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1
Content available remote Memristive devices In three-phase systems
EN
The aim of the research presented in a paper was to provide trustworthy simulation results for symmetrical three-phase systems with memristive load. The memristors in the system are combined with linear resistors in order to limit the current in the element. Linear drift model of the memristorwasconsideredinMatlabsimulations. ItisbasedonStrukovmodelwithBiolekwindow. Highnonlinearityofmemristorresultsindeformation of most of the signals in the system. Since the voltage of the neutral point is highly non-sinusoidal it affects on other signals like phase voltage, phase currents, delta voltages. A Fast Fourier Transform (FFT) is applied to chosen signals in order to provide a frequency spectrum. On this basis a Total Harmonic Distortion (THD) parameter was calculated.
PL
W pracy zaprezentowano wyniki badań symulacyjnych nad układem trójfazowym symetrycznym z obciążeniem elementami memrystorowymi. Memrystory w obwodzie odbiornika są połączone szeregowo z rezystorami liniowymi w celu ograniczenia prądu. W obliczeniach symulacyjnych przyjęto model memrystora "linear drift", bazujący na modelu Strukova z oknem Biolka. Wysoka nieliniowość elementów memrystorowych skutkuje odkształceniem większości sygnałów w obwodzie. Skoro napięcie punktu neutralnego odbiornika wykazuje wysoką nieliniowość, to skutkuje to odkształceniem pozostałych sygnałów, t.j. napięć fazowych, prądów fazowych czy napięć przewodowych. Do wybranych sygnałów zastosowano Szybką Transformatę Fouriera (FTT) w celu zaprezentowania widma częstotliwościowego. Na tej podstawie obliczono Współczynnik Zawartości Harmonicznych.
EN
In this paper, we prove the existence of a unique weak solution for a class of fractional systems of Schrodinger equations by using the Minty-Browder theorem in the Cartesian space. To this aim, we need to impose some growth conditions to control the source functions with respect to dependent variables.
EN
The global (absolute) stability of nonlinear systems with fractional positive and not necessarily asymptotically stable linear parts and feedbacks is addressed. The characteristics u = f(e) of the nonlinear parts satisfy the condition k1e ≤ f(e) ≤ k2e for some positive k1 and k2. It is shown that the fractional nonlinear systems are globally asymptotically stable if the Nyquist plots of the fractional positive linear parts are located on the right-hand side of the circles (−1/k1,−1/k2).
EN
The global stability of positive continuous-time standard and fractional order nonlinear feedback systems is investigated. New sufficient conditions for the global stability of these classes of of positive nonlinear systems are established. The effectiveness of these new stability conditions is demonstrated on simple examples of positive nonlinear systems.
EN
A new two-stage approach to the identification of polynomial Wiener systems is proposed. It is assumed that the linear dynamic system is described by a transfer function model, the memoryless nonlinear element is invertible and the inverse nonlinear function is a polynomial. Based on these assumptions and by introducing a new extended parametrization, the Wiener model is transformed into a linear-in-parameters form. In Stage I, parameters of the transformed Wiener model are estimated using the least squares (LS) and instrumental variables (IV) methods. Although the obtained parameter estimates are consistent, the number of parameters of the transformed Wiener model is much greater than that of the original one. Moreover, there is no unique relationship between parameters of the inverse nonlinear function and those of the transformed Wiener model. In Stage II, based on the assumption that the linear dynamic model is already known, parameters of the inverse nonlinear function are estimated uniquely using the IV method. In this way, not only is the parameter redundancy removed but also the parameter estimation accuracy is increased. A numerical example is included to demonstrate the practical effectiveness of the proposed approach.
EN
This investigation is concerned with robust analysis and control of uncertain nonlinear systems with parametric uncertainties. In contrast to the methodologies from the field of linear parameter varying systems, which employ convex structures of the state space representation in order to perform analysis and design, the proposed approach makes use of a polytopic form of a generalisation of the characteristic polynomial, which proves to outperform former results on the subject. Moreover, the derived conditions have the advantage of being cast as linear matrix inequalities under mild assumptions.
EN
The positivity and absolute stability of a class of fractional nonlinear continuous-time and discrete-time systems are addressed. Necessary and sufficient conditions for the positivity of this class of nonlinear systems are established. Sufficient conditions for the absolute stability of this class of fractional positive nonlinear systems are also given.
EN
This paper presents a novel approach to the design of fuzzy state feedback controllers for continuous-time non-linear systems with input saturation under persistent perturbations. It is assumed that all the states of the Takagi–Sugeno (TS) fuzzy model representing a non-linear system are measurable. Such controllers achieve bounded input bounded output (BIBO) stabilisation in closed loop based on the computation of inescapable ellipsoids. These ellipsoids are computed with linear matrix inequalities (LMIs) that guarantee stabilisation with input saturation and persistent perturbations. In particular, two kinds of inescapable ellipsoids are computed when solving a multiobjective optimization problem: the maximum volume inescapable ellipsoids contained inside the validity domain of the TS fuzzy model and the smallest inescapable ellipsoids which guarantee a minimum *-norm (upper bound of the 1-norm) of the perturbed system. For every initial point contained in the maximum volume ellipsoid, the closed loop will enter the minimum *-norm ellipsoid after a finite time, and it will remain inside afterwards. Consequently, the designed controllers have a large domain of validity and ensure a small value for the 1-norm of closed loop.
9
Content available Investigation of the memristor nonlinear properties
EN
The study of nonlinear systems is an important research topic for scientists and researchers. Memristor, for a long time, it remained just as a theoretical element and rarely appeared in the literature because of having no simple and practical realization. In this paper, we reviewed the theoretical substantiation of the memristor and conducted a practical study of its nonlinear properties using the memristor company KNOWM of series BS-AF-W 16DIP. We also investigated the characteristics of the memristor via the LabView environment.
PL
Badanie systemów nieliniowych jest ważnym tematem dla badaczy i naukowców. Memrystor przez długi czas pozostawał elementem teoretycznym i rzadko pojawiał się w literaturze z powodu braku prostej i praktycznej realizacji. W tym artykule zostały przedstawione teoretyczne uzasadnienie memrystora i badania jego właściwości nieliniowych na przykładzie memrystora firmy KNOWM serii BS-AF-W 16DIP. Zostały przeprowadzone badania charakterystyk memrystora w środowisku LabView.
EN
Backstepping is a method designed to control nonlinear systems. Formulated for the first time and described by Petar Kokotovic around 1990. The main purpose of backstepping is stabilisation of each subsystem’s structure; the function needs to be of an adequate class. The present task consists in minimising the vehicle body displacement from the position of equilibrium after it has been knocked out of it with the force exerted on the wheel, which has the purpose of simulating the wheel encountering an obstacle. The model depicts ¼ of the vehicle suspension with a conical spring or classical spring, and the damper with magnetorheological fluid which modifies damping of the suspension. The Mathcad programme facilitated the calculations, the model was designed using the Matlab – Simulink environment. Simulations were carried out on the model with the linear characteristics of a spring, as well as on the model with the implemented nonlinear spring. All the investigated cases were accompanied by the control tests that comprised building the model without control, i.e. with the constant value of damping
EN
The purpose of this work is to propose and characterize fractional descriptor reduced-order perfect nonlinear observers for a class of fractional descriptor discrete-time nonlinear systems. Sufficient conditions for the existence of these observers are established. The design procedure of the observers is given and demonstrated on a numerical example.
EN
In this study the fixed-fixed column subjected to axial Euler’s load has been investigated. The load is placed between the fixed ends of the structure and its location can be changed along column’s length. The boundary problem of free vibrations of the mentioned system has been formulated on the basis of Bernoulli – Euler theory and taking into account non-linear axial deformation relationship. Due to non-linear expressions the solution of the problem was done with small parameter method. In the paper the change of the first vibration frequency in relation to location and magnitude of the loading force was obtained. The relationship between natural vibration frequency and the amplitude is also discussed.
PL
W pracy przedstawiono analizę wpływu zmiany parametrów strony pierwotnej układu zapłonowego na wartość energii wyładowania iskrowego. Przeprowadzono również analizę zakresu zmian wartości energii wyładowania iskrowego dla zmiennych wartości wszystkich elementów strony pierwotnej układu. Badania symulacyjne przeprowadzono w autorskim programie opracowanym w środowisku Matlab-Simulink, a zweryfikowano je eksperymentalnie na stanowisku badawczym bateryjnych układów zapłonowych.
EN
The paper discusses how the parameter change of the primary side of the ignition system affects the value of spark discharge energy. The extent of changes in spark discharge energy values for changing values of all elements of the primary system is analyzed. Simulation studies are carried out in the program, developed by the authors in Matlab - Simulink and verified experimentally on a test stand for battery ignition systems.
EN
The wastewater treatment plant is classified as a complex system due to its nonlinear dynamics, large uncertainty in the disturbance inputs, multiple time scales in the internal process dynamics and multivariable structure. Aeration is an important and expensive activity that is carried out during wastewater treatment plant operation. A precise aeration control in biological processes for all the operating conditions is necessary in order to guarantee adequate biological conditions for microorganisms. Therefore, the most important is to operate the biological processes so that a minimal energy was consumed and minimal DO concentration demand was applied. The paper proposes a two advanced control systems to track the dissolved oxygen reference trajectory. A decentralized and multivariable nonlinear predictive control algorithms are designed and compared. Simulation tests for the case study wastewater treatment plant are presented.
EN
We propose a new observer where the model, decomposed in generalized canonical form of regulation described by Fliess, is dissociated from the part assuring error correction. The obtained stable exact estimates give direct access to state variables in the form of successive derivatives. The dynamic response of the observer converges exponentially, as long as the nonlinearities are locally of Lipschitz type. In this case, we demonstrate that a quadratic Lyapunov function provides a number of inequalities which guarantee at least local stability. A synthesis of gains is proposed, independent of the observation time scale. Simulations of a Düffing system and a Lorenz strange attractor illustrate theoretical developments.
EN
Fractional descriptor reduced-order nonlinear observers for a class of fractional descriptor continuous-time nonlinear systems are proposed. Sufficient conditions for the existence of the observers are established. The design procedure for the observers is given and demonstrated on a numerical example.
EN
The problem of fault detection and isolation in a class of nonlinear systems having a Hamiltonian representation is considered. In particular, a model of a planar vertical take-off and landing aircraft with sensor and actuator faults is studied. A Hamiltonian representation is derived from an Euler–Lagrange representation of the system model considered. In this form, nonlinear decoupling is applied in order to obtain subsystems with (as much as possible) specific fault sensitivity properties. The resulting decoupled subsystem is represented as a Hamiltonian system and observer-based residual generators are designed. The results are presented through simulations to show the effectiveness of the proposed approach.
EN
The paper presents algorithms for parameter identification of linear vessel models being in force for the current operating point of a ship. Advantages and disadvantages of gradient and genetic algorithms in identifying the model parameters are discussed. The study is supported by presentation of identification results for a nonlinear model of a drilling vessel.
EN
A method of analysis of the fractional descriptor nonlinear discrete-time systems with regular pencils of linear part is proposed. The method is based on the Weierstrass-Kronecker decomposition of the pencils. Necessary and sufficient conditions for the positivity of the nonlinear systems are established. A procedure for computing the solution to the equations describing the nonlinear systems are proposed and demonstrated on a numerical example.
EN
This paper presents a new concept of modeling of fractional-order nonlinear systems using a block-oriented Wiener model. The Wiener model uses two block covering a linear dynamics and a static nonlinearity. The dynamic model is described by fractional-order Orthonormal Basis Functions and the static nonlinearity by an artificial neural network.
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