Cross-coupling Terms Research Articles

Using mode shape residuals for model updating of a nonlinear structure featuring 1:1 internal resonance

Internal resonance isa unique phenomenon in nonlinear structures. It can lead to pronounced energy transfer between vibrating modes, causing unexpected stress concentrations in local areas and posing a risk to structural integrity. This paper presents a general model updating procedure for nonlinear structures with such internal resonances using experimentally measured data. The test involves using multiple amplitudes of sinusoidal excitations to drive the structure to several required vibration amplitudes, enabling the underlying linear dynamics, uncoupled nonlinear dynamics, and internal resonances to be activated individually. The underlying linear system, uncoupled nonlinear terms, and cross-coupling terms in the dynamic equation are updated sequentially, with updating the cross-coupling terms being the most challenging task. Unlike conventional practices that heuristically pre-assume a model for the cross-coupling force terms, this paper minimises their number by using the coupling potential energies and identifies their type via an interaction map. A novel mode shape residual is then proposed to tune the coefficients of the cross-coupling terms, which allows energy transfer between coupled modes to be captured quantitatively. A diesis-like structure featuring 1:1 bending-torsion coupling was experimentally investigated using multi-level stepped-sine excitations to demonstrate the proposed model updating procedure. The vibrations of its first resonance veered from a bending-dominant motion to a bending-torsion coexisting motion as the driving forces increased, indicating strong amplitude-dependent mode shapes on the occurrence of internal resonance. The experimental data also showed that the softening and hardening trend of the torsional mode was dependent on the vibration amplitude of the bending mode, a peculiar vibration phenomenon seldom reported for realistic structures in the literature. Using the proposed model updating procedure, a two-mode coupled nonlinear model was identified from the frequency response functions and validated by comparing the backbone curves and amplitude-dependent mode shapes. Results showed that the updated model could predict the resonant vibration patterns of the structure away from and around its internal resonance with sufficient accuracy. It was also revealed that the softening and hardening behaviours of the torsional mode were attributed to different branches of Nonlinear Normal Modes (NNMs).

Evaluation of Cross-Coupling Decoupling in Islanded Microgrid Control with Inductor Current Feed-Forward Technique

To control the voltage source inverter in an islanded microgrid, the d-q reference frame is employed chiefly because of its ability to model inverter's dynamic models accurately. It allows the use of a simple proportional-integral controller for control purposes. However, its use is plagued with the cross-coupling terms introduced by the transformation into the d-q frame in the inner current and outside voltage control loops. This paper presents stepwise design and modelling of the inverter dynamics in the d-q reference frame. The systematic algebraic elimination method with inductor current feed-forward was employed for decoupling cross-coupling terms in the current and voltage loop controller design. The method's effectiveness was evaluated in the voltage and current control; overshoots and distortions resulting from load change were better mitigated. Simulation results were presented for evaluating the controller performance in cross coupling terms.

Macroscopic dynamics of ferromagnetic smectic-A.

We derive the macroscopic dynamic equationsfor ferromagnetic smectic-A liquid crystals for which the spontaneous magnetization is parallel to the layer normal of the layering. As additional macroscopic variables when compared to simple fluids, we have the layer displacement u, familiar from smectic liquid crystals, and the magnetization density M. We find a number of reversible and dissipative cross-coupling terms to the additional macroscopic variables and discuss possible experiments to detect them. Among other effects, we point out that the velocity of first sound becomes anisotropic due to the influence of the modulus of the magnetization, while the magnitude of the velocity of second sound is modified. As for the static behavior, we find cross-coupling terms between the magnitude of the magnetization, on the one hand, and layer compression as well as osmotic pressure, on the other hand. In addition, we point out that as a dissipative effect, temperature gradients can induce gradients in the magnetization parallel to the layer normal, mediated by layer compressions.

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Design of complex vector regulator for Linear Induction Motor

The edge-end effect in the operation of a Linear Induction Motor (LIM) will lead to great changes in motor parameters, and the d and q axes of LIM have cross-coupling terms. The PI regulator usually used in traditional vector control has a high requirement on the accuracy of parameters, and the PI regulator cannot realize the complete axis decoupling control of d and q, which will lead to the decline of the control accuracy. In this paper, the mathematical model of the LIM considering side effects is adopted, and a complex vector regulator is used to replace the traditional PI regulator, which realizes decoupling control of the d-q axes and eliminates the influence of coupling terms. Finally, this paper is verified on dSPACE semi-physical platform. Results show that the decoupling effect of d-q axes using complex vector regulator is due to the PI regulator.

The Effect of Cross-Coupling on the Dynamic Performance of a Dual Phase Shift Controlled BiWPT System

In a bidirectional wireless power transfer (BiWPT) system, dual phase-shift (DPS) control is used to maintain the optimal efficiency at constant output power over varying misalignment. The presence of multiple control and output variables in DPS control creates cross-coupling between transmitter and receiver side, making BiWPT a multiple-input multiple-output (MIMO) system. Due to cross coupling, any change in control variable in one side of the BiWPT system will affect the output of the same side as well as output and control input in the other side. This results in an uncertain dynamic behaviour of the output response. The cross-coupling effect has not been adequately researched in the literature. Hence, this paper presents an accurate dynamic model using a generalized state-space averaging approach (GSSA) and an extended describing function (EDF) method for a multivariable control of the S-S compensated BiWPT system. This model is used to derive the system’s relative gain array (RGA), which is used to study the effect of cross-coupling terms on the output variables. A 1 kW S-S compensated BiWPT experimental set-up is used to validate the effect of cross-coupling on the dynamic behavior of the system by comparing DPS and single phase-shift (SPS) controlled experimental waveforms. The steady-state and transient behavior of the BiWPT system has also been investigated with simulation and experimental results.

Cross-coupling contribution to the isothermal entropy change in multicaloric materials

Multiferroic materials with strong coupling between different degrees of freedom are prone to exhibit giant multicaloric effects resulting from the application or removal of diverse external fields. These materials exhibit a synergic response to the combined action of two fields when the monocaloric effects are both conventional (or both inverse), while a non-synergic response occurs when one of the monocaloric effects is conventional and the other is inverse. In all cases, the multicaloric properties (isothermal entropy and adiabatic temperature changes) do not result from the simple addition of the corresponding monocaloric quantities because there is a contribution from the interplay between degrees of freedom (cross-coupling term). In this paper, we analyse in detail the contribution of the cross-coupling term to the multicaloric entropy values obtained for both synergic and non-synergic multicaloric materials. We first introduce basic thermodynamic concepts accounting for the multicaloric effects, and next the contribution from the cross-coupling term is illustrated via several model examples. We finally analyse the realistic situation for two prototype materials with synergic and non-synergic multicaloric effects.

A Boundary Element Method for the Prediction of Hydrodynamic Ship–Ice–Wave Interactions in Regular Waves

AbstractFor ships navigating in ice floe fields, ship–ice–wave interactions may affect ship performance and ice impact forces. This paper presents an approach to evaluate the cross-coupling added mass and hydrodynamic damping between a passing ship and a free-floating small/medium size ice floe based on the boundary element method (BEM). The influences of added mass and hydrodynamic damping are explored for different wave frequencies and headings. Results are presented for a regular waves scenario whereby a tanker progressing at a slow speed is passing by a free-floating ice floe modeled as a round disk. Radiation and diffraction potentials of the interacting floating bodies are linearly superimposed to reflect the influence of hydromechanical coupling on responses. Parametric analysis of response amplitude operators (RAOs) indicates that the cross-coupling terms of added mass and hydrodynamic damping are of the same order of magnitude as those of the ice floe but smaller by one or two orders of magnitude than those of the ship. It is concluded that hydrodynamic interactions primarily influence the motions of the ice floe and are significant attributes in terms of suitably idealizing ship–ice system dynamics.

The effect of hydro-mechanical coupling on the onset and orientation of localisation bands in partially saturated soils

Constant suction triaxial tests on partially saturated soils demonstrate the dependence of the onset and orientation of localisation bands upon different mechanical loading and saturation conditions, in addition to the material properties of soils. This effect of hydro-mechanical coupling, via the combination of effective stress and suction, on the onset and inclination of the shear bands is investigated in this paper using a model with a single yield surface dependent on both stress and suction. The cross-coupling terms in the asymmetric tangent stiffness allow the model to capture the coupled effects of suction and effective stress on the behaviour upon yielding and hence facilitate the bifurcation analysis for the onset and orientation of localisation bands in various loading and hydraulic states. The model parameters are determined with its experimental bifurcation characteristics, showing the sensitiveness of conditions that favour bifurcation under the effect of hydro-mechanical coupling and dilation.

Implementation of Effective Scale Factor Matching and Axial Centripetal Error Compensation for a Rotating Accelerometer Gravity Gradiometer

Rotating accelerometer gravity gradiometer (RAGG) is the only gravity gradient measuring device in the world to achieve commercial applications. When the parameter consistency among multiple accelerometers of the RAGG is not sufficient, its combined output cannot effectively suppress common-mode noise in the environment. A method for suppressing RAGG’s linear and angular motion noise is presented in this article by projecting the parameters, including scale factor, misalignment angle, second-order terms, and cross-coupling terms, onto the Cartesian coordinate system of the turntable plane. Proposing the algorithm implementation scheme of three effective scale factor solver loops, and for further canceling the motion residual error, high-precision gyroscope compensation loops are introduced. The added error compensation loop obtains the angular acceleration by differencing the angular velocity measured by the gyroscope, which in turn adjusts the loop parameters. Experimental results show that with the proposed method, the noise suppression of linear motion common-mode acceleration reaches 6.5 orders of magnitude, that is, the noise level <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2.7 \times {10^{ - 8}} {\mathrm{ g/}}\sqrt {{\mathrm{Hz}}} $ </tex-math></inline-formula> of the accelerometer at the rotation frequency, and the angular motion common-mode acceleration noise is suppressed by six orders of magnitude, and the noise level <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$6.8 \times {10^{ - 8}} {\mathrm{ g/}}\sqrt {{\mathrm{Hz}}} $ </tex-math></inline-formula> of the accelerometer at the swing frequency is also obtained.

A Hybrid-Frame Control Based Impedance Shaping Method to Extend the Effective Damping Frequency Range of the Three-Phase Adaptive Active Damper

The grid-connected inverter may get unstable due to variation of grid impedance. To improve the system stability, an adaptive active damper, which emulates an adaptive tuning virtual resistor, can be introduced at the point of common coupling. However, subject to the control bandwidth, the virtual resistor is actually a frequency- dependent impedance, and its damping performance is impaired. In this article, we propose an impedance shaping method to make the virtual impedance be resistive in a wider frequency range, and it is implemented under hybrid frame for directly controlling the active power of the active damper and eliminating the influence of the cross-coupling terms on the emulation of a virtual resistor. Finally, the prototypes of a 3-kVA three-phase active damper and a 6-kVA three-phase <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LCL-</i> type grid-connected inverter are fabricated and tested in the lab. The experimental results are provided to verify the effectiveness of the proposed control methods for the three-phase adaptive active damper.

A constant parameter time domain model for dynamic modelling of multi-body system with strong hydrodynamic interactions

It is well known that direct evaluation of the wave-induced dynamics of floating structures by Cummins equation is time-consuming due to the convolution integrals. Particularly, for a multi-body system, a complete matrix of the impulse response functions, namely the kernel of the convolution integral in Cummins equation, is required as the cross-coupling terms in the hydrodynamic matrices are important in accurately evaluating the dynamic responses, resulting in increased computation time. Rather than solving the convolution kernel, state-space models have been adopted as an alternative, working well for single body cases. However, it has the disadvantage of numerical instability, which may cause significant errors for strongly resonant phenomena, e.g. in the multi-body interactions. To overcome this issue, the practise is to introduce a damping lid to the free surface in the gap between multiple bodies in frequency domain. Based on the hydrodynamic coefficients obtained in the frequency domain, this study presents a time domain model that combines the damping lid method and state-space model, resulting in a Constant Parameter Time Domain Model (CPTDM). Due to the nature of the time domain model, it is possible to account for nonlinear viscous damping, wherever it is appropriate. The finding shows that the damping lid method helps to stabilize the numerical simulation of the multi-body system which undergoes gap resonances. It is found that a larger damping lid factor favors the decaying of the impulse response functions and the development of lower-order state-space models. The developed CPTDM is found to work well for different wave frequencies and wave headings, with better accuracy and higher efficiency than AQWA's time-domain simulations. Particularly, at the resonant frequency, the developed CPTDM still retains good accuracy as compared with the RAO-based responses.

A Multivariable Phase-Locked Loop-Integrated Controller for Enhanced Performance of Voltage Source Converters Under Weak Grid Conditions

This article proposes a new control strategy in stationary frame to improve the operational robustness of voltage source converters (VSCs) under weak grid conditions. First, dynamics of the phase-locked loop (PLL) are incorporated into the model of a grid-connected VSC in stationary reference frame. It is rigorously shown that the three-phase PLL introduces cross-coupling terms between the two control channels. Second, based on the augmented model, a multivariable controller is proposed which combines the current control feedback gains with PLL feedback gains. Third, the gains of the controller are designed using an optimal control theory approach. It is shown through theoretical analysis, computer simulations, and a laboratory experimental setup that the proposed controller improves the stability margins of the VSC during weak grid conditions. More specifically, under a given identical operating conditions, while the conventional controller’s responses become increasingly oscillatory for short-circuit ratio (SCR) below 1.95 and eventually becomes unstable at SCR=1.26, the proposed controller exhibits smooth and stable responses for SCR as low as 1. The proposed controller also produces cleaner sinusoidal currents during unbalanced grid voltages.

Approximate solutions of the Riemann problem for a two-phase flow of immiscible liquids based on the Buckley–Leverett model

The article proposes an approximate method based on the "vanishing viscosity" method, which ensures the smoothness of the solution without taking into account the capillary pressure. We will consider the vanishing viscosity solution to the Riemann problem and to the boundary Riemann problem. It is not a weak solution, unless the system is conservative. One can prove that it is a viscosity solution actually meaning the extension of the semigroup of the vanishing viscosity solution to piecewise constant initial and boundary data. It is known that without taking into account the capillary pressure, the Buckley–Leverett model is the main one. Typically, from a computational point of view, approximate models are required for time slicing when creating computational algorithms. Analysis of the flow of a mixture of two immiscible liquids, the viscosity of which depends on pressure, leads to a further extension of the classical Buckley–Leverett model. Some two-phase flow models based on the expansion of Darcy’s law include the effect of capillary pressure. This is motivated by the fact that some fluids, e.g., crude oil, have a pressure-dependent viscosity and are noticeably sensitive to pressure fluctuations. Results confirm the insignificant influence of cross-coupling terms compared to the classical Darcy approach.

Macroscopic behavior of the P1 ( β ) and P2 (distorted β ) phases of superfluid He3 : Soundlike excitations

We describe the macroscopic behavior of superfluid $^{3}\mathrm{He}$ in the ${P}_{1}$ ($\ensuremath{\beta}$) phase in an anisotropic aerogel. It turns out that the ${P}_{1}$ phase shares many features with superfluid $^{3}\mathrm{He}\text{\ensuremath{-}}{\mathrm{A}}_{1}$. It exists only in an external magnetic field and has only one spin orientation in its superfluid condensate. In the ${P}_{1}$ phase, the direction of the external magnetic field, the preferred direction in orbit space $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\mathbf{m}}$ and the average preferred direction of the silica strands ${\ensuremath{\zeta}}_{i}$, are all parallel. While the preferred direction in orbit space and the average preferred direction of the silica strands are even under time reversal, the preferred direction $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\mathbf{w}}$ in spin space is odd under time reversal. As new macroscopic variables compared with superfluid $^{3}\mathrm{He}$ we have for the superfluid ${P}_{1}$ phase in an aerogel the strain field associated with the aerogel network. As a result of these additional macroscopic variables we find new static and dynamic cross-coupling terms, which come as reversible (zero entropy production) as well as as irreversible contributions. As an outstanding feature of the ${P}_{1}$ phase we find that second sound and, to a lesser extent, fourth sound assume spin-wave character, a feature that should be testable experimentally. This result closely parallels that for the ${A}_{1}$ phase of bulk superfluid $^{3}\mathrm{He}$ in spite of the fact that the $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\mathbf{l}}$ vector of the ${A}_{1}$ phase, which is odd under time reversal, does not exist in the ${P}_{1}$ phase. We also discuss briefly the macroscopic behavior of the distorted $\ensuremath{\beta}$ (${P}_{2}$) phase, which shares several features with the distorted $A$ phase of bulk superfluid $^{3}\mathrm{He}$, in particular with respect to its properties in spin space.

Transient Performance Improvement of Battery Integrated Stand-alone PMSG Wind Energy System using Active Disturbance Rejection Controller

This paper proposes a new control approach using Active Disturbance Rejection Control (ADRC) to assess the transient performance of battery integrated standalone based PMSG wind turbine under unpredictable wind and sudden load variations. An external and internal disturbance such as wind speed variations, load changing conditions, the parametric variations and cross coupling terms between dq axes currents degrades the performance of the conventional PI controller. Hence, to cancel aforementioned internal and external disturbances, ADRC is developed for machine and load side converter of PMSG wind energy system. The main objective of proposed approach for machine and load side converter is to extract maximum power tracking and to enhance the performance under internal and external disturbances. Simulations results are carried out in MATLAB/SIMULINK platform with several case studies to validate the efficacy of the proposed approach. The results achieved with proposed approach are compared with conventional vector PI control. This paper also shows the potentiality of the proposed method for effective power management between PMSG, load, and battery to ensure reliable supply to load.

A Two-Fluid Model for the Macroscopic Behavior of Nematic Fluids and Gels in a Chiral Solvent

We present the macroscopic dynamics of nematic liquid crystals in a two-fluid context. We investigate the case of a nematic in a chiral solvent as well as of a cholesteric in a non-chiral solvent. In addition, we analyze how the incorporation of a strain field for nematic gels and elastomers in a chiral solvent modifies the macroscopic dynamics. It turns out that the relative velocity between the nematic subsystem and the chiral solvent gives rise to a number of cross-coupling terms, reversible as well as irreversible, unknown from other two-fluid systems considered so far. Possible experiments to study those novel dynamic cross-coupling terms are suggested. As examples we just mention that gradients of the relative velocity lead, in cholesterics to heat currents. We also find that in cholesterics shear flows give rise to a temporal variation in the velocity difference perpendicular to the shear plane, and in cholesteric gels uniaxial stresses or strains generate temporal variations of the velocity difference. Finally, the exotic chiral Q phase of tetragonal (D_4) symmetry is analyzed for an isotropic non-chiral solvent in a two-fluid scenario.

Enhanced control and operation for brushless doubly-fed induction generator based wind turbine system under grid voltage unbalance

This paper presents an enhanced control and operation for brushless doubly-fed induction generator (BDFIG) based wind turbine system under grid voltage unbalance by considering the controls of machine side converter(MSC) and grid side converter(GSC) together. The MSC is controlled to eliminate torque oscillations and realize decoupling control of power winding(PW) average active and reactive power while the GSC is controlled to eliminate oscillations in the total output active power. A single current closed-loop controller composed of a positive sequence current controller in the positive synchronous reference frame and a negative sequence current controller in the negative synchronous reference frame is designed for both MSC and GSC. To achieve decoupling control and improve system dynamic response, in current loops, all the disturbances and cross-coupling terms are derived and used for feedforward control. A fast sequence decomposition algorithm is employed to reduce the considerable time delays of using notch filers. In order to validate the effectiveness of proposed control, simulations for a 2WM BDFIG based wind generation system were carried out, the results demonstrated that the proposed control can effectively eliminate oscillations of BDFIG torque and total output active power, and has good dynamic and stable performance.

A two-fluid model for the macroscopic behavior of polar nematic fluids and gels in a nonchiral or a chiral solvent

We present the macroscopic dynamics of polar nematic liquid crystals in a two-fluid context. We investigate the case of a nonchiral as well as of a chiral solvent. In addition, we analyze how the incorporation of a strain field for polar nematic gels and elastomers in a solvent modifies the macroscopic dynamics. It turns out that the relative velocity between the polar subsystem and the solvent gives rise to a number of cross-coupling terms, reversible as well as irreversible, unknown from the other two-fluid systems considered so far. Possible experiments to study those novel dynamic cross-coupling terms are suggested. As examples we just mention that gradients of the relative velocity lead, in polar nematics to heat currents and in polar cholesterics to temporal changes of the polarization. In polar cholesterics, shear flows give rise to a temporal variation in the velocity difference perpendicular to the shear plane, and in polar nematic gels uniaxial stresses or strains generate temporal variations of the velocity difference.Graphical abstract

Composite Decoupling Control of PMSM Based on Extended State Observer

In order to solve the problem that the dynamic decoupling performance of the traditional decoupling method is reduced due to the parameter disturbance of permanent magnet synchronous motor (PMSM), a composite decoupling control method based on extended state observer (ESO) is proposed in this paper. In this method, voltage drop across stator resistance, cross coupling terms, internal uncertains and external load torque are taken as disturbances. The disturbance is observed in real time by using the extended state observer and compensated to the output end of the current controller, so as to realize the current decoupling control of the system and achieve the purpose of precise control of the current loop. The results of theoretical analysis show and simulation show that the composite decoupling control strategy based on extended state observer has better dynamic decoupling effect.