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In our previous work, the authors presented an effective nonlinear proportional-integral-derivative (PID) controller by incorporating a nonlinear function. The proposed controller is based on a conventional PID control architecture, wherein a nonlinear gain is coupled in series with the integral action to scale the error. Three new tuning rules for processes represented as the first-order plus time delay (FOPTD) model were obtained by solving an optimization problem formulated to minimize three performance indices. The main feature of the proposed controller is that it preserves the numbers of tuning gains even though nonlinearity is introduced and remains easy implementation in real applications. However, due to the introduction of a nonlinear element, the stability problem of the proposed controller may be raised. This paper presents one sufficient condition in the frequency domain for the absolute stability of the nonlinear PID controller, based on circle stability theory. It is proved that the nonlinear gain used is in the sector [0, 1]. The condition of the linear block F(s) is derived for the overall feedback system to be stable. Checking the stability and the effectiveness and robustness of the feedback system for setpoint tracking are demonstrated through a set of simulation works on three processes with uncertainty.

This paper considers the problem of rational function approximation of the relay with hysteresis characteristic. The relay with hysteresis element has differential-based characteristic with memory, which is rate dependent and two-valued, involving the input signal velocity in its description. The presented model includes two ideal relay characteristics, which selection is depending on the input behavior. The rational function description is implemented for analytical approximation of the relay switching behavior. Both relay discontinuous jumps are approximated in terms of a hyperbolic tangent function, which on its own turn is replaced by continued fraction and Pade series expressions. The nearness of approximation is achieved by using one parameter descriptions for the hyperbolic tangent function. The errors of approximation of the ideal relay characteristic are also evaluated.

Lumped nonlinear transmission lines (NLTLs) have been studied for the generation of radio frequency (RF) signals in the range of the order of tens of megahertz (MHz) up to a few hundreds of MHz depending on the nonlinear element used in the LC line. The oscillations obtained at the output of these lines are applied in defense mobile platforms and communications systems. Low power NLTLs use varactor diodes as nonlinear elements, which show a strong nonlinear effect with capacitance variation of the order of 90% at their p-n junction with the applied voltage, which is an excellent performance to obtain oscillations at the line output. However, these semiconductor devices operate at low voltage, producing small voltage modulation depth (VMD), low power, and consequently reduced signal range. Looking for increasing the VMD of the signal generated with NLTLs, this work developed a RF amplifier using a metal–oxide–semiconductor field-effect transistor (MOSFET) model RD06HVF1. A 30-section line using varactor diodes MV209 as nonlinear elements can work as an RF source to obtain oscillations with a frequency of 33.3 MHz at the line output. Using SPICE simulations, it has been demonstrated that an amplifier circuit connected to the output of this varactor diode transmission line can produce an increase of the VMD produced at line output from 10.7 to 40 V approximately, thus allowing higher level power to electromagnetic wave propagation and consequently higher signal range. Experimental comparison using a printed circuit board (PCB) prototype with the corresponding simulation will be also shown.

Memristor is a kind of passive nonlinear element, which is widely used in nonlinear systems, especially chaotic systems, because of its nanometer size, nonvolatile property, and good nonlinear characteristics. Compared with general chaotic systems, chaotic systems based on memristors have richer dynamic characteristics. However, the current research mainly focuses on the binary and continuous chaotic systems based on memristors, and studies on the tri-valued and multi-valued memristor chaotic systems are relative scarce. For this reason, a mathematical model of tri-valued memristor is proposed, and the circuit characteristics of the model are studied. Furthermore, based on this model, a new chaotic system is designed and analyzed. This innovation enriches the types of chaotic systems and lays the foundation for the application of tri-valued and multi-valued memristors in nonlinear systems.

In this paper, a double-layer half-cycle generator (HCG) has been designed and built. The proposed HCG creates sinusoidal flow with 400 A peak and 5 µs pulse width which feeds RLC load with 100 kHz work frequency, within resonance mode. Previous HCGs have been designed based on saturable reactor (SR). It should be noted that SR is a nonlinear element, and it will be distanced from its desirable performance upon change of temperature and under impact; however, a double-layer HCG has been proposed with no such defects. In proposed HCG, thyristor has been used instead of SR which is controllable, and it has none of aforementioned problems. Also, when SR is eliminated, its reverse retrieval needs no minority carriers. This way, sweep-out circuit may be also eliminated. From among other advantages of proposed HCG, reduction in number of circuit layers may be referred to, comparing to previous HCG. This results in reduction in number of equipment which in turn optimizes proposed HCG, in terms of volume and manufacturing costs. Finally, proposed HCG has been simulated in Matlab, while it has been implemented practically. Comparing simulation results and laboratory sample confirms correctness of relationships, in analytical design of HCG.

The integrator is an important building block in circuit design and its transfer characteristic is inherently frequency-dependent. When it is implemented as an $RC$ op-amp circuit, a nonlinear element (the amplifier) is placed within a frequency-dependent feedback loop. Conventional techniques allow us to obtain the nonlinear error easily at certain frequencies only. Furthermore, when the integrator is periodically reset, the circuit is not in steady-state and conventional techniques assuming a steady-state behavior do not apply. It is not obvious how the actual error relates to the circuit parameters when the integrator is driven with a wideband signal. In this paper we present an approach to quickly estimate the normalized mean squared error (NMSE) as a function of the circuit and signal parameters. We show that, to first-order, the NMSE is proportional to the ratio of the signal bandwidth and the dominant pole of the integrator. For an integrator with reset, the signal builds up from zero and results in an additional, integration-time dependent NMSE reduction.

We propose a novel equivalent model for a quantizer with noisy input (the desired signal corrupted by measurement noise). It presents the quantizer output as a sum of the desired signal after it passes through a nonlinear element with a known equivalent transfer function and an equivalent additive white noise. The equivalent transfer function takes the form of a conditional expectation of the quantizer output given the desired signal portion of its input. The proposed model proves to be effective for the analysis and design of MIMO systems employing low-resolution quantizers (analog to digital and digital to analog converters, ADCs and DACs, respectively). We also demonstrate the efficacy of the model through several example applications for 1) the design of digital dither that mitigates the effect of DAC quantization error in a MIMO transmitter and significantly reduces the DAC resolution requirement; 2) the determination of the minimal ADC resolution required for operation of conventional MIMO receivers designed for infinite-resolution ADC arrays, without incurring significant performance degradation; and 3) the design of simple MIMO receivers (ML and MMSE) that mitigate the effect of insufficient ADC resolution, thereby extending the receiver SNR operating range without an undue complexity increase.

B.B. Saidov1, 2, matem.1994@mail.ru, V.I. Tambovtsev1, tamboval@mail.ru, I.I. Prokopov1, Prokopovii@susu.ru 1 South Ural State University, Chelyabinsk, Russian Federation, 2 Tajik Technical University named after academician M.S. Osimi, Dushanbe, Republic of Tajikistan. Саидов Бехруз Бадридинович, аспирант кафедры инфокоммуникационных технологий, Южно-Уральский государственный университет, г. Челябинск; Таджикский технический университет имени академика М.С. Осими, г. Душанбе, Республика Таджикистан; matem.1994@mail.ru. Тамбовцев Владимир Иванович, д-р физ.-мат. наук, заслуженный изобретатель СССР, действующий член Нью-Йоркской академии наук, профессор кафедры инфокоммуникационных технологий, Южно-Уральский государственный университет, г. Челябинск; tamboval@mail.ru Прокопов Игорь Игоревич, доцент кафедры инфокоммуникационных технологий, Южно- Уральский государственный университет, г. Челябинск; Prokopovii@susu.ru. Introduction. In many physical processes, the spectrum of the modulated signal is transferred to the low-frequency region, which also manifests itself in active dielectrics in radio sound. In the general case, the analysis of the spectrum transformation process is a very difficult task related with solving a system of nonlinear differential equations. And in the accepted form, the principle of superposition is not applicable here, since the parameters of the output signal cannot be determined by algebraic summation of the signals received separately from each source. The spectrum of an input amplitude- modulated signal is nonlinearly related to the spectrum at the output. Aim. The conversion of the current spectrum under supplying an amplitude-modulated voltage to an active non-linear element with a non-linear current-voltage characteristic is considered. Materials and methods. In the analysis of the spectral transformation, a power approximation of the current-voltage characteristic in the form of a polynomial of the third degree with trigonometric functions is used. In the examples, spectrum transformations for a mono signal, amplitude-modulated signal, and beats are considered. Application of amplitude modulation methods is essential for transferring the spectrum of the signal to the low frequency region. Results. A graphical representation of the dependence of the current function on time for an AM signal and beats, as well as their spectral representation, is given. Conclusion. The paper analyzes the transformation of the signal spectrum for the current when applying any, but amplitude-modulated voltage on the ohmic nonlinear element. The carrier signal is represented as a harmonic trigonometric function of the cosine of the current time. However, signal spectrum conversion has not related with detection. Введение. Во многих физических процессах наблюдается перенос спектра модулированного сигнала в низкочастотную область, что проявляется и в активных диэлектриках при радиозвуке. В общем случае анализ процесса преобразования спектра является очень сложной задачей, связанной с решением системы нелинейных дифференциальных уравнений. И в принятой форме принцип суперпозиции здесь не применим, поскольку параметры выходного сигнала не могут быть определены алгебраическим суммированием сигналов, получаемых раздельно от каждого источника. Спектр входного амплитудно-модулированного сигнала нелинейным образом связан со спектром на выходе. Цель исследования. Рассматривается преобразование спектра тока при подаче амплитудно-модулированного напряжения на активный нелинейный элемент с нелинейной вольтамперной характеристикой. Материалы и методы. В анализе спектрального преобразования применяется степенная аппроксимация вольтамперной характеристики в виде полинома третьей степени с тригонометрическими функциями. В примерах рассматриваются преобразования спектра для моносигнала, амплитудно-модулированного сигнала и биений. Применение амплитудных методов модуляции необходимо для переноса спектра сигнала в область низких частот. Результаты. Приводится графическое представление зависимости функции тока от времени для амплитудно-модулированного сигнала и биений, а также их спектрального представления. Заключение. В работе анализируется преобразование спектра сигнала для тока при подаче амплитудно-модулированного напряжения на омическом нелинейном элементе. Несущий сигнал представлен в виде гармонических тригонометрических функций косинуса текущего времени. Однако преобразование спектра сигнала никак не связано с детектированием.

A proper understanding of the complex physics associated with nonlinear dynamics can improve the accuracy of predictive engineering models and provide a foundation for understanding nonlinear response during environmental testing. Several researchers and studies have previously shown how localized nonlinearities can influence the global vibration modes of a system. This current work builds upon the study of a demonstration aluminum aircraft with a mock pylon with an intentionally designed, localized nonlinearity. In an effort to simplify the identification of the localized nonlinearity, previous work has developed a simplified experimental setup to collect experimental data for the isolated pylon mounted to a stiff fixture. This study builds on these test results by correlating a multi-degree-of-freedom model of the pylon to identify the appropriate model form and parameters of the nonlinear element. The experimentally measured backbone curves are correlated with a nonlinear Hurty/Craig-Bampton (HCB) reduced order model (ROM) using the calculated nonlinear normal modes (NNMs). Following the calibration, the nonlinear HCB ROM of the pylon is attached to a linear HCB ROM of the wing to predict the NNMs of the next-level wing-pylon assembly as a pre-test analysis to better understand the significance of the localized nonlinearity on the global modes of the wing structure.

To realize efficient nonlinear metamaterials, we investigate a method for enhancing the local electric field in a metamolecule composed of two radiatively coupled cut-wire resonators where resonance of the cut-wire resonators and low-group-velocity propagation of an incident electromagnetic wave simultaneously occur. Numerical analysis shows that the local electric field in the metamolecule can be enhanced by decreasing the electrode size and the gap of the capacitor structure of the cut-wire resonators while keeping the equivalent electrical circuit parameters of the metamolecule constant. We measure and compare the threshold incident power for a gas discharge in the metamolecule fabricated in our previous study and that in the metamolecule with shrunken capacitor structures. The experiment reveals that shrinking the capacitor structure while keeping the resonance frequency of the metamolecule decreases the threshold incident power for a gas discharge and may increase the gas pressure where the threshold incident power is minimum. Further development of this work will enable us to realize efficient nonlinear metamaterials that have atmospheric-pressure gas as a nonlinear element., 11 pages, 4 figures. This is the version of the article before peer review or editing, as submitted by an author to Journal of Physics D: Applied Physics. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at https://doi.org/10.1088/1361-6463/ac0d50

Operational amplifiers (opamps) are often designed in stages. Distortion analysis of multistage opamps is challenging due to multiple non-linearity sources. Therefore, one effective analysis method is to consider a multistage opamp model as a cascade of condensed stages, with each stage modelled by one weakly non-linear element. Then, in order to obtain a satisfactory distortion model, accurate characterisation of the non-linearity of each stage is necessary. In this Letter, the authors propose an analytical calculation method for modelling the weak non-linearity of an amplifier stage consisting of several interconnected transistors. A stage circuit model created by this method can be used to produce analytical harmonic distortion characterisation of closed-loop circuits with peripheral elements. Numerical accuracy of the analytical method has been validated by transistor-level simulation.

© 2019 Elsevier Ltd A new framework is developed for the fast and accurate analysis of large-scale engineering structures considering material nonlinearity. A fundamental linear model is constructed first by assigning nominal linear material parameters for each of the potentially nonlinear elements, and then, for each nonlinear element, a Nonlinear Deviation Force Vector (NDFV) is defined as the difference between the true nonlinear nodal force vector and the vector calculated using the nominal linear material parameters. In this way, the displacement of the nonlinear model can be expressed as a linear combination of a set of basis solutions of the fundamental linear model. These basis solutions include nodal displacement solutions due to the applied load and all unit components of NDFVs of nonlinear elements. Therefore, the values of these NDFVs, as combination coefficients in the displacement expression are the only unknowns for the whole structure and can be determined by considering a much smaller nonlinear equation system. It is noteworthy that no approximation is introduced in the proposed model order reduction scheme and the new scheme can be applied to the iterative solution process of both static and dynamic problems. Numerical examples are presented to show the effectiveness of the proposed scheme.

We present a novel nonlinear formulation for modeling reactive-compositional flow and transport in the presence of complex phase behavior due to a combination of thermodynamic and chemical equilibria in multi-phase systems. We apply this formulation to model precipitation/dissolution of minerals in reactive multiphase flow in subsurface reservoirs. The proposed formulation is based on the consistent element balance reduction of the molar (overall composition) formulation. To predict the complex phase behavior in such systems, we include the chemical equilibrium constraints to the multiphase multicomponent negative flash calculations and solve the thermodynamic phase and chemical phase equilibria simultaneously. In this solution, the phase equilibrium is represented by the partition coefficients, whereas the chemical equilibrium reaction is represented by the activity coefficients model. This provides a generic treatment of chemical and thermodynamic equilibrium within the successive substitution loop of mulmultiphase flash to accommodate chemical equilibrium reactions (precipitation and dissolution reactions). Equilibrium Rate Annihilation matrix allows us to reduce the governing component conservation equations to element conservation equations, while the coupling between chemical and thermodynamic equilibrium is captured by a simultaneous solution of modified multiphase flash equations. The element balance equation written in terms of overall component mole fractions is modified and defined in terms of element mole fractions. Therefore, the primary set of governing equations are the element balance equations and the kinetic equations. This element composition of the mixture serves as an input to the modified multiphase flash computations, whereas the output is fractions of components in each phase, including solids. The nonlinear element–based governing equations are solved with the modified version of the operator-based linearization (OBL) approach where the governing equations are formulated in terms of space- and state-dependent parameters constrained by the solution of the extended multiphase flash. The element balance molar formulation along with the modified multiphase flash has been tested in a simple transport model with dissolution and precipitation reactions. The simulation of multidimensional problems of practical interest has been performed using the adaptive OBL technique. This is the first time when a robust multiphase multicomponent flash based on element fractions is coupled with an element balance–based compositional formulation and tested for multidimensional problems of practical interest. The proposed technique improves both robustness and performance of complex chemical models.

In this work, a harmonically excited generalized two degree of freedom nonlinear system is used to manifest the functions of both the vibration absorber and energy harvester simultaneously. The generalized system has been reduced to a linear primary system with linear/nonlinear absorber and harvester or nonlinear primary system with linear/ nonlinear absorber and harvester. Multi harmonic balance method (MHBM) along with arc length continuation is used for generating frequency response plots for different absorber and energy harvester system parameters with constant primary system parameters and excitation amplitude. The frequency response plot shows multiple branches of stable periodic solutions and jump at certain frequency ranges for systems with nonlinearity. The absorber and energy harvester parameters are optimized using an optimization procedure based on genetic algorithm in combination with response surface methodology. The method is validated with analytical solutions available in the literature for a linear primary system with linear absorber and harvester and nonlinear primary system with nonlinear absorber alone. This study demonstrates that the proposed optimization framework along with MHBM is suitable for generating the optimal frequency response for multi functional energy harvesting systems or systems with nonlinear absorber. The frequency response plots with optimal parameter values reiterates the fact that the absorber system with nonlinear element perform better compared to its linear counterpart over a wider band of frequencies. This study also reports the comparison of the performance of a combined nonlinear absorber harvester system with that of a nonlinear energy sink (NES) absorber harvester system.

Frequency multipliers are used in electronic devices to generate spectrally pure sinusoidal signals in the frequency range from a few to tens of GHz. The multipliers are used to multiply the frequency of highly stable but more low-frequency devices with the subsequent extraction of the necessary harmonics from the frequency spectrum of the received microwave range. The frequencies selected after multiplication (set) have significantly higher energy, spectral and range characteristics, which allows them to be used as local oscillators and synthesizers in receiving and transmitting systems. The authors of this paper theoretically substantiate and practically demonstrate the possibility of an unconventional implementation of a microstrip multiplier of the microwave range based on a directional traveling wave filter. The proposed implementation does not require the use of active semiconductor elements. The well-known circuit and technological principles for the creation of microstrip microwave multipliers are considered in the paper. The features, problems and shortcomings arising from their implementation are analyzed. The effectiveness of using the balanced circuit for frequency multiplication is confirmed. A list of mandatory requirements and conditions necessary for the implementation of the microwave multipliers is given. It is demonstrated that the features of the microstrip travelling-wave filter are identical to the conditions and requirements for the implementation of balanced multipliers. It is shown and substantiated how an unconventional implementation of a passive microwave multiplier is possible due to the electromagnetic interaction of the input and output nodes of such a filter with an annular travelling-wave resonator. Using the example of modifying a block diagram of a directional filter into a multiplier circuit, the possibility of creating a microwave doubler is confirmed by separating a given frequency from the frequency spectrum of a traveling-wave ring resonator.

For the nonlinear, time-variable and unpredictable environment (such as the manipulator workspace that has many random and moveable obstacles), a Hammerstein adaptive (HA) impedance controller based on a Hammerstein impedance model is proposed in this paper. The model consists of a static nonlinear element and a linear dynamic element, which can describe the nonlinearity of the environment. Then, an adaptive law is designed by a Lyapunov function, which can adjust the parameters of the static nonlinear element, so that the model has good adaptability and robustness for the environment. By introducing a parameters self-adjust model-free adaptive controller as the inner position controller, the HA impedance control system is built, which does not require the knowledge of the robot dynamics. In order to verify the force-control performance of the proposed control scheme, some simulations and experiments are done on a bionic wrist joint actuated by pneumatic muscles. Compared with the conventional impedance controller with constant parameters, experimental results demonstrate that HA impedance controller has better force tracking characteristic and can restrict the contact force effectively, no matter how the external environment changes, which increases the safety between robots and humans or operation objects.

В роботi представлена модифiкована хаотична схема Чуа, яка реалiзує хаотичну поведiнку. Приведена система диференцiйних рiвнянь, що описує дану схему при певних значеннях системних параметрiв та початкових умов, генерує хаотичний атрактор. Ця схема має простий нелiнiйний елемент, спроектований так, щоб мати кусково-лiнiйну характеристику, тобто комбiнацiю операцiйного пiдсилювача з двома дiодами, що ввiмкненi назустрiч один одному. Для реалiзацiї нелiнiйностi, для двох дiодiв не потрiбно окремого джерела живлення, достатньо лише одного двополярного живлення для операцiйного пiдсилювача. Приведено схему для дослiдження нелiнiйного елементу та результати комп’ютерного моделювання, тобто вольт-амперну характеристику (ВАХ) при певних значеннях номiналiв компонентiв схеми. Ця модифiкована схема Чуа, яка генерує хаотичний та контрольований атрактор з фiксованим перiодом, може використовуватися в сучасних системах передавання та приймання iнформацiї. Управлiння хаотичними коливаннями є досить важливим процесом в радiотехнiцi та телекомунiкацiях. Число видiлених окремих перiодичних (контрольованих) атракторiв може використовуватися як ключi для маскування iнформацiйного носiя. За допомогою програмного середовища MultiSim проведено схемотехнiчний аналiз i представлено результати моделювання нелiнiйного елемента та модифiкованої хаотичної схеми Чуа. Дослiджена поведiнка системи за допомогою чисельного моделювання, використовуючи вiдомi iнструменти нелiнiйної теорiї, такi як хаотичний атрактор i часовi розподiли хаотичних координат. Приведено опис порогового методу для здiйснення управлiння хаотичними коливаннями та представлено результати практичного застосування даного методу до модифiкованої хаотичної схеми Чуа. Практичними результатами є видiленi 2- та 3-перiоднi контрольованi орбiти iз хаотичного атрактора. Introduction. General scientific fields where can be used circuits that realize chaotic behavior and generate chaotic oscillations are presented.Methods for control of chaotic oscillations are also presented. For modelling, analysis and demonstrate results was selected MultiSim software environment. Modelling and Analysis of Non-Linear Element. This modified Chua’s circuit has a simple non-linear element, designed to have a piecewise-linear characteristic, that is, a combination of an opamp with two diodes that are mutually inline. For realization of nonlinearity, for two diodes do not need a separate power source, only one bipolar power source for the opamp is enough. The scheme for modelling of the nonlinear element and the results of computer simulation, i.e. the volt-ampere characteristic (VAC) at certain values of the components of the scheme’s nominal values, is presented. This modified Chua’s circuit, which generates a chaotic and controlled attractor with a fixed period, can be used in modern transmission and reception systems of information. Modeling and Analysis of the Modified Chaotic Chua’s Generator. System’s behavior is investigated through numerical simulations, by using well known tools of nonlinear theory, such as chaotic attractor and time distributions of the chaotic coordinates. Threshold Method for Control of Chaotic Oscillations. System of equations that realize chaotic oscillations of Chua’s circuit is presented. Using threshold method was practical realization of the control of chaotic attractor. This modified Chua’scircuit that generate a chaotic and controlled attractor with a fixed period can be used in modern systemstransmitting and receiving information. Number of periodic (controlled) attractor can be used as a keys formasking of information carrier. Conclusions. For the first time was used threshold method forcontrol of chaotic oscillations for modified Chua’schaotic generator. This modified Chua’s circuit thatgenerate a chaotic and controlled attractor with afixed period can be used in modern systems transmittingand receiving information. Number of periodic(controlled) attractor can be used as a keys for maskingof information carrier. В работе представлена модифицированная хаотичная схема Чуа, которая реализует хаотическое поведение. Эта схема имеет простой нелинейный элемент, спроектированный так, чтобы иметь кусочно-линейную характеристику. Эта модифицированная схема Чуа, которая генерирует хаотический и контролируемый аттрактор с фиксированным периодом, может использоваться в современных системах передачи и получения информации. Количество периодических (контролируемых) аттракторов может использоваться как ключи для маскировки информационного носителя. С помощью программной среды MultiSim проведен схемотехнический анализ и представлены результаты моделирования нелинейного элемента и модифицированной хаотической схемы Чуа. Исследовано поведение системы с помощью численного моделирования, используя известные инструменты нелинейной теории, такие как хаотичный аттрактор и временные распределения хаотических координат. Приведено описание порогового метода для осуществления управления хаотическими колебаниями и представлены результаты практического применения данного метода к модифицированной хаотической схеме Чуа. Практическими результатами являются выделенные 2- и 3-периодные контролируемые орбиты с хаотического аттрактора.

Recently there has been increased research interest in the study of the hybrid dynamical systems (Sun & Ge, 2005) and (Li et al., 2005). These systems involve the interaction of discrete and continuous dynamics. Continuous variables take the values from the set of real numbers and the discrete variables take the values from finite set of symbols. The hybrid systems have the behaviour of an analog dynamic system before certain abrupt structural or operating conditions are changed. The event driven dynamics in hybrid control systems can be described using different frameworks from discrete event systems (Cassandras & Lafortune, 2008) such as timed automata, max-plus algebra or Petry nets. For dynamic systems whose component are dominantly discrete event, main tools for analysis and design are representation theory, supervisory control, computer simulation and verification. From the clasical control theory point of view, hybrid systems may be considered as a switching control between analog feedback loops. Generally, hybrid systems can achieve better performance then non-switching controllers because they can to reconfigure and reorganize their structures. For that is necessery correct coordination of discrete and analog control variables. The mathematical model for real process, generally, has the Hammerstein-Wiener form (Crama & Atkins, 2001) and (Zhao & Chen, 2006). It means that on the input and output of the process are present nonlinear elements (actuator and sensor). Here we will consider Hammerstein model which has the input saturation as nonlinear element. That is the most frequent nonlinearity encountered in practice (Hippe, 2006). Also, unmodeled dynamics with matching condition is present. As a control strategy will be used switching control. The switched systems can be viewed as higher abstraction of hybrid systems. The design of switching controllers having guaranted stability, known as the picewise linear LQ control (PLC), is first considered in (Wredenhagen & Belanger, 1994). The picewise linear systems are systems that have different linear dynamics in different regions of the continuous state space (Johansson, 2003). The PLC control has the associated switching surfaces in form of positively invariant sets and yields a relatively low-gain controller. In the LHG (low-and-high gain) design a low gain feedback law is first designed in such a way

International audience; Kerr comb generation is usually based on the nonlinear dynamics of the intracavity field in a whispering-gallery-mode resonator pumped by a continuous-wave laser. However, using a pulsed instead of a continuous-wave pump opens an alternative research avenue from both the theoretical and experimental viewpoints, as it permits us to tailor the spectral properties of ultrashort pulse trains with a single passive nonlinear element. In this article we study the dynamics of Kerr optical frequency combs when the whispering-gallery-mode resonator is pumped by a synchronous pulse train. We propose a model that is based on an extension of the Lugiato-Lefever equation, which accounts for both the pulsed nature of the pump and the mismatch between the free-spectral range of the resonator and the repetition rate of the pulse train. We lay a particular emphasis on the effect of pump-cavity desynchronization on the spectral shape of the output combs. The numerical simulations are successfully compared with experimental measurements where the optical pulses are generated via time-lens soliton compression, and the resonator is a millimeter-size magnesium fluoride resonator with a billion quality factor at the pump wavelength.

Non-intrusive model-order reduction methods are beneficial for reducing the computational costs of dynamic analysis of nonlinear finite element models, developed in programs that do not release nonlinear element forces and Jacobians (e.g., commercial software). One of the key aspects for developing a displacement-based non-intrusive reduced order model is a proper construction of the reduction basis, which has to be small in size, easy to compute, and must span the subspace in which the full solution lives. In this paper, we propose a non-intrusive model order reduction method based on modal derivatives stemming from a selected set of vibration modes of the linearized system. By definition, modal derivatives do not require the knowledge of the applied load. We name this load-independent basis. The method we propose is also simulation-free, meaning that no nonlinear dynamic simulations of the full model are required to construct the reduction basis. The method is tested with three examples of increasing complexity., Mechanical Systems and Signal Processing, 147, ISSN:0888-3270, ISSN:1096-1216

The digital implementation of a nonlinear audio circuit often employs the Newton-Raphson (NR) method for solving the corresponding system of implicit ordinary differential equations in the discrete-time domain. Although its quadratic convergence speed makes NR attractive for real-time audio applications, quadratic convergence is not always guaranteed, since it depends on initial conditions, and also divergence might occur. For this reason, especially in the context of Virtual Analog modeling, techniques for increasing the robustness of NR are in order. Among the various approaches, the Wave Digital (WD) formalism recently showed potential to rethink traditional circuit simulation methods. In this manuscript, we discuss an original formulation of the NR method in the WD domain for the solution of audio circuits with multiple one-port nonlinearities. We provide an in-depth theoretical analysis of the proposed iterative method and we show how its quadratic convergence strongly depends on the free parameters (called port resistances) introduced when modeling the reference circuit in the WD domain. In particular, we demonstrate that the size of the basin where the WD NR solver can be initialized to converge on a solution with quadratic speed is a function of the free parameters. We also show that by setting each port resistance value as close as possible to the derivative w.r.t. current of the nonlinear element $v$ – $i$ characteristic we keep the basin size large. We finally implement an audio ring modulator circuit with four diodes in order to test the proposed iterative method.

The integrating process with time delay (IPTD) is a fundamentally unstable open-loop system due to poles at the origin of the transfer function, and designing controllers with satisfactory control performance is very difficult because of the associated time delay, which is a nonlinear element. Therefore, this study focuses on the design of an intelligent proportional-integral-derivative (PID) controller to improve the regulatory response performance to disturbance in an IPTD, and addresses problems related to optimally tuning each parameter of the controller with a real coded genetic algorithm (RCGA). Each gain of the nonlinear PID (NPID) controller consists of a product of the gains of the linear PID controller and a simple nonlinear function. Each of these nonlinear functions changes the gains in the controller to on line by nonlinearly scaling the error signal. A lead-lag compensator or first-order filter is also added to the controller to mitigate noise, which is a disadvantage of ideal derivative action. The parameters in the controller are optimally tuned by minimizing the integral of time-weighted absolute error (ITAE) using a RCGA. The proposed method is compared with three other methods through simulation to verify its effectiveness.

Circuit quantum electrodynamics, where photons are coherently coupled to artificial atoms built with superconducting circuits, has enabled the investigation and control of macroscopic quantum-mechanical phenomena in superconductors. Recently, hybrid circuits incorporating semiconducting nanowires and other electrostatically-gateable elements have provided new insights into mesoscopic superconductivity. Extending the capabilities of hybrid flux-based circuits to work in magnetic fields would be especially useful both as a probe of spin-polarized Andreev bound states and as a possible platform for topological qubits. The fluxonium is particularly suitable as a readout circuit for topological qubits due to its unique persistent-current based eigenstates. In this Letter, we present a magnetic-field compatible hybrid fluxonium with an electrostatically-tuned semiconducting nanowire as its non-linear element. We operate the fluxonium in magnetic fields up to 1T and use it to observe the $\varphi_0$-Josephson effect. This combination of gate-tunability and field-compatibility opens avenues for the exploration and control of spin-polarized phenomena using superconducting circuits and enables the use of the fluxonium as a readout device for topological qubits.

SU(1,1) interferometers, based on the usage of nonlinear elements, are superior to passive interferometers in phase sensitivity. However, the SU(1,1) interferometer cannot make full use of photons carrying phase information as the second nonlinear element annihilates some of the photons inside. Here we focus on improving phase sensitivity and propose a different protocol based on a modified SU(1,1) interferometer, where the second nonlinear element is replaced by a beam splitter. We utilize two coherent states as inputs and implement balanced homodyne measurement at the output. Our analysis suggests that the protocol we propose can achieve the sub-shot-noise-limited phase sensitivity and is robust against photon loss as well as background noise. Our work is important for practical quantum metrology using SU(1,1) interferometers.

This paper focuses on the bogie-carbody nonlinear dynamic interaction of a Shinkansen high-speed rail vehicle. The Euler-Bernoulli beam model is used to simulate vertical elastic vibrations of the carbody. As a novelty, the traction rod that connects the bogie frame and the carbody is considered a nonlinear element. The equivalent linearization method is used to analyze the nonlinear vehicle system in the frequency domain. The analytical spectrum solution was compared with the measured data from the running test and the numerical solution in the time domain. When the dynamic interaction due to the carbody’s flexibility is considered as nonlinear rather than linear, the maximum amplitude of the bounce acceleration relevant to the first bending mode increases by 38.2 percent at a travel speed of 300 km/h. Ride comfort improvement can be achieved with the inclusion of the nonlinear interaction. It is also feasible to manipulate the vehicle’s ride comfort by altering its bogie-base The authors gratefully acknowledge precious remarks and valuable propositions from Professor Takahiro Tomioka during this research. The third author would also like to acknowledge the funds provided by the NVTRail project (Noise and Vibrations induced by railway traffic in tunnels: an integrated approach), funded by FEDER funds through COMPETE2020 and by national funds (PIDDAC) through FCT/MCTES, with grant reference POCI-01-0145-FEDER-029577; and by the VIBWAY project (Fast computational tool for railwayinduced vibrations and re-radiated noise assessment), with reference RTI2018-096819-B-I00, supported by the Ministerio de Ciencia e Innovación, Retos de Investigación 2018

In this paper we report the control and synchronisation of chaos in a memristive Murali–Lakshmanan–Chua (MLC) circuit. This circuit, introduced by the present authors in 2013, is basically a non-smooth system having two discontinuity boundaries by virtue of it having a flux-controlled active memristor as its nonlinear element. While the control of chaos has been effected using state feedback techniques, the concept of adaptive synchronisation and observer-based approaches have been used to effect synchronisation of chaos. Both these techniques are based on state space representation theory which is well known in the field of control engineering. As in our earlier works on this circuit, we have derived the Poincare discontinuity mapping (PDM) and zero time discontinuity mapping (ZDM) corrections, both of which are essential for realising the true dynamics of non-smooth systems. Further, we have constructed the observer- and controller-based canonical forms of the state-space representations, have set up the Luenberger observer, derived the controller gain vector to implement state feedback control and calculated the gain matrices for switch feed back and finally performed parameter estimation for effecting observer-based adaptive synchronisation. Our results obtained by numerical simulation include time plots, phase portraits, estimation of the parameters and convergence of error graphs and phase plots showing complete synchronisation.

Systems containing linear first-order dynamics and static nonlinear elements (i.e., nonlinear elements whose outputs depend only on the present value of inputs) are often encountered; for example, certain automobile engine subsystems. Therefore, system identification of static nonlinear elements becomes a crucial component that underpins the success of the overall identification of such dynamical systems. In relation to identifying such systems, we are often required to identify models in differential equation form, and consequently, we are required to describe static nonlinear elements in the form of functions in time domain. Identification of such functions describing static elements is often a black-box identification exercise; although the inputs and outputs are known, correct mathematical models describing the static nonlinear elements may be unknown. Therefore, with the aim of obtaining computationally efficient models, calibrating polynomial models for such static elements is often attempted. With that approach comes several issues, such as long time requirements to collect adequate amounts of measurements to calibrate models, having to test different models to pick the best one, and having to avoid models over-fitting to noisy measurements. Given that premise, this paper proposes an approach to tackle some of those issues. The approach involves collecting measurements based on an uncertainty-driven Active Learning scheme to reduce time spent on measurements, and simultaneously fitting smooth models using Gaussian Process (GP) regression to avoid over-fitting, and subsequently picking best fitting polynomial models using GP-regressed smooth models. The principles for the single-input-single-output (SISO) static nonlinear element case are demonstrated in this paper through simulation. These principles can easily be extended to MISO systems.

This paper introduces a computational strategy to collaboratively develop the Galerkin Finite Volume Method (GFVM) as one of the most straightforward and efficient explicit numerical methods to solve structural problems encountering material nonlinearity in a small limited area, while the remainder of the domain represents a linear elastic behavior. In this regard, the Element Free Galerkin method (EFG), which is remarkably robust and accurate, but presumably more expensive, has locally been employed as a nonlinear sub-model to cover the shortcomings of the GFVM in the elastoplastic analysis. Since the formulations of these two methods are fundamentally different, the iterative zonal coupling has been accomplished using overlapping Multi-Grid (MG) patches with a non-matching interface and Iterative Global/Local (IGL) approach. The main property of such an algorithm is its non-intrusiveness, which means the complex nonlinear EFG solver is locally utilized over an elastic global GFVM without any geometric modification. This method is verified and investigated with available analytical and numerical solutions which gave quiet promising results showing the robustness and accuracy of the method. The Moving Least-Square approximation (MLS) has widely been applied on transfer level due to the non-conforming interface at the patch edges, and easily allows us to attach complex geometries with different mesh patterns. The new type of Quasi-Newtonian accelerator is adopted on the global material constitutive matrices and its convergence property and accuracy is compared with dynamic Aitken accelerators for two-dimensional problems in MATLAB. Finally, various accelerator types and mapping strategies are also concerned in the examination.

Запропоновано метод збільшення глибини виявлення металевих об‘єктів шляхом використання нелінійних властивостей окислених металів. Структура метал-оксид, що виникає в металевих об‘єктах, які знаходяться в середовищі, що містить активний ки-сень, розглядається як електричний перехід, що має нелінійну вольт-амперну характе-ристику. Це дозволяє ідентифікувати метал на частотах кратних частоті опромінення. Наводяться результати досліджень, що підтверджують працездатність запропонованого методу. A method for increasing the depth of detection of metal objects by using the nonlinear properties of oxidized metals is proposed. The metal oxide structure that occurs in metal objects that are in an environment containing active oxygen is considered to be an electrical transition that has a nonlinear volt-ampere characteristic. This allows you to identify the metal at frequencies multiples of the irradiation frequency. The results of researches confirming efficiency of the offered method are resulted.

This paper addresses a phenomenon caused by resetting only one of the two states of a so-called second order 'Constant in gain Lead in phase' (CgLp) element. CgLp is a recently introduced reset-based nonlinear element, bound to circumvent the well-known linear control limitation - the waterbed effect. The ideal behaviour of such a filter in the frequency domain is unity gain while providing a phase lead for a broad range of frequencies, which clearly violates the linear Bode's gain phase relationship. However, CgLp's ideal behaviour is based on a describing function, which is a first order approximation that neglects the effects of higher order harmonics in the output of the filter. Consequently, achieving the ideal behaviour is challenging when higher order harmonics are relatively large. It is shown in this paper that by resetting only one of the two states of a second order CgLp, the nonlinear filter will act as a linear one at a certain frequency, provided that some conditions are met. This phenomenon can be used to the benefit of reducing higher order harmonics of CgLp's output and achieving the ideal behaviour and thus better performance in terms of precision.

Summarization: The classical Chua’s circuit that realizes chaotic behavior is presented. This circuit having a simple nonlinear element designed to be accurately piecewise-linear modelled. The circuit was modelled by using MultiSim software environment. The system’s behavior is investigated through numerical simulations, by using well-known tools of nonlinear theory, such as chaotic attractor and time distributions of the chaotic coordinates. Using threshold method was practical realization of the control of chaotic attractor. This classical Chua’s circuit that generates a chaotic and controlled attractor with a fixed period can be used in modern systems transmitting and receiving information. Number of periodic (controlled) attractor can be used as a key for masking of information carrier. Παρουσιάστηκε στο: 12th Chaotic Modeling and Simulation International Conference

In the present world, distributed signal processing plays a significant role in applications ranging from surveillance and tracking to exploration and monitoring. In this paper, an online distributed framework of spatio-temporal Wiener model is presented. A conventional Wiener model is extended to nonlinear distributed parameter systems (DPSs), which comprises of a linear time-invariant (LTI) system in series with a static nonlinear element. The standard Wiener model identification framework is reformulated as the minimization of multiple constrained optimization subtasks that get solved using alternating direction method of multipliers (ADMM) along with coordinate descent techniques. DPSs are significantly used in industrial processes e.g. thermal process, fluid process, etc. Almost all the real-time data contain non-linearity in them which is modeled using several methods: Wiener modeling is one of them. Adaptive as well as distributed implementation of such model is considered to take the advantages of both adaptive and distributed signal processing. The proposed method overcomes the limitations concerning fusion center (FC) and least-square (LS) based approaches. Unknown parameters of Wiener DPS are identified in an adaptive and distributed manner. To dignify the effectiveness of the proposed methodology, simulations on a catalytic rod (an example of a parabolic system) are illustrated.

The small parameter method, implemented in frequency domain, was used for the analytical analysis of nonlinear electrical circuits of electrotechnical systems. To have the possibility of calculations in frequency domain, the automated method of forming orthogonal harmonic components of electrical magnitudes based on the algorithm of discrete convolution was used. The characteristic of a nonlinear element was represented by the polynomial function of third degree. It was shown that application of the small parameter method with its realization in frequency domain makes it possible to simplify the process of analyzing electrical circuits with nonlinear elements by automating calculations in the mathematical package. Analytical and numerical calculations of a circuit with actively inductive load demonstrated sufficient accuracy of the proposed method, the relative error for the main harmonic of current did not exceed 6 %. The conducted comparative analysis of the proposed small parameter method with the classic small parameter method on the example of calculation of an electrical circuit with RL load showed that the developed method provides better adequacy of results and high calculation accuracy in comparison with the existing one. Relative error by amplitude of first and third harmonics of current does not exceed 2.5 %, and by phase, it does not exceed 1.042·10 -3 %. The method of numerical structural modeling was used to determine the reference values of current of the researched circuit. The results of the research can be used in calculations of electrotechnical devices, containing semiconductor components and electrical devices with nonlinear characteristics. In addition, the obtained results will make it possible to improve the processes of active compensation of harmonics of current in electrical networks with nonlinear load and to develop the tools of passive compensation

This study examines the performance of a new type of composite column: L-shaped columns comprising concrete-filled steel tubes connected by double-vertical steel plates (LCFST-D). The fundamental structural behaviour of the LCFST-D columns is discussed. Seven LCFST-D columns were tested under axial compression. In the experiments, the variables were the height and the width of the vertical steel plates. The experimental results were used to assess the load-deformation relationship, strain distribution, and strength index. The tests demonstrated that the axial-compressive performance of the LCFST-D columns was favourable and showed that the mono-columns worked more cooperatively in the LCFST-D column structural form. Next, 3D nonlinear element models were used to analyse the mechanical properties and axial compressive behaviour of the LCFST-D columns. The results of the finite-element analysis were in good agreement with the experimental results. Based on the finite-element model, parametric studies were conducted to investigate the effects of the thickness and width of the vertical steel plates; the slenderness ratio, size and thickness of the steel tube; and the steel and concrete strengths. A method is proposed to calculate the slenderness ratio. This method considers the material properties of the steel and concrete and the sectional shape. Based on the confined effects of the concrete-filled steel tube, a method is proposed to calculate the axial-compressive bearing capacity of an LCFST-D column. The calculation results are in good agreement with the finite-element and experimental results, and the error is

The controllable reactor is one of the most effective methods for compensating reactive power. A novel type of high temperature superconducting (HTS) controllable reactor with orthogonally configured core has been proposed, analyzed, and developed. However, for the controllable reactor with dynamic inductance, the excitation analysis based on field circuit coupled method is inefficient and the excitation parameters optimization is more difficult. In this paper, an excitation system containing a voltage source converter and buck–boost converter is established. The reactor is built as a self-defined nonlinear element in the system model based on the dynamic inductance. The inductance matrix, core saturation, leakage magnetic field at HTS winding, and total magnetic flux in the excitation core are included in the self-defined element. The parameters of the excitation system have been optimized easily. The simulation result of the output characteristic of the reactor is consistent with the experimental observations of the prototype. The dynamic inductance method is proved to be fast and effective.

To protect the RF front end from electronic warfare, many studies have focused on damage phenomena of the low-noise amplifiers (LNAs). Existing studies have focused on the damage points of semiconductor devices because the peripheral circuit elements of LNAs are less susceptible to breakdown than nonlinear elements. However, their theoretical analysis is insufficient to explain the damage mechanism of LNAs under conditions such as changes in input power, frequency, and design parameters. To analyze the relationship between damage rate and parameters of the peripheral circuit of an LNA, this paper proposes a new definition of the power absorbed to a nonlinear element when input power to an LNA is very high by high-power electromagnetic pulses. In addition, LNAs having different input impedances and output impedances are designed to verify the power absorption. From the results, this paper identified parameters that increase the damage rate of LNAs, and suggested designs to reduce the damage rate.

Locating a fault in a series-capacitor-compensated transmission line (SCCTL) is a challenging task due to the action of a metal-oxide varistor a nonlinear element present as a part of the protection system of the series capacitor. In this paper, an accurate fault-location algorithm that uses synchronized measurements from both ends of the SCCTL is presented which provides fault-location results without using the model of MOV or natural fault loop for single-phase-to-ground, and double-phase-to-ground faults. Another salient feature of the proposed technique is that the subroutines for locating faults in different sections transmission line yield almost identical fault-location results regardless of which section the transmission line is faulted. The proposed technique could also be extended to the double-circuit transmission lines. First, the proposed technique is introduced and its features are elaborated through detailed mathematical analysis. Thereafter, a 500- $\text{kV}$ system with an SCCTL is designed in PSCAD, while the fault-location algorithm is modeled in MATLAB. The proposed algorithm is tested through simulations covering various fault scenarios in an SCCTL. For performance evaluation, the comparative analysis of the proposed technique with a well-known existing technique is performed in this paper.