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The purpose of this paper is to investigate and restrain the cross-coupling effect among X, Y and Z-axes of a three degrees of freedom hybrid magnetic bearing (3-DOF HMB). The influence of the cross-coupling effect on the force characteristics and stiffnesses are analysed. Two additional methods are proposed to eliminate the cross-coupling effect.

Analysis with finite element method (FEM) is time-consuming because of the requirement of a 3D model for the studied 3-DOF HMB. Hence, an improved magnetic circuit model considering the leakage, cross-coupling and saturation effects is used to investigate the cross-coupling effect in this paper. In addition, two restraining methods are proposed. One is adding an auxiliary coil between radial and axial stators. The other is adding an iron ring between the PM and radial or axial stator.

The X-axis (or Y-axis) force characteristics and stiffnesses are significantly influenced by the Z-axis current, while other axes force characteristics and stiffnesses do not show the cross-coupling effect. Moreover, this cross-coupling effect is inversely related to the distance between axial thrust disk and radial MB part. Besides, adding an auxiliary coil can effectively eliminate the cross-coupling effect in whole work range and adding an iron ring can reduce the cross-coupling effect.

The cross-coupling effect and its restraining methods of a 3-DOF HMB are investigated, which is beneficial to the design and control of such 3-DOF HMB.

The purpose of this paper is to investigate the influence of end‐effect and cross‐coupling on the torque‐speed characteristics of switched flux permanent magnet (SFPM) machines.

The torque‐speed characteristics are predicted using two different methods. These are direct and indirect finite element methods, at different cross‐coupling levels, namely, full cross‐coupling on both PM flux linkage and dq‐axis inductances, partial cross‐coupling on the PM flux linkage only and without cross‐coupling.

The influence of the cross‐coupling on dq‐axis inductances of the studied machine is relatively small. However, it is more significant on the PM flux linkage. Therefore, the partial cross‐coupling model, which is much easier and faster, exhibits almost the same accuracy as the full cross‐coupling model. Furthermore, the end‐effect causes a large reduction in torque‐speed characteristics. However, such a reduction is more significant in the flux weakening operation region.

This is the first time that the influence of end‐effect of SFPM machines on the torque‐speed characteristics, especially in flux weakening region, and on the dq‐axis inductances has been investigated.

The purpose of this paper is to develop an attitude control strategy for the reusable boosted vehicle with large angle of attack, and to remove the cross coupling among roll, pitch and yaw channels.

The coordinated gain scheduling control strategy consists mainly of two parts. First, initially ignoring dynamic coupling, single channel gain scheduling controller is designed based on linearized models, respectively. Second, with respect to main channel gain scheduling controller, coordinated scheduling controller is used to generate intentionally cross coupling to partly cancel inter‐channel cross coupling of reusable boosted vehicle.

A coordinated gain scheduling control strategy is presented, and no such analytical solution can be found for the reusable boosted vehicle.

The design idea of coordinated gain scheduling strategy is straightforward in physical concepts and has great value for engineering applications.

Coordinated gain scheduling control strategy is novel in that single channel gain scheduling design does not involve small perturbation linearization and coordinated channel is scheduled.

The dynamic model of radial active magnetic bearings, which is based on the current and position dependent partial derivatives of flux linkages and radial force characteristics, is determined using the finite element method. In this way, magnetic nonlinearities and cross‐coupling effects are considered more completely than in similar dynamic models. The presented results show that magnetic nonlinearities and cross‐coupling effects can change the electromotive forces considerably. These disturbing effects have been determined and can be incorporated into the real‐time realization of nonlinear control in order to achieve cross‐coupling compensations.

The purpose of this paper is to investigate torque ripple and magnetic force on the teeth in interior permanent magnet (IPM) machines over a wide range of speed operation for electrical power steering (EPS) applications.

The flux-weakening capability of IPM machines has been analysed by finite element method considering the effect of cross-coupling between d- and q-axis current. The traditional method of analysing torque ripple is based on constant torque and flux-weakening region. However, the cross-coupling need to be considered when applying this technique to flux-weakening region. Meanwhile, the torque ripple with current amplitude and angle and with different speed in the flux-weakening region is also investigated. In addition, the magnetic force on the teeth due to the separated teeth with stator yoke is also investigated during the constant torque and flux-weakening region.

The torque ripple and magnetic force on teeth in IPM machine are dependent on current and current angle. Both the lowest torque ripple and magnetic force on teeth exist over the whole torque-speed region.

The purely sinusoidal currents are applied in this analysis and the effects of harmonics in the current on torque ripple and magnetic force on teeth are not considered in this application. The 12-slot/10-pole IPM machine has been employed in this analysis, but this work can be continued to investigate different slot/pole number combinations.

This paper has analysed the torque ripple and magnetic force on the teeth in IPM machines for EPS application over a wide range of operation speed, which are the main cause of vibration and acoustic noise. The variation of torque ripple with current amplitude and angle as well as speed in the flux-weakening region is also investigated. In addition, the magnetic force on the teeth is also investigated over the whole torque-speed region.

The wireless power transmission (WPT) system with an embedded coil will achieve a more flexible charging operation and higher system efficiency. However, the comprehensive analysis considering cross-coupling for WPT with embedded coil is rarely investigated. This study aims to improve the system efficiency of WPT with the embedded coil based on circuit analysis and optimization of embedded coil loops.

The circuit model of WPT system with the non-resonant compensated embedded coil is developed by taking the cross-coupling of all coils and the circuit compensation degree of the embedded coil into consideration. On the basis of system characteristics analysis, optimization of embedded coil position and non-resonant compensation are proposed to improve the efficiency of WPT system with embedded coil. Experimental studies demonstrate the correctness of theoretical research.

The WPT system with embedded coil designed by optimizing the position and non-resonant compensation achieves higher efficiency than those of the system with two-coil mode and the three-coil system with a resonant compensated embedded coil.

A WPT system with embedded coil could be more efficient by using a non-resonant compensated coil embedded into the buffer material of the storage box for sophisticated electrical equipment.

The cross-coupling between all coils is considered in circuit analysis for WPT system with embedded coil. Optimization of the position and non-resonant compensation of embedded coil achieves higher efficiency.

The increasing demand on high performance fighter aircraft has introduced areas of concern associated with the handling qualities, control and safety at high angles of incidence. Pilots are limiting combat effectiveness by cautiously avoiding hazardous regions of the flight envelope. This paper presents the results of the work undertaken in analysing the F‐16 aircraft’s handling characteristics during the departure condition. In‐flight experience shows that there are two types of F‐16 control problems when flying at high angles of attack: the “pitch departures” and the resulting “deep stall trim”. Avoidance of the departure requires the aeroplane to have sufficient nose‐down pitch and roll control moment. This paper investigates departure condition during high angles of attack and suggests a method of recovery.

To control one of the joints during the actual movement of the hydraulically driven quadruped robot, all the other joints in the leg need to be locked. Once the joints are unlocked, there is a coupling effect among the joints. Therefore, during the normal exercise of the robot, the movement of each joint is affected by the coupling of other joints. This brings great difficulties to the coordinated motion control of the multi-joints of the robot. Therefore, it is necessary to reduce the influence of the coupling of the hydraulically driven quadruped robot.

To solve the coupling problem with the joints of the hydraulic quadruped robot, based on the principle of mechanism dynamics and hydraulic control, the dynamic mathematical model of the single leg mechanism of the hydraulic quadruped robot is established. On this basis, the coupling dynamics model of the two joints of the thigh and the calf is derived. On the basis of the multivariable decoupling theory, a neural network (NN) model reference decoupling controller is designed.

The simulation and prototype experiment are carried out between the thigh joint and the calf joint of the hydraulic quadruped robot, and the results show that the proposed NN model reference decoupling control method is effective, and this method can reduce the cross-coupling between the thigh and the calf and improve the dynamic characteristics of the single joint of the leg.

The proposed method provides technical support for the mechanical–hydraulic cross-coupling among the joints of the hydraulic quadruped robot, achieving coordinated movement of multiple joints of the robot and promoting the performance and automation level of the hydraulic quadruped robot.

On the basis of the theory of multivariable decoupling, a new decoupling control method is proposed, in which the mechanical–hydraulic coupling is taken as the coupling behavior of the hydraulic foot robot. The method reduces the influence of coupling of system, improves the control precision, realizes the coordinated movement among multiple joints and promotes the popularization and use of the hydraulically driven quadruped robot.

Consider the mutual coupling between loads, the purpose of this paper is to study the total transmission efficiency based on different load coil positions relative to the charging platform, to provide the theoretical basis for the design and parameter optimization of one-to-multiple wireless charging platform.

Based on the dual-load series-resonant wireless power transfer system, the expression of system efficiency and its calculation model is achieved using the equivalent circuit theory. Finally, a 96 kHz magnetic resonance wireless power transmission test platform is built up to verify the theoretical analysis given in this paper.

For the completely resonant circuit, the transmission efficiency can be improved by increasing the transmitter-receiver coupling and reducing the coupling between receivers. The total transmission efficiency achieves its lowest value when two loads are with equal competitive capability.

Through the simulation analysis of efficiency formula, the selection principle of impact factors can be applied to the optimization analysis of the transmission efficiency.

When magnetic saturation in ac machines is evolved, the theory of main flux saturation in d-q axes remains the best. Because of its simplicity, it is the most used in either motoring or generating mode for synchronous or asynchronous machines. Although, it is considered as a global way of introducing the iron saturation, compared to other methods, today, its fidelity has no contest in predicting complex ac machine operations. For this purpose, the aims of this paper consists of modeling these machines whatever the state-space variables values are taking into account the magnetic saturation. Two unified procedures are proposed. The first one deals with a common approach to establishing a complete and detailed model synthesis in d-q axes. The second also presents a unified approach to introducing magnetic saturation of the iron core in the characteristic equations. The analysis takes the salient pole synchronous machine as a general case of study. Then the approaches are extended to undamped and smooth air gap synchronous machines as well as induction machines. The paper aims to discuss these issues.

The present paper, which is a first part of a work under study dealing with a unified method to derive multiple models of saturated ac machines, is intended to the description of an alternative method and its application for induction and synchronous machines. It mainly consists of the following parts: first, after writing the stator and rotor space vector d-q equations, the number of possible models is immediately discussed. By considering the currents and fluxes as state-space variables, 14 models are obtained for AC induction machine (IM and SM). They are classified into three families, current (three), flux (three) and mixed models (eight). Second, in order to easily introduce the magnetic saturation in the 14 developed models, a method is presented. It consists of just elaborating the model with the winding currents as state variables, then deriving all the other models from it. Third, to emphasize the influence of the presence of magnetic saturation, in each model, each inductance along the d and q axes is written with a fundamental expression which exists with or without saturation and an additional one due purely to saturation. Hence the additional terms can be studied and quantified in an easy way or simply removed when linear case is assumed. Fourth, adopting such strategy to write the different coefficients of the models had led to the definition of common saturation factors. In turn, the definition of common saturation factors had allowed the definition of different groups of models within each family. Fifth, an alternative to evaluate the static and dynamic saturation coefficients is also proposed. It is shown that by proper fitting of the experimental magnetizing curve, all saturation coefficients can be written only in terms of which is simply the magnitudes ratio of the magnetizing flux and current. Sixth, although the theory of the main flux saturation is now admitted, an investigation was carried out on a self-excited induction generator and the build-up of voltage and current phases of a standalone alternator, to prove the equivalence between the all developed models.

The number of models based on the state-space variables choice, of a saturated ac machine, is reviewed. A simple method consisting of elaborating just the winding currents model, with magnetic saturation and deriving all the other models from it, is presented. In this study special interest was particularly focussed on either novel models or existing models cited in the literature but cannot be obtained by other approaches. In all cases, if the differential equations of the machine are formulated in terms of a set of variables other than the winding currents, a noticeable reduction in the size of equations may be obtained and consequently less time computing. The approach seems to be able to derive any possible model whatever the state-space variables and the type of the ac machine and hence can be classified as a general approach.

The experiments of synchronous and induction machine transients prove the validity of the method.

By suitable choice of state-space characteristic vectors among the fluxes and the currents, a synthesis of AC machine models in d-q axes is established. To introduce magnetic saturation in each model, an approach-based uniquely on the elaboration of the winding currents model is exposed and applied. In addition, the analysis gives a detailed classification of all found models taking into account the state variables nature as well as the cross-coupling coefficient considered as a saturation factor. The study is completed with a simple alternative to evaluate all saturation factors by just calculating the static magnetizing inductance.