On numerical stationary distribution of overdamped Langevin equation in harmonic system

Efficient numerical algorithm for stochastic differential equation has been an important object in the research of statistical physics and mathematics for a long time.In this work we study the highly accurate numerical algorithm for the overdamped Langevin equation.In particular,our interest is in the behaviour of the numerical schemes for solving the overdamped Langevin equation in the harmonic system.Based on the large friction limit of the underdamped Langevin dynamic scheme,three algorithms for overdamped Langevin equation are obtained.We derive the explicit expression of the stationary distribution of each algorithm by analysing the discrete time trajectory for both one-dimensional case and multi-dimensional case.The accuracy of the stationary distribution of each algorithm is illustrated by comparing with the exact Boltzmann distribution.Our results demonstrate that the“BAOA-limit”algorithm generates an accurate distribution of the harmonic system in a canonical ensemble,within a stable range of time interval.The other algorithms do not produce the exact distribution of the harmonic system.

ADAPTIVE HARMONIC CANCELLATION APPLIED IN ELECTRO-HYDRAULIC SERVO SYSTEM WITH ANN

The method for harmonic cancellation based on artificial neural network (ANN)is proposed. The task is accomplished by generating reference signal with frequency that should beeliminated from the output. The reference input is weighted by the ANN in such a way that it closelymatches the harmonic. The weighted reference signal is added to the fundamental signal such thatthe output harmonic is cancelled leaving the desired signal alone. The weights of ANN are adjustedby output harmonic, which is isolated by a bandpass filter. The above concept is used as a basis forthe development of adaptive harmonic cancellation (AHC) algorithm. Simulation results performedwith a hydraulic system demonstrate the efficiency and validity of the proposed AHC control scheme.

Harmonic balance method with alternating frequency/time domain technique for nonlinear dynamical system with fractional exponential

Comparisons of the common methods for obtaining the periodic responses show that the harmonic balance method with alternating frequency/time （HB-AFT） do- main technique has some advantages in dealing with nonlinear problems of fractional exponential models. By the HB-AFT method, a rigid rotor supported by ball bearings with nonlinearity of Hertz contact and ball passage vibrations is considered. With the aid of the Floquet theory, the movement characteristics of interval stability are deeply studied. Besides, a simple strategy to determine the monodromy matrix is proposed for the stability analysis.

Nonlinear vibration analysis of a circular micro-plate in two-sided NEMS/MEMS capacitive system by using harmonic balance method

In this study, forced nonlinear vibration of a circular micro-plate under two-sided electrostatic, two-sided Casimir and external harmonic forces is investigated analytically. For this purpose, at first, von Karman plate theory including geometrical nonlinearity is used to obtain the deflection of the micro-plate. Galerkin decomposition method is then employed, and nonlinear ordinary differential equations (ODEs) of motion are determined. A harmonic balance method (HBM) is applied to equations and analytical relation for nonlineaT frequency response (F-R) curves are derived for two categories (including and neglecting Casimir force) separately. The analytical results for three cases:(1) semi-linear vibration;(2) weakly nonlinear vibration;(3) highly non linear vibration, are validated by comparing with the numerical solutio ns. After validation, the effects of the voltage and Casimir force on the natural frequency of two-sided capacitor system are investigated. It is shown that by assuming Casimir force in small gap distances, reduction of the natural frequency is considerable. The influences of the applied voltage, damping, micro-plate thickness and Casimir force on the frequency response curves have been presented too. The results of this study can be useful for modeling circular parallel-plates in nano /microelectromechanical transducers such as microphones and pressure sensors.

Tuning control system of a third harmonic superconducting cavity in the Shanghai Synchrotron Radiation Facility

Beam lifetime is dominated by Touschek scattering at the Shanghai Synchrotron Radiation Facility(SSRF).Touschek loss rate is affected by probability for scattering beyond the RF acceptance and the volume charge density of the bench.In the phaseⅡupgrade of the SSRF,a third harmonic superconducting cavity will be used to enhance the Touschek lifetime by lengthening the bunches.The Touschek lifetime improvement factor is affected by the voltage of a harmonic cavity.To stabilize the cavity voltage,a tuning control system was designed to control it.The design of the tuning control system was based on the SSRF third-generation low-level RF control system.Some hardware and specialized algorithms were redesigned to fit the harmonic cavity control.The design of the tuning control system is complete,and the control system has been tested.The test result shows that the fluctuation of amplitude is<±0.34%within 1.5 h,which satisfies the stability requirement.

Stochastic resonance in an under-damped bistable system driven by harmonic mixing signal

Stochastic resonance（SR） is studied in an under-damped bistable system driven by the harmonic mixing signal and Gaussian white noise. Using the linear response theory（LRT）, the expressions of the spectral amplification at fundamental and higher-order harmonic are obtained. The effects of damping coefficient, noise intensity, signal amplitude, and frequency on spectral amplifications are explored. Meanwhile, the power spectral density（PSD） and signal-to-noise ratio（SNR） are calculated to quantify SR and verify the theoretical results. The SNRs at the first and second harmonics exhibit a minimum first and a maximum later with increasing noise intensity. That is, both of the noise-induced suppression and resonance can be observed by choosing proper system parameters. Especially, when the ratio of the second harmonic amplitude to the fundamental one takes a large value, the SNR at the fundamental harmonic is a monotonic function of noise intensity and the SR phenomenon disappears.

ADAPTIVE FEED-FORWARD COMPENSATOR FOR HARMONIC CANCELLATION IN ELECTRO-HYDRAULIC SERVO SYSTEM

Since the dead zone phenomenon occurs in electro-hydraulic servo system, the output of the system corresponding to a sinusoidal input contains higher harmonic besides the fundamental input, which causes harmonic distortion of the output signal. The method for harmonic cancellation based on adaptive filter is proposed. The task is accomplished by generating reference signals with frequency that should be eliminated from the output. The reference inputs are weighted by the adaptive filter in such a way that it closely matches the harmonic. The output of the adaptive filter is a harmonic replica and is injected to the fundamental signal such that the output harmonic is cancelled leaving the desired signal alone, and the total harmonic distortion （THD） is greatly reduced. The weights of filter are adjusted on-line according to the control error by using least-mean-square （LMS） algorithm. Simulation results performed with a hydraulic system demonstrate the efficiency and validity of the proposed adaptive feed-forward compensator （AFC） control scheme

STUDY ON SENSOR-BASED CONTROL METHOD FOR HARMONIC DRIVE SYSTEM

A new type of robust traje ctory tracking control for harmonic using joint torque sensor and joint acceleration sensor information is concerned with.Joint torque sensor information is used to compensate the uncertainty of link and load parameters. Joint acceleration feedback control will enhace the robustness of the driving system, resist the dynamic uncertainties and disturbing torque acted on the joint axis within definite bandwidth, improve the joint tracking performance, and resist the vibration of the load side of the harmonic drive system. Experimental studies are carried out and comparison of several controllers , such as PD and sensor- based control, the experimental results clearly illustrate the effectiveness of the proposed methods.

Proton Transport in Hydrogen-bonded Systems in Anharmonic Interaction Approximation : an Analytical Approach

We study the collective proton motion in hydrogen-bonded systems in anharmonic interaction approximation,and obtain analytical solutions of kinkantikink solitons.The asymmetric feature of kink-antikink solitons can be clearly seen from the solutions.Some basic physical quantities of the kink and antikink solitons are calculated in anharmonic interaction approximation.

Harmonic Analysis of Hoist Drive System FED by Power Converter and Cycloconverter

There are a lot of large capacity nonlinear loads in power systems in coal mine, such as, hoist supply system fed by power converter and cycloconverter. The harmonics generated by those nonlinear loads are very serious. The model for harmonic analysis of power electronic converter and cycloconverter is established, and a novel method for harmonic analysis is proposed in this paper. The suggested method has advantages of less memory capacity need, fast estimation and high accuracy. The comput-ing results are good agreed with the measuring results. The suggested method is much useful for the harmonic prediction of power system in coal mine.

Torque estimation for robotic joint with harmonic drive transmission based on system dynamic characteristics

In the applications of joint control and robot movement,the joint torque estimation has been treated as an effective technique and widely used.Researches are made to analyze the kinematic and compliance model of the robot joint with harmonic drive to acquire high precision torque output.Through analyzing the structures of the harmonic drive and experiment apparatus,a scheme of the proposed joint torque estimation method based on both the dynamic characteristics and unscented Kalman filter(UKF)is designed and built.Based on research and scheme,torque estimation methods in view of only harmonic drive compliance model and compliance model with the Kalman filter are simulated as guidance and reference to promote the research on the torque estimation technique.Finally,a promoted torque estimation method depending on both harmonic drive compliance model and UKF is designed,and simulation results compared with the measurements of a commercial torque sensor,have verified the effectiveness of the proposed method.

Reactive Power Compensation and Harmonic Suppression for Power Supply System of HT-7U Superconductive Tokamak

In this paper, a strategy for the reactive power compensation and harmonic suppression of the power supply system in HT-7U superconductive Tokamak is proposed. The optimized approach is given in the parameters design for passive filter. Also a controlling method with fast response time and good accuracy is put forward for the compensator, which is more suitable for the dynamic load.

DC System Modeling and AC/DC System Harmonic Calculation under Asymmetric Faults

The accurate DC system model is the key to fault analysis and harmonic calculation of AC/DC system. In this paper, a frequency domain analysis model of DC system is established, and based on it a unified fundamental frequency and harmonic iterative calculation method is proposed. The DC system model is derived considering the dynamic switching characteristic of converter and the steady-state response features of dc control system synchronously. And the proposed harmonic calculation method fully considers the AC/DC harmonic interaction and fault interaction under AC asymmetric fault condition. The method is used to the harmonic analysis and calculation of CIGRE HVDC system. Compared with those obtained by simulation using PSCAD/EMTDC software, the results show that the proposed model and method are accurate and effective, and provides the analysis basis of harmonic suppression, filter configuration and protection analysis in AC/DC system.

Harmonic detection an AC excited generation system based on in-phase correlation filtering

The paper reports results of investigation on the harmonic detection technique of a complicated power supply system such as an AC excited generation system, which has a variable fundamental frequency and low order harmonics with rich sub-harmonics whose frequencies are lower than the fundamental one. The in-phase correlation filtering technique, based on the frequency shifting principle, is proposed in this paper.Theoretical analysis and experimental results validate the effectiveness of this technique for the harmonic detections of AC excited generation systems.

New trajectory linearization control for nonlinear systems undergoing harmonic disturbance

This paper presents a new trajectory linearization control scheme for a class of nonlinear systems subject to harmonic disturbance. It is supposed that the frequency of the disturbance is known, but the amplitude and the phase are unknown. A disturbance observer dynamics is constructed to estimate the harmonic disturbance, and then the estimation is used to implement a compensation control law to cancel the disturbance. By Lyapunov＇s direct method, a rigorous poof shows that the composite error of the closed-loop system can approach zero exponentially. Finally, the proposed method is illustrated by the application to control of an inverted pendulum. Compared with two existing methods, the proposed method demonstrates better performance in tracking error and response time.

Noncovariant Lagrangians Are Presented Which Yield Two-Component Equations of Motion for a Class of Relativistic Mechanical Systems in 1 + 1 Dimensions Including the Harmonic Oscillator

First, a Lagrangian is presented and authenticated for a Relativistic Harmonic Oscillator in 1 + 1 dimensions. It yields a two-component set of equations of motion. The time-component is the missing piece in all previous discussions of this system! The second result is that this Oscillator Langrangian generalizes to Langrangians for a class of particles in 1 + 1 dimensions subject to an arbitrary potential V which is space dependent only.

Study and Design of a DC/AC Energy Converter for PV System Connected to the Grid Using Harmonic Selected Eliminated (HSE) Approach

Nowadays, distributing network-connected photovoltaic (PV) systems are expanded by merging a PV system and a Direct Current (DC)/Alternating Current (AC) energy converter. DC/AC conversion of PV energy is in great demand for AC applications. The supply of electrical machines and transfer energy to the distribution network is a typical case. In this work, we study and design a DC/AC energy converter using harmonic selective eliminated (HSE) method. To this end, we have combined two power stages connected in derivation. Each power stage is constituted of transistors and transformers. The connection by switching of the two rectangular waves, delivered by each of the stages, makes it possible to create a quasi-sinusoidal output voltage of the inverter. Mathematical equations based on the current-voltage characteristics of the inverter have been developed. The simulation model was validated using experimental data from a 25.2 kWp grid-coupled (PV) system, connected to Gridfit type inverters. The data were exported and implemented in programming software. A good agreement was observed and this shows all the robustness and the technical performances of the energy converter device. It emerges from this analysis that the inverter output voltage and the phase angle thus simulated are very important to control in order to orientate the transfer of the power flow from the continuous cell to cell to the alternating part. Simulated and field-testing results also show that increases in the value of the modulation factor (m) for low power output are highly significant. This study is an important tool for DC/AC inverter designers during initial planning stages. A short presentation of the design model of the inverter has been proposed in this article.

Modulation of High-Order Harmonic Generation from a Monolayer ZnO by Co-rotating Two-Color Circularly Polarized Laser Fields

By numerically solving the two-dimensional semiconductor Bloch equation,we study the high-order harmonic emission of a monolayer ZnO under the driving of co-rotating two-color circularly polarized laser pulses.By changing the relative phase between the fundamental frequency field and the second one,it is found that the harmonic intensity in the platform region can be significantly modulated.In the higher order,the harmonic intensity can be increased by about one order of magnitude.Through time-frequency analysis,it is demonstrated that the emission trajectory of monolayer ZnO can be controlled by the relative phase,and the harmonic enhancement is caused by the second quantum trajectory with the higher emission probability.In addition,near-circularly polarized harmonics can be generated in the co-rotating two-color circularly polarized fields.With the change of the relative phase,the harmonics in the platform region can be altered from left-handed near-circularly polarization to right-handed one.Our results can obtain high-intensity harmonic radiation with an adjustable ellipticity,which provides an opportunity for syntheses of circularly polarized attosecond pulses.

Power System Harmonic Detection Using Frequency-Domain Interpolation Wavelet Transform

Aiming at harmonic detection, fast Fourier transform can only detect integer harmonics precisely, short time Fourier transform can detect non-integer harmonics with low resolution, and some former wavelet based methods have no aliasing-reduction scheme which result in low measurement precision and poor robustness. A frequency-domain interpolation algorithm to detect harmonics is proposed by choosing Shannon wavelet. Shannon wavelet is an orthogonal wavelet possessing best ideal frequency domain localization ability, it can restrict wavelet abasing but bring about Gibbs oscillation phenomenon simultaneously. An interpolation algorithm is developed to overcome this problem. Simulation reveals that the proposed method can effectively cancel aliasing, spectral leakage and Gibbs phenomenon, so it provides an effective means for power system harmonic analysis.

A SYSTEM OF BOUNDARY INTEGRO-DIFFERENTIAL EQUATIONS FOR HARMONIC ELASTIC WAVES IN R3

Here we derive a new representation of the derivative of the double-layer potential for harmonic elastic waves in R3.Based on this new representation,the Neumann internal problem and the Neumann external problem of harmonic elastic waves are reduced to a system of boundary integro-differential equations,which is convenient for numerical approximation.