Phase-frequency Characteristics Research Articles

Checking the adequacy of the method for generating a random process of disturbance of oscillations of rail carriages according to the impulse response of the forming filter

Usually, to study the vibrations of rail carriages, the equivalent geometric unevenness of the track obtained as a result of processing the records of the track measuring car is taken as a disturbance. Such a record contains a certain set of irregularity wavelengths, for example, 50, 25 and 12.5 m. However, when it is used to simulate disturbances at different operation speeds, these wavelengths will correspond to frequencies depending on the given speed of motion, which is not permissible, since a stable frequency range from 0.2 to 10 Hz is required to excite the vibrations of all the bodies included in the carriage. To eliminate this drawback, in the previously performed works it was proposed to generate a random process of geometric irregularities for a given operation speed by changing the set of wavelengths included in the irregularities. In this paper, based on the study of random oscillations of a simplified model of a rail carriage, as a system with one degree of freedom, the adequacy of the method for generating a random disturbance process is verified in two ways. In the first method, it was found that the characteristics of random oscillations of such a model, obtained in the time domain on the basis of numerical integration of the equation of motion when specifying the generated disturbance, have satisfactory convergence with similar characteristics found by the frequency method using Shannon's formula. In the second verification method, the cross-correlation function and the mutual spectral density between the disturbance and the bouncing oscillations were determined from the generated disturbance realization and obtained by numerical integration of the vibration process realization. Then, using the method of identifying the dynamic system, experimental amplitude and phase frequency characteristics were found, which showed satisfactory convergence with the corresponding calculated characteristics obtained by numerically solving the equation of oscillations of the model under study. On the basis of the results obtained, it was concluded that the considered method of generating a random process of disturbance is sufficiently adequate and that it can be applied to solve problems of the dynamics of rail carriages.

Application of the wavelet phase method of signal study to the analysis of asymmetric barycentric motions of the Sun and changes in processes occurring on the Sun, near-earth space and in the interior of the Earth

A set of studies has been carried out, indicating that solar activity and processes associated with the activity of the Sun: changes in the main magnetic fluxes, areas of polar spots, the number of polar torches at the poles of the Sun; -index of geomagnetic activity and -index of the ratio of plasma pressure to magnetic solar wind (SW), slow and high-speed flows of SW, cosmic ray intensity (CR); average annual values of the interplanetary magnetic field vector and its components; the temperature, density, and flow rate of the SW plasma, the synodic period of the revolution of the Sun as a star, and the radius of the Sun in relative units; the distance of the Earths geographic pole from the conventional international origin, the rate of change of the position of the Earths north magnetic pole, the main ionospheric parameters; the angle of the Earth's axis of rotation and volcanic eruptions; asymmetric movement of the Sun around the solar system of the solar system (in fractions of the solar radius); the distances from the solar systems CM to the Sun in km, the distances from the solar systems CM to the Earth, with high accuracy, are consistent with the movement of the Sun relative to the barycenter. The research is based on the wavelet transformation of the observations listed above variables in various time intervals with the subsequent calculation of their phase-frequency and phase-time characteristics, correlation matrices between characteristics. The studied variables are divided into groups, which include the barycentric movement of the Sun and changes in solar activity. The calculated two correlation matrices of the wavelet characteristics of the group of variables and the graphs of these characteristics in two coordinate systems reflect the consistency of changes in the group.
 The studies carried out indicate that the thermonuclear reaction occurring in the interior of the Sun, the external manifestation of which is solar activity, is controlled by the movements of the large planets of the Solar System relative to the Sun.

Theoretical and experimental investigation on novel 2D maglev servo proportional valve

This paper presents a novel two-dimensional maglev servo proportional cartridge valve (2D maglev valve), where a contactless maglev coupling is introduced between electro-mechanical converter and valve body to realize functions of force transmission, spool position feedback and linear-rotary motion conversion. Such configuration can effectively reduce cost of both valve manufacturing and electro-mechanical converter, while still maintain features of 2D valve such as null pilot leakage, high power-to- weight ratio and excellent anti-pollution capacity. Firstly, the characteristic equation of the valve is derived using linear theory, and the stability criterion is established for parameter determination. The influences of crucial structural parameters such as initial height of overlapping area, width of high-pressure and low-pressure holes, acting radius of magnetic force, pitch angle of maglev coupling, length of sensitive chamber and system pressure on the dynamic response are investigated based on AMESim numerical simulation. The prototype valve is then designed and manufactured and a special test rig is built. The no-load flow characteristic, load flow characteristic, leakage characteristic, amplitude and phase frequency characteristics and step response under different system pressures are measured. The experimental results are in a good agreement with the simulated analysis. As an over-damped system, the prototype valve has excellent working stability, which can reach a no-load flow rate of 105.9 L/min with hysteresis of 3.51%, amplitude bandwidth of 28.7 Hz and phase bandwidth of 42.8 Hz under 21 MPa. The research indicates that the 2D maglev valve can be a potential solution of flow rate control valve for flight control surface system of civil aircraft with high pressure and large flow rate application.

Application of Improved Droop Control Based on Grid Impedance in Photovoltaic Grid-Connected Power Generation system

When the power grid impedance mutates, the output power of the grid-connected photovoltaic power generation system controlled by drooping will become very unstable. To solve this problem, an improved droop control algorithm based on network impedance detection is proposed. Taking photovoltaic grid-connected power generation system as the research object, the influence of power grid impedance on traditional droop control is firstly expounded by introducing power grid impedance value into traditional droop control. Then the method of real-time network impedance extraction is introduced. Furthermore, according to the bandwidth and phase angle constraints of the equivalent output impedance phase frequency characteristics of the photovoltaic grid-connected inverter, the controller parameters are updated in real time to achieve the purpose of adaptive network impedance mutation. Finally, the proposed method is tested and verified by real-time simulation in the loop respectively. The results show that the proposed method is correct.

Optimization of PSVR parameters of condenser based on MATLAB/Simulink simulation

Installing a power system voltage regulator (PSVR) on the condenser can enhance the dynamic voltage control capability of the local high-voltage bus voltage, but there are still few studies on the optimization of PSVR parameters. The dynamic model of the condenser is built to determine the analytical expression between the system voltage disturbance and the change of the control target, and the influence trend of PSVR on the dynamic voltage characteristics of the condenser is analyzed. Furthermore, in the MATLAB/Simulink environment, a PSVR-containing condenser model is built, and a quantitative index for evaluating the phase-frequency characteristics of the condenser is proposed. Based on this index, the PSVR time constant is optimized through the simulation of the dynamic voltage characteristics of the condenser, and using eigenvalue root locus method combined with dynamic simulation to coordinate PSVR gain coefficient, achieve PSVR parameter optimization. The simulation results under the single-machine and three-machine systems show that after the PSVR parameter optimization, the voltage oscillation mode of the condenser is effectively improved.

Dynamics of impulse seals with tubular feeders

The paper presents a technique for calculating forced axial oscillations and stability of impulse seals with tubular feeders. Unlike the existing methods of calculation, wherein, for the sake of simplicity, the influence of the feeder conductance is neglected, this article describes a conductance effect on the dynamic characteristics of the impulse face seal. The proposed calculation technique makes it possible to determine amplitudes of forced oscillations of the axially movable bushing and stability limit for the geometric parameters chosen in the static calculation. As an example, the authors described a calculation of the impulse face seal of the rotor of the main Reactor Coolant Pump (RCP 20000-100). The amplitude and phase-frequency characteristics for different values of the nominal gap are constructed.

Research on Nonlinearity in In situ Calibration of Permanent Magnet Sodium Flowmeter Without Bluff Body

The permanent magnet sodium flowmeter (PMSF) without the bluff body installed on the large-diameter pipe in the fast reactors to measure the sodium coolant flow rate has to be calibrated in situ owing to the degradation of the magnetic field. Since the length of the magnetic field of the PMSF is limited in practical engineering applications, the characteristic between the cross correlation flow rate (CCFR) and the standard flow rate is nonlinear in in situ calibration based on the cross correlation method. Moreover, the nonlinear characteristic has a large repeatability error, which is difficult to apply to in situ calibration. In order to realize the in situ calibration, an “M-type” mean velocity profile in the pipe is obtained by analyzing the influence of the magnetic field on the fluid field. The distribution of the CCFR of the signal at each frequency is analyzed by using the phase-frequency characteristic of the cross-power spectral density (CPSD) of the two signals, and a physical model of the turbulence distribution in the pipe cross section is obtained combining with the “M-type” mean velocity profile. A nonlinearity correction method based on signal frequency band selection is proposed according to the physical model. The in situ calibration experiments of DN150 PMSF without the bluff body are carried out at the sodium temperatures of 400 °C. The signals within 11–20 and 18–35 Hz are used to calculate the CCFR for correcting the nonlinear characteristic, and sodium flow rate measurement accuracy is ±3.0%.

Transient Primary Resonance Phase-Frequency Characteristics of Stay Cables With Different Tensions

Transient Primary Resonance Phase-Frequency Characteristics of Stay Cables With Different Tensions

Nonlinear distortion of angle modulation signal in output power amplifiers

The output power amplifier is operated in nonlinear mode to increase its efficiency, at which the signal is distorted more. The goal is to analyze effects of nonlinearity on the modulating signal of angle-modulated signal distortions for single-ended and push-pull output power amplifiers with memory and without it. The amplifier characteristic ic(vBE) is preset by the cubic polynomial. The output voltage of memoryless amplifier uout(t) is found by Ohm's law. And in case with amplifier with memory, the output voltage uout(t) is found by Complex amplitude method with a Fourier series of function ic(t). The output voltage uout(t) is represented as the narrowband process with envelope of the waveform U1(t) and initial phase Ф1(t) to determine the angular modulation law Ф1(t) at the amplifier output. The function U1(t) is defined as combination of in-phase А(t) and quadrature В(t) components. The distortion estimate based on Total Harmonic Distortion (THD). The measurement of THD is defined as the ratio of the RMS amplitude of a set of higher harmonic frequencies to the RMS amplitude of the first harmonic. The spectrum of function Ф1(t) is represented a Fourier series. In single-ended memoryless amplifier and non-cutoff mode, the THD decreases as m increases and THD of modulating signal is {37.6; 18.8; 6.3%} at m {0.5; 1; 3}. In cutoff mode, the smallest THD is {15.18; 5.13%} at m {1; 3} as θ = 140o. In push-pull memoryless amplifier and θ = 90o, the THD is {22.2; 11.1; 3.7%} at m {0.5; 1; 3} which is 1.7 times less than in a single-ended amplifier without cutoff. This is due to compensation even-order harmonic of amplified signal at the output of a pushpull amplifier. In this case of memoryless amplifier, the transistor load is a parallel RLC circuit. The distortion decreases under m increases at first (up m is 1.5), but then rapidly increases (from m is 1.7). This is due to increase of the parasitic harmonics level caused by the nonlinearity of the phase-frequency characteristic of RLC circuit. The calculations show that THD of modulating signal is 3.35, 9.02 and 22.88 % at Q = 10 and m {0.5; 1; 3}, respectively. In cutoff mode, the smallest THD is at θ = 90o and it does not depend on θ at large values of m. In push-pull amplifier with memory, the THD is 2.8, 2.5 and 3.0 times less than for a singleended amplifier without cutoff at Q {2.5; 5; 10}, respectively. The results of this paper can be used for the design of signal processing systems.

Measurement of resonance frequency by amplitude and phase methods using digital frequency scanning

A theoretical and experimental study of methods for measuring the resonance frequency from the amplitude-frequency and phase-frequency characteristics of the resonator (amplitude and phase methods, respectively) has been carried out. In this case, digital frequency scanning was used to determine the resonant frequency. On the basis of the theory of probabilities, analytical expressions are derived that describe the dependences of systematic and random errors on the position of the resonance frequency in the interval between the nearest discrete frequencies, as well as on the noise level. The reliability of the derived expressions was confirmed in the course of a virtual experiment with a computer model of the resonator. It is also shown that the errors of the amplitude and phase methods for the noise level, at which no more than two discrete frequencies are recorded, practically coincide. However, if more than two discrete frequencies are recorded, then the indicated errors differ significantly, which is demonstrated using the experimental graphs. In this case, the errors in measuring the resonance frequency by the phase method practically do not depend on the frequency tuning step with a decrease in this step and linearly depend on the phase noise level. When measuring the resonance frequency by the amplitude method, the errors decrease with decreasing frequency tuning step, and for this case, an empirical formula is proposed for the dependence of systematic and random errors on the frequency tuning step and the amplitude noise level. The research results can be used in the construction of digital resonance sensors.

The periodic response of a fractional oscillator with a spring-pot and an inerter-pot

Abstract The fractional oscillation system with two Weyl-type fractional derivative terms $_{ - \infty }D_t^\beta x$ (0 < β < 1) and $_{ - \infty }D_t^\alpha x$ (1 < α < 2), which portray a “spring-pot” and an “inerter-pot” and contribute to viscoelasticity and viscous inertia, respectively, was considered. At first, it was proved that the fractional system with constant coefficients under harmonic excitation is equivalent to a second-order differential system with frequency-dependent coefficients by applying the Fourier transform. The effect of the fractional orders β (0 < β < 1) and α (1 < α < 2) on inertia, stiffness and damping was investigated. Then, the harmonic response of the fractional oscillation system and the corresponding amplitude–frequency and phase–frequency characteristics were deduced. Finally, the steady-state response to a general periodic incentive was obtained by utilizing the Fourier series and the principle of superposition, and the numerical examples were exhibited to verify the method. The results show that the Weyl fractional operator is extremely applicable for researching the steady-state problem, and the fractional derivative is capable of describing viscoelasticity and portraying a “spring-pot”, and also describing viscous inertia and serving as an “inerter-pot”.

Simulation of the Flat-parallel Movement of a Bridge Agricultural Unit with an Articulated Frame

Abstract The work presents foundations of the dynamics of the flat-parallel movement of a bridge agricultural unit in a horizontal with the kinematic method of its control (turning the wheels) by changing the position of one of its parts relative to the other. The analysis of assessment of the degree of impact of the scheme and parameters of the investigated agricultural tool upon its controllability and stability of movement is based on the amplitude and phase frequency characteristics. The mathematical models of the movement of the bridge agricultural unit are presented in a differential and an operator form of recording. Based on mathematical models, the calculated amplitude and phase frequency characteristics of the dynamic control system of the control impact, presented as the angular displacement of its half-frames ψ, are constructed for various parameters and operating modes. The constructed mathematical models, amplitude and phase frequency characteristics make it possible to assess the impact of the control parameter of the bridge agricultural unit, as well as its design and other parameters upon the controllability of the movement.

Mathematical Model of Fractional Duffing Oscillator with Variable Memory

The article investigates a mathematical model of the Duffing oscillator with a variable fractional order derivative of the Riemann–Liouville type. The study of the model is carried out using a numerical scheme based on the approximation of the fractional derivative of the Riemann–Liouville type by a discrete analog—the fractional derivative of Grunwald–Letnikov. The adequacy of the numerical scheme is verified using specific examples. Using a numerical algorithm, oscillograms and phase trajectories are constructed depending on the values of the model parameters. Chaotic regimes of the Duffing fractional oscillator are investigated using the Wolf–Bennetin algorithm. The forced oscillations of the Duffing fractional oscillator are investigated using the harmonic balance method. Analytical formulas for the amplitude-frequency, phase-frequency characteristics, and also the quality factor are obtained. It is shown that the fractional Duffing oscillator possesses different modes: regular, chaotic, multi-periodic. The relationship between the order of the fractional derivative and the quality factor of the oscillatory system is established.

Monocular Vision-Based Calibration Method for Determining Frequency Characteristics of Low-Frequency Vibration Sensors

Calibration is required to determine the frequency characteristics of vibration sensors to ensure their measurement accuracy in engineering applications. Thus, a monocular vision-based calibration method for low-frequency vibration sensors is investigated in this study. A sub-pixel edge detection method which based on Gaussian curve fitting is applied to extract the edges of motion sequence images in order to accurately measure the excitation acceleration of the sensors. Because the motion sequence images and the output signal of the sensors cannot be collected synchronously, it is very difficult to align the excitation acceleration signal obtained from the images and the output signal in the time domain. Although the misalignment only has a negligible effect on the magnitude frequency characteristic calibration, it dramatically decreases the calibration accuracy of the phase frequency characteristic, especially with the increasing of the frequency. A time-spatial synchronization technique is proposed to accurately calibrate the phase frequency characteristic by determining the phase of the excitation acceleration signal at a specific spatial position and that of the output signal at the corresponding time. Finally, both the magnitude and phase frequency characteristics are simultaneously calibrated by the investigated method with a flexible and low-cost vision system. The experimental results compared with laser interferometry show that the investigated method accomplishes the high-accuracy magnitude and phase frequency characteristics calibration in a broad low-frequency range. Its calibration accuracy is superior to that of laser interferometry when the frequency is less than 0.3 Hz, and is equivalent at other frequencies.

Analytical evaluation of equivalent energy loss in causal frequency selection filters in the processing of quadrature amplitude modulation signals

In this paper, we consider the need to assess the influence of the parameters of a linear time-invariant causal system in the processing of quadrature amplitude modulation signals of various positionality and constellation diagram irregularity. We describe the equations that determine the energy balance of a radio line and the total losses arising in route. We have developed mathematical expressions to assess the equivalent energy losses caused by the irregularity of amplitude-frequency and phase-frequency characteristics of the frequency selection filters. We propose a procedure to assess the non-noise losses in the frequency selection filters when designing high-speed radio systems for transmitting the information.

A [formula omitted]-order R-L high-pass filter modeled by local fractional derivative

As an important electronic device, filter is applied to all kinds of electronic products. In this paper, a new ℘-order R-L High-pass filter (HPF) modeled by the local fractional derivative (LFD) is proposed for the first time. With the help of the local fractional Laplace transform (LFLT), we obtain the non-differentiable(ND) transfer function, and present the expressions of ND amplitude-frequency characteristic (AFC) and ND phase-frequency characteristics (PFC). The corresponding parameters and properties of the ℘-order R-L HPF are also studied. What’s interesting is that the ℘-order R-L HPF becomesthe ordinary one in the exceptional case at ℘ = 1. The obtained results in this paper reveal the sufficiency of the local fractional derivative for analyzing the circuit systems in fractal space.

ИССЛЕДОВАНИЕ ИЗМЕНЕНИЙ ГЛОБАЛЬНОГО КЛИМАТА С ИСПОЛЬЗОВАНИЕМ ВЕЙВЛЕТНЫХ ФАЗО-ЧАСТОТНЫХ ФУНКЦИЙ, ФАЗО-ЧАСТОТНЫХ И ФАЗО-ВРЕМЕННЫХ ХАРАКТЕРИСТИК ГЕЛОКОСМИЧЕСКИХ И КЛИМАТИЧЕСКИХ ПЕРЕМЕННЫХ ЧАСТЬ 2

Актуальность исследования обусловлена необходимостью установления истинных причин и закономерностей изменений глобального климата на Земле. Цель: применить разработанный в первой части статьи метод анализа изменений климата с вычислением временных вейвлетных фазо-частотных функций, фазо-частотных и фазо-временных характеристик переменных с использованием непрерывных вейвлетных преобразований для установления закономерностей изменений глобального климата; в частности, согласованности изменений гелиокосмических переменных с самоорганизованными Тихоокеанским декадным, Североатлантическим и Южным/Эль-Ниньо колебаниями, изменениями озонового слоя в стратосфере и потеплением в Арктической зоне России, тектоническими процессами Земли. Объекты: временные ряды изменений гелиокосмических и климатических переменных, индексы Североатлантического и Южного/Эль-Ниньо колебаний, Тихоокеанского декадного колебания, ряды изменений тектонических процессов Земли, ряды изменений озонового стоя в стратосфере и температуры воздуха в Арктике. Методы: непрерывное прямое вейвлет-преобразование исходных данных с использованием комплексного вейвлета с вычислением временных вейвлетных фазо-частотных функций, фазо-частотных и фазо-временных характеристик переменных, кластерный анализ; оценка и анализ плотностей распределений фазо-временных характеристик; оценка и анализ коэффициентов корреляций между фазо-частотными и фазо-временными характеристиками переменных в равных интервалах времени. Результаты. Вычислением матриц корреляций между вейвлетными фазо-частотными характеристиками переменных, построением совместных графиков фазо-частотных и фазо-временных характеристик этих же переменных в заданных интервалах времени получено, что изменения гелиокосмических переменных, солнечной активности, вулканических извержений Земли, концентрации в атмосфере двуокиси углерода СO2, озонового слоя в стратосфере, землетрясений, цунами и природных катастроф, изменения скорости вращения Земли и продолжительности земных суток принадлежат к одному классу изменчивостей переменных. Эти изменчивости обусловлены изменениями расстояния Солнца от барицентра. Установлена тесная взаимосвязь между колебательными процессами гелиокосмических переменных, солнечной активности и вулканических процессов на Земле, изменений концентрации двуокиси углерода СO2 в атмосфере с самоорганизованными процессами Североатлантического, Тихоокеанского и Южного колебаний/Эль-Ниньо, связанная с изменениями скорости вращения Земли и продолжительности земных суток. Обосновано, что рост вулканической деятельности Земли в современности приводит к снижению озонового слоя в стратосфере, усилению солнечной радиации и росту приземной температуры. В особенности эти процессы сильно проявляются в Арктической зоне России. Показано, что изменения приземной температуры на Земле обусловлены изменениями солнечной активности, парниковым эффектом, изменениями теплосодержания океана и температуры воздуха над сушей и океаном. Построение изображений временных вейвлетных фазо-частотных функций фазо-временных характеристик переменных позволяет визуализировать историю изменений переменных во времени и в фазо-частотной области и прогнозировать эти изменения на некоторый временной горизонт на характерных частотах.

Using Hilbert Transform in Diagnostic of Composite Materials by Impedance Method

The article is devoted to the problem of the increasing of information quality for the impedance method of nondestructive testing. The purpose of this article is to get for the pulsed impedance method of nondestructive testing the additional informative parameters. Instantaneous values of the information signal's amplitude is a sensitive parameter to the effects of interference, in particular friction, which necessitates the use of additional informative features. It was experimentally measured signals from defective and defectless areas of the test pattern. Using of the Hilbert transform gave possibility to determine phase characteristics of these signals and realize demodulation to extract a low-frequency envelope for further analysis of its shape. It was received the informative features as a result of researches. Among them are instantaneous frequency of a signal, the integral of a phase characteristic on the selected interval and the integral of a difference signal phase characteristics. In order to compare quality of the defect detection using selected parameters it was carried out evaluation of the testing result reliability for a product fragment made of a composite material. Considering the influence of the change in the mechanical impedance of the researched area on the phase-frequency characteristics of the output signal of the converter, it is proposed to use as the diagnostic signs: the instantaneous frequency and the value of the phase characteristic of the current signal for certain points in time. The proposed informative features enable to increase general reliability of composite materials testing by the pulsed impedance method.

ИССЛЕДОВАНИЕ ИЗМЕНЕНИЙ ГЛОБАЛЬНОГО КЛИМАТА КАК СЛОЖНОЙ СИСТЕМЫ С ИСПОЛЬЗОВАНИЕМ ВЕЙВЛЕТНЫХ ФАЗО-ЧАСТОТНЫХ ФУНКЦИЙ, ФАЗО-ЧАСТОТНЫХ И ФАЗО-ВРЕМЕННЫХ ХАРАКТЕРИСТИК ГЕЛИОКОСМИЧЕСКИХ И КЛИМАТИЧЕСКИХ ПЕРЕМЕННЫХ ЧАСТЬ 1

Актуальность исследования обусловлена необходимостью установления истинных причин и закономерностей изменений глобального климата на Земле как сложной системы. Цель: разработать и предложить эффективный метод извлечения информации об изменчивости переменных, содержащейся в исходных данных изменений гелиокосмических и климатических переменных, заданных в виде временных рядов, и применить этот метод для обоснования климатических изменений на Земле. Объекты: временные ряды изменений гелиокосмических и климатических переменных. Методы: непрерывное прямое вейвлет-преобразование исходных данных с использованием комплексного вейвлета 'cgau5' с вычислением их временных вейвлетных фазо-частотных функций, фазо-частотных и фазо-временных характеристик; оценка спектра периодичностей функций по фазо-временным характеристикам переменных; оценка и анализ плотностей распределений фазо-частотных и фазо-временных характеристик; оценка и анализ коэффициентов корреляций между фазо-частотными и фазо-временными характеристиками переменных в равных интервалах времени. Результаты. Получены временные вейвлетные фазо-частотные функции и их изображения, позволяющие визуализировать и оценить спектры периодичностей исследуемых переменных; оценки вейвлетные фазо-частотные и фазо-временные характеристики переменных, позволяющие проводить весь комплекс сравнительных исследований переменных и установить закономерности их изменений. К этим исследованиям относятся: оценивание плотностей распределений этих характеристик, позволяющих идентифицировать факторы, влияющие на эти изменения; вычисление матриц корреляций между вейвлетными фазо-частотными и фазо-временными характеристиками переменных в заданных равных интервалах времени, позволяющие оценить степени согласованности изменений переменных в фазо-частотной области и в области фазо-временных изменений. Установлена тесная взаимосвязь между колебательными процессами гелиокосмических переменных, солнечной активностью и вулканическими процессами на Земле, изменениями концентрации двуокиси углерода CO2 в атмосфере. Показано, что движение Солнца относительно барицентра, обусловленное движением планет-гигантов Cолнечной системы, управляет cолнечной активностью, тектоническими процессами на Земле, в том числе вулканическими извержениями, климатом на Земле.

Frequency model of an essentially nonlinear steering drive with a digital microcontroller

When designing a stabilization system for highly maneuverable unmanned aerial vehicles (UAVs), one of the relevant tasks is to study the operation of the steering drive in the frequency band corresponding to the flexural vibrations of the UAV body. To ensure the stability of the UAV stabilization system, quite conflicting requirements may be imposed on the dynamic characteristics of the drive. In particular, the requirement for a sharp suppression of the amplitude-frequency characteristic at the frequency of UAV bending vibrations with minimal phase distortions in the control band of the longitudinal and lateral channels of the stabilization system can significantly complicate the task of researching the stability of the UAV motion control system. The article discusses an electric drive prototype with a digital microcontroller, designed for a highly maneuverable UAV. Adaptive algorithms of the digital controller make it possible to provide the necessary phase delays in the control frequency band and at the same time almost completely suppress the harmonic components of the control signals at the frequencies of the bending vibrations of the UAV body. The algorithms are essentially nonlinear in nature and are based on a change in the gain of the direct circuit of the drive depending on the frequency of the input signal, which greatly complicates the calculation of the transfer function of the steering drive for use in the frequency model of the stabilization system. Generally, the steering drive is described by a linear minimum-phase system, presented as a transfer function of one of the typical blocks of the first or second order, but for the specified steering drive with given dynamic characteristics, this approach is untenable. As a result of the study, a method for obtaining a frequency model of the steering drive is proposed, which is implemented as a non-minimum phase system, the main property of which is the independence of the amplitude-frequency and phase-frequency characteristics. In the process of research, the results obtained on the proposed model are compared with the results of experiments on a drive prototype and its complete non-linear time model. The main advantage of the proposed frequency model is a fairly simple description of the steering drive in the frequency domain, convenient for use as part of the frequency model of the stabilization system in the study of problems of ensuring the stability of UAV flight.