback stability for linear time-varying, discrete-time systems(International Journal of Factory Automation, Robotics and Soft Computing, 2007) Orlowski, Przemyslaw; Institute of Control Engineering, Szczecin University of TechnologyThe paper concerns on extending the classical Nyquist theorem to stability analysis of linear time-varying (LTV) discrete-time (DT) feedback control systems. Frequency methods, are well- known tool for analysis and synthesis for linear time-invariant systems. Unfortunately, the methods cannot be applied for LTV systems. The main objective is to show that Bode plots approximated using SVD-DFT are adequate methods for evaluating stability margins as well as external stability for LTV systems. We assume discrete-time state space models with time dependent system matrices defined on a finite time horizon. To solve the problem we employ discrete Fourier transform and singular value decomposition of a system matrix operator as well as properties of power spectral density.Pozycja Open Access Porównanie systemów sterowania zapasami ze zmiennym opóźnieniem dostaw i zaburzonym zapotrzebowaniem: cyklicznego oraz z regulatorem PD i predyktorem Smitha(Społeczna Akademia Nauk, 2016) Orłowski, Przemysław; Chołodowicz, Ewelina; Zachodniopomorski Uniwersytet Technologiczny w Szczecinie; Zachodniopomorski Uniwersytet Technologiczny w SzczecinieIn this paper, we use a mathematical model of an inventory system with time-varying delivery delay and two control systems in order to compare their properties with different variance of noise for the goods flow optimization problem in the inventory systems. Control systems structures based on mathematical discrete equations are given for optimization: a Periodic Inventory System with adaptive maximal inventory level and Proportional-derivative Inventory Control System with Smith predictor and adaptive reference stock proposed by the authors in previous works. Parameters were selected for each of the control system structures through solving bictriterial optimization task for a specific scenario of variable market demand using SPEA2 in Matlab/Simulink. In this article, we mainly highlight which control structure reaches better performance taking account probabilistic disturbance in market demand.