Cross-coupling Terms Research Articles

Two-fluid model for a fluid with tetrahedral-octupolar order.

We investigate the macroscopic dynamics of a two-fluid system with tetrahedral order. As all normal-fluid two-fluid systems one has-compared to a simple fluid-the velocity difference between the two subsystems and the concentration of one component as additional macroscopic variables. Depending on the type of system, the concentration can either be a conserved quantity or relax on a long, but finite timescale. Due to the existence of the tetrahedral order such a system breaks parity symmetry. Here we discuss physical systems without preferred direction in real space, meaning that our description applies to optically isotropic materials. We find a number of reversible as well as dissipative dynamic cross-coupling terms due to the additional octupolar order, when compared to a fluid mixture. As the most interesting cross-coupling term from an experimental point of view, we identify a dissipative cross-coupling between the relative velocity and the usual velocity gradients. Applying a shear flow in a plane, this dissipative cross-coupling leads to a velocity difference perpendicular to the shear plane. As a result one can obtain a spatially homogeneous oscillation of the relative velocity. In addition, this induced relative velocity can couple as a function of time and space to the concentration, which gives rise to an overdamped propagating soundlike mode, where the overdamping arises from the fact that velocity difference is a macroscopic variable and not strictly conserved. We also show that electric field gradients are connected with an analogous reversible cross-coupling and can lead in a planar shear geometry to an overdamped propagating mode as well.

Nuclear pasta structures and symmetry energy

In the framework of the relativistic mean field model with Thomas-Fermi approximation, we study the structures of low density nuclear matter in a three-dimensional geometry with reflection symmetry. The numerical accuracy and efficiency are improved by expanding the mean fields according to fast cosine transformation and considering only one octant of the unit cell. The effect of finite cell size is treated carefully by searching for the optimum cell size. Typical pasta structures (droplet, rod, slab, tube, and bubble) arranged in various crystalline configurations are obtained for both fixed proton fractions and $\beta$-equilibration. It is found that the properties of droplets/bubbles are similar in body-centered cubic (BCC) and face-centered cubic (FCC) lattices, where the FCC lattice generally becomes more stable than BCC lattice as density increases. For the rod/tube phases, the honeycomb lattice is always more stable than the simple one. By introducing an $\omega$-$\rho$ cross coupling term, we further examine the pasta structures with a smaller slope of symmetry energy $L = 41.34$ MeV, which predicts larger onset densities for core-crust transition and non-spherical nuclei. Such a variation due to the reduction of $L$ is expected to have impacts on various properties in neutron stars, supernova dynamics, and binary neutron star mergers.

Macroscopic behavior of materials composed of two elastic media

In the present paper we investigate macroscopic two-fluid effects in systems composed of two elastic media. Using two strain tensors as macroscopic variables, we present a nonlinear analysis in the regime of long wavelengths and low frequencies. We also discuss the description in terms of relative strains and total strains. Generalizing earlier work on relative rotations for systems such as nematic elastomers or uniaxial magnetic gels, we investigate how this concept can be applied to the case of two elastic media in the linear domain. For the two strain fields and relative rotations between the two elastic media, we find a number of reversible and dissipative cross-coupling terms that couple velocity differences, mean velocities, strain fields, and relative rotations to each other as well as to temperature and concentration gradients. The question of relative translations is also analyzed. A linearized description using relative translations is physically meaningful as well as technically consistent with using strain fields and relative rotations. Finally, we apply this description to the swinging of two coupled homogeneous elastic media relative to each other, and to the oscillating actuation or active stress introduced through one of the elastic compounds.

Implementation of Cross-Coupling Terms in Proportional-Resonant Current Control Schemes for Improving Current Tracking Performance

The proportional-integrator (PI) controller in the synchronous reference frame (dq-frame) and the proportional-resonant (PR) controller in the stationary reference frame (αβ-frame) are two typical linear current control schemes for three-phase voltage source converters. It is generally believed that the plant model is mathematically uncoupled in αβ-frame. Hence, the decoupling control required to attenuate the axis cross-coupling effect in dq-frame is regarded as not necessary in αβ-frame. However, detailed analysis with complex coefficient transfer functions reveals differences in the control performance between the fully decoupled PI control scheme in dq-frame and the PR control scheme in αβ-frame. When regulating sinusoidal currents in αβ-frame, the α-axis and β-axis current references are strongly correlated with each other, which implies a cross-coupling effect equivalent to that of dq-frame. In analogy to the dq-frame decoupling control, cross-coupling terms can be employed together with the conventional PR control scheme. It can bring the benefit of improving the transient response of current tracking and reducing the sensitivity of the resonant controller to frequency variation, especially for low-switching-frequency applications with limited current control bandwidth. Furthermore, the cross-coupling terms based on reference current feed-forward are proposed to improve the performance of both positive- and negative-sequence current control. Experimental results are shown to validate the analysis and the performance of the proposed control scheme.

Focus Improvement of Airborne High-Squint Bistatic SAR Data Using Modified Azimuth NLCS Algorithm Based on Lagrange Inversion Theorem

In this paper, a modified azimuth nonlinear chirp scaling (NLCS) algorithm is derived for high-squint bistatic synthetic aperture radar (BiSAR) imaging to solve its inherent difficult issues, including the large range cell migration (RCM), azimuth-dependent Doppler parameters, and the sensibility of the higher order terms. First, using the Lagrange inversion theorem, an accurate spectrum suitable for processing airborne high-squint BiSAR data is introduced. Different from the spectrum that is based on the method of series reversion (MSR), it is allowed to derive the bistatic stationary phase point while retaining the double square root (DSR) of the slant range history. Based the spectrum, a linear RCM correction is used to remove the most of the linear RCM components and mitigate the range-azimuth coupling, and, then, bulk secondary range compression is implemented to compensate the residual RCM and cross-coupling terms. Following this, a modified azimuth NLCS operation is applied to eliminate the azimuth-dependence of Doppler parameters and equalize the azimuth frequency modulation for azimuth compression. The experimental results, with better focusing performance, prove the high accuracy and effectiveness of the proposed algorithm.

Modeling and Coordinated Control Design for Brushless Doubly-Fed Induction Generator-Based Wind Turbine to Withstand Grid Voltage Unbalance

Grid codes require wind turbines to have capability to withstand a certain grid voltage unbalance without tripping. However, existing controls for brushless doubly-fed induction generator (BDFIG) based wind turbine under grid unbalance have many problems such as difficulty in realizing decoupling control, involvement with flux or current estimations, and complex control structure. Moreover, the existing studies only focused on the control of machine side converter (MSC), but the coordinated control between MSC and grid side converter (GSC) and the control objectives of overall BDFIG wind turbine system have not yet been addressed so far. To overcome these problems and improve the control capability, this paper proposes a coordinated control strategy by considering MSC and GSC together. First, the enhanced control objectives for overall BDFIG wind turbine system are determined. Second, the simple single current closed-loop controllers without involving with any flux or current estimations are designed for MSC and GSC, respectively. Meanwhile, in current loops, all the disturbances and cross-coupling terms on <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">dq</i> axes are derived and used for feedforward control so as to achieve decoupling control and improve system dynamic response. Further, a fast sequence decomposition approach is employed to enhance the control characteristics of the whole system. Finally, the effectiveness of proposed control is validated through case studies for a 2 MW BDFIG based wind generation system. The results demonstrate that the proposed control can effectively achieve the control objectives of overall wind turbine system under grid voltage unbalance and provide excellent dynamic and stable performance.

A Power De-coupling Control Strategy for MMC-HVDC System

Modular multilevel converter (MMC) has a wide range of applications in the field of HVDC. However, some of the electricity in MMC is coupled, which makes the design of control system more difficult and have a negative impact on the stable operation of the system. This paper puts forward a strategy to eliminate the coupling control, this method compensates the current cross-coupling terms of the d-axis and the q-axis in the dq coordinate system, SOGI(Second Order Generalized Integrator) and Q-PR(Quasi-PR) controller are used to accurately control the double frequency circulation in the internal unbalanced current, the coupling caused by the internal unbalance current and the sub-capacitor module voltage is compensated in the three-phase coordinate system. Finally, the simulation verification is carried out in PSCAD, which is compared with the traditional control method to verify that the proposed method can achieve complete power decoupling.

Virtual charge‐based synchronisation and feedback linearisation‐based current control of a three‐phase grid‐connected inverter without grid voltage sensors

A conventional synchronous (rotating) reference frame control requires small-signal models and introduces cross-coupling terms. In this study, a virtual charge-based scheme for grid synchronisation with only current measurements has been proposed for a three-phase grid-connected inverter with a first-order filter. The methodology described in this study curbs the dependency of the inverter on the information of the grid voltage to generate unit vectors from the phase-locked loop. This kind of estimation is especially important during grid voltage sensor failures or a distant point common coupling or weak grid conditions. In the proposed estimation scheme, no noisy differentiation is involved and only the nominal values of the interfacing filter parameters are utilised, making the implementation easier in digital microcontrollers. Also, a current control architecture based on feedback linearisation concept has been explored and embedded with the proposed grid voltage estimation technique, and the corresponding performance has been evaluated via simulation and experimental studies.

Macroscopic behavior of the distorted A and B phases and the polar phase of superfluid He3 in an anisotropic aerogel

We describe the macroscopic behavior of superfluid $^{3}\mathrm{He}$ in the polar and the distorted $A$ and $B$ phases in an anisotropic aerogel. It turns out that the distorted $A$ phase shares many features with superfluid $^{3}\mathrm{He}\ensuremath{-}A$. Its order parameter contains the polar phase as well as the $A$ phase as a smooth limiting case. The former is in agreement with the fact that the phase transition polar to distorted $A$ is observed to be of second order. Due to the different structure of the order parameter, the unit vector $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{l}$, which is characteristic of the superfluid $^{3}\mathrm{He}\ensuremath{-}A$ and the distorted $A$ phase, is not present in the polar phase. As new macroscopic variables compared to superfluid $^{3}\mathrm{He}$ we have for the superfluid distorted $A$ phase in an aerogel the strain field associated with the aerogel network. In addition, we have in superfluid $^{3}\mathrm{He}$ relative rotations between the anisotropic gel network and the $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{l}$ vector as a macroscopic variable. 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. The polar phase in an anisotropic aerogel is anisotropic in its elastic properties. We have as additional macroscopic variables relative rotations similar to those of a nematic liquid crystalline elastomer, since the preferred direction in the polar phase is even under time reversal and not odd as for the distorted $A$ phase. These additional features lead to static and dissipative cross-coupling terms, which cannot exist for a polar phase in an isotropic aerogel. For the distorted $B$ phase we find for the orbital part a macroscopic dynamic behavior which shares some features with that of the polar phase. In contrast to the polar phase, however, the distorted $B$ phase does not show relative rotations, since there is only one preferred direction. The preferred direction in the distorted $B$ phase leads to a preferred direction in spin space as well. As a consequence the spin waves become anisotropic and longitudinal and transverse spin waves become coupled, even in the absence of a magnetic field. We also discuss briefly the coupling to the spin degrees of freedom in the polar and the distorted $A$ phase.

An Equation of State for Magnetized Neutron Star Matter and Tidal Deformation in Neutron Star Mergers

Abstract We derive an equation of state (EOS) for magnetized charge-neutral nuclear matter relevant for a neutron star (NS). The calculations are performed within an effective chiral model based on the generalization of the σ model with nonlinear self-interactions of the σ mesons along with the ρ−σ cross-coupling term. This model is extended by introducing the contributions of a strong magnetic field on the charged particles. The contributions arising from the effects of the magnetic field on the Dirac sea of charged baryons are also included. The resulting EOS for the magnetized dense matter is used to investigate the NS properties like its mass, radius, and tidal deformability. The magnitude of the magnetic field at the core of the NS considered here is in the range of 1015–1018 G, for which the relative deformation from spherical symmetry turns out to be less than 1%, giving a post facto justification for the spherically symmetric treatment of the NS structure. The dimensionless tidal deformability Λ1.4 is 526 for an NS with mass 1.4 M ⊙, which is consistent with the recent observation of GW 170817. The maximum mass of the NS in the presence of a strong magnetic field is consistent with the observational constraints on the mass of the pulsar PSR J0348–0432, and its radius at a mass of 1.4 M ⊙ is also in agreement with the empirical bounds.

GPIO-Based Nonlinear Predictive Control for Flux-Weakening Current Control of the IPMSM Servo System

This paper proposes a generalized proportional integral observer (GPIO) based nonlinear predictive control (NPC) for an interior permanent magnet synchronous motor (IPMSM) to improve the flux-weakening (FW) current control performance against the complex nonlinear cross-coupling terms and the IPMSM parameters’ variations. First, the IPMSM is remodeled to further analyze the FW control difficulties caused by such cross-coupling terms and parameters variations. Considering the parameters’ variations as a kind of disturbance, a GPIO is then designed to compensate for such disturbance. A GPIO-based NPC is finally designed to handle the nonlinear cross-coupling terms to obtain an optimized current control performance. Experiments on a digital signal processor (DSP) based IPMSM servo system validate the workability of the proposed control scheme.

Macroscopic two-fluid effects in magnetorheological fluids.

We investigate macroscopic two-fluid effects in magnetorheological fluids generalizing a one-fluid model studied before. In the bulk of the paper we use a model in which the carrier fluid, with density ρ_{1}, moves with velocity v_{1}, while the magnetic component (density ρ_{2}) and, therefore, the magnetization and the magnetic-field-induced relaxing strain field move with velocity v_{2}. In the framework of macroscopic dynamics we find, in particular, reversible dynamic and dissipative cross-coupling terms between the magnetization and the velocity difference. Experiments to detect some of these cross-coupling terms are suggested. We also compare the results of the two-fluid model presented here with two-fluid models available for electrorheological fluids. In two appendices we discuss the simplifying assumptions made to arrive at the model used in this paper and we also outline how to detect potential deviations from this model.

Control Design and Stability Analysis of Power Converters: The MIMO Generalized Bode Criterion

Three-phase dynamic systems and multiphase generators are frequently modeled and controlled in the synchronous reference frame. To properly model the cross-coupling terms in this reference frame, complex vector theory and transfer function matrices are commonly applied, obtaining multiple-input multiple-output (MIMO) dynamic models. The stability of MIMO systems can be assessed through the Nyquist generalized stability criterion. However, the use of the Nyquist diagram complicates the controller design. The Bode diagram is a more intuitive tool for the controller design; however, the Bode stability criterion is not applicable to MIMO systems. In this article, the MIMO generalized Bode criterion is proposed. Since this stability criterion is based on the Nyquist generalized stability criterion, it can be applied to any system. Furthermore, it is simple to use, as it only requires information contained in the open-loop transfer matrix and the Bode diagram. The proposed stability criterion thus offers an interesting tool for the controller design procedure in MIMO systems, as it is shown in this article for two common applications: the current control loop of a power converter, a 2 × 2 system, and the current control loop of two independent power converters in parallel, a 4 × 4 system.

Systematic Modeling of a Class of Microgrids and Its Application to Impact Analysis of Cross-Coupling Droop Terms

This paper presents an approach for systematically modeling a class of microgrid (MG) systems. The derived model accommodates grid-connected and islanded operation of the MG simultaneously, and allows modeling of converter-based as well as directly interfaced resources. Full modeling of virtual synchronous machines and actual synchronous generators is addressed. The originally nonlinear model is then converted to a linear model whose eigenvalues determine local stability of the MG. The model is used to analyze impacts of cross-coupling droop terms on the MG stability. The conclusions of this analysis are as follows. Addition of cross-coupling droop terms reduces the losses, compromises the stability in the grid-connected mode, and improves the stability in standalone mode. Therefore, for an MG that is intended to continuously operate at grid-connected and standalone mode, only a modest amount of cross-coupling terms is recommended to increase the efficiency without compromising the grid-connected stability. Simulation and experimental results are presented to verify the derivations.

Improvement of non‐linear chirp‐scaling algorithm for highly squint bistatic SAR data focusing

Bistatic synthetic aperture radar (SAR) has specific advantages, e.g. weak targets detecting, reducing system vulnerability, and anti-interference with low cost and flexible working modes. However, great challenges exist in data processing procedure due to its complicated geometry and 2-D spatial variance, which become more serious when the squint angle increases. Here, an improved non-linear chirp scaling method is proposed to handle highly squint bistatic SAR data. On one hand, Keystone transform is first performed, then linear range walk is removed to deduce the residual range cell migration correction factor, which is used for range compression and removing cross-coupling terms. On the other hand, frequency modulation rates and high-order phase based on the transmitter range offset (RO) and receiver RO are derived according to the geometric configuration. Simulation results show the effectiveness of the proposed algorithm.

Non-linear anisotropic hyperelasticity for granular materials

We describe a non-linear anisotropic hyperelastic model appropriate for geomaterials, deriving the full stress-strain response from strain energy or complementary energy functions. Specific forms of the functions are chosen so that the stiffness and compliance matrices have the appropriate minor symmetries. The model employs two material parameters to describe basic volumetric and shear response, one to express nonlinearity of stiffness as a function of mean stress, and two more (together with the directions of the principal axes of anisotropy) to express the degree of anisotropy. The model is modular, so that non-linearity and anisotropy can be included separately or in combination. For specific parameter settings it reduces to simpler cases such as linear isotropic elasticity. Because the model employs hyperelasticity, thermodynamic acceptability is ensured and all appropriate cross-coupling terms are included between the shear and volumetric behaviour.

Small-Signal Converter Admittance in the $pn$-Frame: Systematic Derivation and Analysis of the Cross-Coupling Terms

In this paper, a methodology is presented to derive the small-signal admittance of a converter-based control system in the $pn$ -frame. Such a methodology makes use of a set of derived equations that link the $qd$ -frame small-signal admittance data to the corresponding $pn$ -frame small-signal admittance terms. Compared to existing results providing the $pn$ -frame small-signal impedance of a grid-connected converter, the presented technique allows a calculation of the $pn$ -frame small-signal admittance (or impedance) when additional elements are present in the controller, as in many practical designs. The presented technique is therefore generic and provides a systematic way to calculate the $pn$ -frame admittance regardless of the used converter control scheme. In this study, the method has been applied to assess how different parts of the controller affect the $pn$ -frame admittance terms and, in particular, the cross-coupling that exists between its positive and negative sequence terms. Thereby, the results of the proposed methodology have been used to study the impact of the negative sequence current compensator on the stability performance of a grid-connected converter. Experimental tests using a real hardware setup are used to support the obtained results.

The modal analysis of a double disc flexible rotor-bearing system with isotropic stiffness and damping properties

This paper shows the analysis of the modal characteristics of a flexible rotor system having two non-identical discs mounted on it using the finite element method. It uses the Timoshenko beam elements theory including shear deformation, rotary bending effects and gyroscopic effects. The bearing is considered to be isotropic having translational stiffness and damping values constant in x and y directions. There are no cross-coupling terms. The conduct of the framework is investigated by reference to natural frequency maps and mode shape diagrams. A comparative study has been conducted between this system having isotropic bearings of stiffness and damping properties and the one in which the bearings have only stiffness keeping other parameters same. The gyroscopic effect is seen to be prominent at higher rotating speeds for both the cases which cause the splitting of frequency pairs into forward and backward whirls. The Campbell diagram is computed which helps in finding the critical speeds associated with each pair of diverging natural frequencies. The bearing system represented by stiffness and damping properties shows a comparatively better control over the critical speed range.

The effect of nonlinear cross-coupling on reduced-order modelling

The use of reduced-order models (ROMs) for nonlinear systems has received significant attention due to their potential to greatly reduce computational cost, compared to full nonlinear finite-element models. Here, we consider and compare two indirect methods; the applied modal force and enforced modal displacement techniques, paying particular attention to the effect of nonlinear cross-coupling terms. The analysis we present shows that the applied modal force technique is able to account for some effects arising from modes that are not retained in the ROMs, but the resulting accuracy of the ROM depends on the amplitudes selected for the set of forces used to estimate the coefficients of the ROMs. This analysis also shows that the enforced modal displacement technique does not compensate for the effect of modal interactions with modes that are not included in the ROM, but its accuracy is independent of the amplitude of the forces used to estimate the coefficients. The mechanisms that lead to the differences between these techniques is firstly demonstrated using a two conceptually-simple, discrete systems, before a nonlinear beam model is considered.

Experimental study on coupled caloric effect driven by dual fields in metamagnetic Heusler alloy Ni50Mn35In15

The multicaloric and coupled caloric effect of metamagnetic shape memory alloy Ni50Mn35In15 driven by hydrostatic pressure and magnetic field has been systematically investigated. The existence of pressure significantly changes the relationship between the magnetic volume coupling coefficient and temperature. Thermodynamic analysis indicates that the magnetocaloric effect at a certain pressure is equivalent to the magnetocaloric effect at ambient pressure adjusted by the coupled caloric effect (ΔScp). This theoretical result is verified by magnetic measurements under various pressures for the Ni50Mn35In15 with the inverse magnetocaloric effect. When a pressure of 0.995 GPa is applied, the peak value of entropy change can be as high as |ΔS| ∼ 25.7 J kg−1 K−1 upon a magnetic field change of 5–0 T, which increases by 8% compared to that of ambient pressure though the magnetization change (ΔM) across martensitic transition reduces 20% owing to the shift of the transition to higher temperature by 30 K. Detailed analysis indicates that the coupled caloric effect involving the strengthened magnetostructural coupling under pressure is responsible for the enhanced entropy change. The quantitative analysis of cross coupling term driven by dual fields reveals the essence of regulated magnetocaloric effect by pressure, which will be helpful for designing new materials based on the magnetostructural coupling strength.