Nonlinear Damped Oscillators on Riemannian Manifolds:Fundamentals

The classical theory of mass-spring-damper-type dynamical systems on the ordinary flat space R^3 may be generalized to higher-dimensional Riemannian manifolds by reformulating the basic underlying physical principles through differential geometry.Nonlinear dynamical systems have been studied in the scientific literature because they arise naturally from the modeling of complex physical structures and because such dynamical systems constitute the basis for several modern applications such as the secure transmission of information.The flows of nonlinear dynamical systems may evolve over time in complex,non-repeating(although deterministic) patterns.The focus of the present paper is on formulating the general equations that describe the dynamics of a point-wise particle sliding on a Riemannian manifold in a coordinate-free manner.The paper shows how the equations particularize in the case of some manifolds of interest in the scientific literature,such as the Stiefel manifold and the manifold of symmetric positive-definite matrices.

Propagator for a Time-Dependent Damped Harmonic Oscillator with a Force Quadratic in Velocity

The propagator for a time-dependent damped harmonic oscillator with a force quadratic in velocity is obtained by making a specific coordinate transformation and by using the method of time-dependent invariant.

Multiple scales method for analyzing a forced damped rotational pendulum oscillatorwithgallows

This study reports the analytical solution for a generalized rotational pendulum system with gallows and periodic excited forces.The multiple scales method(MSM)is applied to solve the proposed problem.Several types of rotational pendulum oscillators are studied and talked about in detail.These include the forced damped rotating pendulum oscillator with gallows,the damped standard simple pendulum oscillator,and the damped rotating pendulum oscillator without gallows.The MSM first-order approximations for all the cases mentioned are derived in detail.The obtained results are illustrated with concrete numerical examples.The first-order MSM approximations are compared to the fourth-order Runge-Kutta(RK4)numerical approximations.Additionally,the maximum error is estimated for the first-order approximations obtained through the MSM,compared to the numerical approximations obtained by the RK4 method.Furthermore,we conducted a comparative analysis of the outcomes obtained by the used method(MSM)and He-MSM to ascertain their respective levels of precision.The proposed method can be applied to analyze many strong nonlinear oscillatory equations.

Analytical approximations to a generalized forced damped complex Duffing oscillator:multiple scales method and KBM approach

In this investigation,some different approaches are implemented for analyzing a generalized forced damped complex Duffing oscillator,including the hybrid homotopy perturbation method(H-HPM),which is sometimes called the Krylov-Bogoliubov-Mitropolsky(KBM)method and the multiple scales method(MSM).All mentioned methods are applied to obtain some accurate and stable approximations to the proposed problem without decoupling the original problem.All obtained approximations are discussed graphically using different numerical values to the relevant parameters.Moreover,all obtained approximate solutions are compared with the 4thorder Runge-Kutta(RK4)numerical approximation.The maximum residual distance error(MRDE)is also estimated,in order to verify the high accuracy of the obtained analytic approximations.

New Approach for Solving Master Equations in Quantum Optics and Quantum Statistics by Virtue of Thermo-Entangled State Representation

By introducing a fictitious mode to be a counterpart mode of the system mode under review we introduce the entangled state representation （η｜, which can arrange master equations of density operators p（t） in quantum statistics as state-vector evolution equations due to the elegant properties of （η｜. In this way many master equations （respectively describing damping oscillator, laser, phase sensitive, and phase diffusion processes with different initial density operators） can be concisely solved. Specially, for a damping process characteristic of the decay constant k we find that the matrix element of p（t） at time t in 〈η｜ representation is proportional to that of the initial po in the decayed entangled state （ηe^-kt｜ representation, accompanying with a Gaussian damping factor. Thus we have a new insight about the nature of the dissipative process. We also set up the so-called thermo-entangled state representation of density operators, ρ = f（d^2η/π）（η｜ρ〉D（η）, which is different from all the previous known representations.

A new wide area damping controller design method considering signal transmission delay to damp interarea oscillations in power system

Wide area damping controller(WADC) is usually utilized to damp interarea low frequency oscillation in power system. However, conventional WADC design method neglects the influence of signal transmission delay and damping performance of WADC designed by the conventional method may deteriorate or even has no effect when signal transmission delay is beyond delay margin, an index that denotes delay endurance degree of power system. Therefore, a new design method for WADC under the condition of expected damping factor and required signal transmission delay is presented in this work. An improved delay margin with less conservatism is derived by adopting a new Lyapunov-Krasovskii function and more compact bounding technique on the derivative of Lyapunov-Krasovskii functional. The improved delay margin, which constructs the correlation of damping factor and signal transmission delay, can be used to design WADC. WADC designed by the proposed method can ensure that power system satisfies expected damping factor when WADC input signal is delayed within delay margin. Satisfactory test results demonstrate the effectiveness of the proposed method.

The structural basis of oscillation damping in plant stems-biomechanics and biomimetics

Oscillations and their damping were investigated for plant stems of Cyperus alternifolius L., Equisetum hyemale L., Equisetum fluviatile L., Juncus effuses L., Stipa gigantea Link, and Thamnocalamus spathaceus (Franch.) Soderstr. With the exception of T. spathaceus, mechanical damping of the oscillation of individual plant stems, even without side organs, leaves or inflorescences, is quite effective. Our experiments support the hypothesis that embedding stiff sclerenchymatous elements in a more compliant parenchymatous matrix provides the structural basis for the dissipation of mechanical energy in the plant stem. As an application the naturally occurring structures were mimicked in a compound material made from hemp fabrics em- bedded in polyurethane foam, cured under pressure. Like its natural model it shows plastic deformability and viscoelastic be- haviour. In particular the material is characterized by a remarkably high shock absorption capacity even for high impact loads.

Performance Comparison of PI and Fuzzy Logic Based IPFC on Damping of Power System Oscillations

This paper presents a new approach for determining the effective control signals for damping of oscillations by using fuzzy logic based Interline Power Flow Controller [IPFC]. The IPFC performance is tested with PI controllers in comparison with fuzzy logic based controller on Modified Phllips-Heffron Model of Single Machine Infinite Bus System to achieve improved damping performance by selecting effective control signals such as deviation in pulse width modulation index of voltage series converter 1 in line 1, pulse width modulation index of voltage series converter 2 in line 2, deviation in phase angle of the injected voltage of convertor 1, injected voltage phase angle deviation of convertor 2. Investigations reveal that coordinated tuning of Interline Power Flow Controller with Fuzzy Logic Controller provides the robust dynamic performance. The Fuzzy Logic Based Interline Power Flow Controller [IPFC] is designed with simple fuzzy rules to coordinate the additional damping signal. The proposed controllers for IPFC are able to achieve improved designed performance of the power system. Validity of effective control signals has been done by eigen value analysis.

Improvement of Power System Performance Using Fuzzy Logic Based Interline Power Flow Controller [IPFC]

In this paper, the nonlinear dynamic model of a multi machine power system incorporated with Interline Power Flow Controller [IPFC] has been developed for improvement in damping of power system oscillations and transient stability. The IPFC performance is tested with PI controllers in comparison with fuzzy logic based controller under healthy and abnormal operating conditions. The IPFC fuzzy controller is design to coordinate two control inputs: change in voltage and change in capacitor voltage to improve the transient stability of the multimachine system. The Interline Power Flow Controller [IPFC] with fuzzy logic controller is designed with simple fuzzy rules to coordinate the additional damping signal. The proposed controller for IPFC is able to achieve improved designed performance of the power system. Digital simulations are carried out in MATLAB environment.

OSCILLATION THEOREMS FOR SECOND ORDER NONLINEAR DIFFERENTIAL EQUATIONS WITH DAMPING

Some new oscillation theorems are established for the second order nonlinear differential equations with damping of the form where p（t） and q（t） are allowed to change sign on [t0,∞).

Influence of Excitation System＇s Parameters to the Power System Stability

Excitation system is one of the significant elements affecting the dynamic performance of electric power systems. The power engineering as area of science and industry is subjected to rapid modernization, which is caused by technological progress. However, not all elements of the power system are developing simultaneously. The old type of elements sometimes is sufficient to adapt old system to the new operational conditions. The work developed and proposed in this paper deals with analysis of possible optimization of synchronous generator＇s excitation system. Authors examined influence of excitation system＇s parameters to the dynamics of transient processes in the power system. Authors investigated optimal parameters of excitation system of the Kegums hydro power plant. For optimization of parameters objective functions were used. The problem of the mutual influence of excitation systems of neighbor power plants was investigated. Investigation of transient processes using developed model proved that optimization of excitation parameters improves efficiency of regulation of excitation system, damping of active power oscillation and in some cases can prevent out-of-step condition.

Impact of Weather Conditions and Dynamic Load Models on Steady State and Dynamic Response of Power System

This paper gives an insight on the effect of transmission line temperature variations, resulting from loading and weather conditions changes, on a power system＇s steady state and dynamic performance. The impact of dynamic load models on system stability is also studied. The steady-state and dynamic stability simulation results of a 39 bus system for constant line impedance （the traditional simulation practice） are compared to the results with estimated, but realistic, temperature varied line impedances using PSLF （positive sequence load flow） software. The modulated line impedances will affect the thermal loading levels and voltage profiles of buses under steady state response, while the dynamic results will show improved damping in electro-mechanical oscillations at generator buses.

Numerical analysis of a projecting wall type oscillating water column(PW-OWC)wave energy converter in regular waves

Oscillating water column(OWC)based wave energy absorption devices are classic which have been widely used for harnessing ocean wave energy.This paper presents a numerical study on a projecting wall(PW)type OWC wave energy converter in regular waves.The computational fluid dynamics(CFD)modelling of a stationary floating PW-OWC model in a three-dimensional wave flume is achieved by the software Flow-3D.Numerical analyses are carried out based on CFD simulations and the linear potential flow solutions with modifications to account for turbine-induced damping.The present numerical solutions are validated against our previous experimental data.It is found that both the CFD and modified linear potential flow predictions are in reasonably good agreements with the experimental data in the first order results of OWC and air pressure responses.When the nonlinear responses are included in the result,the modified linear potential flow solution is found to slightly under-estimate the wave energy conversion performance at long wavelengths.Regarding the airflows above and below the chamber orifice,the CFD results suggest that they are almost unidirectional,oscillating in not only the base frequency but also subharmonic and ultraharmonic frequencies.The evolution of the OWC responses during an entire period and the phase analysis based on CFD simulations are presented.The phase results provide the crucial evidence to the reasonability of the physics-based modification of the potential flow model in modelling of OWCs.The present results and analysis are expected to be beneficial to the understanding on the physical mechanism of OWCs and the design of phase control strategies.

Damped Oscillation of Liquid Column in Vertical U-Tube for Newtonian and non-Newtonian Liquids

Damped oscillation of Newtonian liquid in a vertical U-tube is one of the well known phenomena and the solution of this liquid motion for the laminar flow regime in the circular pipe was solved, however, generally speaking, even if the period of the oscillational motion by this solution is nearly coincided with that of the experimental result, the estimation of the damped oscillational process with lapse of time by the solved equation is not in agreement with that of the experimental result. Therefore basing upon the experimental results of the velocity distributions of the oscillational motion in the circular U-tube for the Newtonian and non-Newtonian liquids, the velocity distribution of the Bingham plastic flow is assumed. The solutions of the damped oscillation and also of the vertical falling and rising velocities of the free surface in the vertical U-tube of the diameters D= 10mm, 20mm and 40mm are compared with water and water-glycerine solution for the Newtonian liquids and the acrylic co-polymer solutions for the non-Newtorlian liquid. The comparisons of these solved equations by the new flow model are shown in good agreement with the experimental results. The above stated results are described in detail.

Random response of an oscillator with hysteresis damping

The response behaviour of an oscillator with Reid hysteresis damping under stationary Gauss white excitation is studied. By means of numerical simulation conducted on computer, the mean square response, probability density function and power spectral density function for the response are given. These response characteristics are compared with those predicted by equivalent linearization treatment.

Modeling,Control,and Protection of Modular Multilevel Converter-based Multi-terminal HVDC Systems:A Review

Multi-terminal direct current(MTDC)grids provide the possibility of meshed interconnections between regional power systems and various renewable energy resources to boost supply reliability and economy.The modular multilevel converter(MMC)has become the basic building block for MTDC and DC grids due to its salient features,i.e.,modularity and scalability.Therefore,the MMC-based MTDC systems should be pervasively embedded into the present power system to improve system performance.However,several technical challenges hamper their practical applications and deployment,including modeling,control,and protection of the MMC-MTDC grids.This paper presents a comprehensive investigation and reference in modeling,control,and protection of the MMC-MTDC grids.A general overview of state-of-the-art modeling techniques of the MMC along with their performance in simulation analysis for MTDC applications is provided.A review of control strategies of the MMC-MTDC grids which provide AC system support is presented.State-of-the art protection techniques of the MMCMTDC systems are also investigated.Finally,the associated research challenges and trends are highlighted.

Variation of contact resonance frequency during domain switching in PFM measurements for ferroelectric materials

Piezoresponse Force Spectroscopy(PFS)is a powerful technique widely used for measuring the nanoscale electromechanical coupling of the ferro-/piezo-electric materials.However,it is found that certain nonferroelectric materials can also generate the“hysteresis-loop-like”responses from the PFS measurements due to many other factors such as electrostatic effects.This work therefore studies the signal of the contact resonance frequency during the PFS measurements.By comparing the results from ferroelectric and non-ferroelectric materials,it is found there are distinct differences between these two types of materials in the variation of the contact resonance frequency during the PFS measurements.A momentary and sharp increase of the contact resonance frequency occurs when the domain is switched by applying the DC bias,which can be regarded as a unique characteristic for the ferroelectric materials.After analyzing the reliability and mechanism of this method,it is proposed that the contact resonance frequency variation at the coercive bias is capable to differentiate the electromechanical responses of the ferroelectric and non-ferroelectric materials during the PFS measurements.

Finite-time robust control for transformerless H-bridge cascaded STATCOM with star configuration

This article presents a finite-time robust control(FTRC)of a transformerless STATCOM based on a cascaded multilevel H-bridge converter(CMHC)with star configuration.The FTRC is first proposed for the current loop control of a CMHC-based transformerless STATCOM by using the finite time robust control theory.Taking the parameters,perturbations and external disturbances into account and using coordinate transformation method,the nonlinear dynamic model of the CMHC-based transformerless STATCOM is transformed into a standard nonlinear port-controlled dissipative Hamiltonian(PCDH)structure.Based on the PCDH structure,an FTRC is designed for the CMHC-based transformerless STATCOM to improve the transient stability and oscillation damping of power system.Finally,the simulation results demonstrate that the FTRC has better dynamic performance and strong robustness in comparison with the passivity-based control of the CMHC-based transformerless STATCOM.

Integrated Multi-stage LQR Power Oscillation Damping FACTS Controller

This paper presents an approach for oscillation damping with an integrated multi-stage linear quadratic regulator(MSLQR)FACTS controller combining power oscillation damping(POD)capabilities.The particle swarm optimization(PSO)technique has been used for precise tuning initial control parameters of power system stabilizers(PSS)and FACTS devices(such as STATCOM and UPFC)which results in improved controller performance.It is observed that the proposed control structure damps the oscillations adequately and is modular in design methodology.The sample power system comprising six areas is considered to demonstrate the effectiveness of the proposed concept.The states inter-relation which is shown with eigenvalues reflects better regulation with the proposed controller.The step response also validates the controller performance.