Three‐dimensional finite element eddy current analysis by using high‐order vector elements

Sets of high‐order basis functions of a tetrahedral element are systematically constructed and applied to finite element analysis of eddy current problems. A polynomial space is divided into a lot of subspaces assigned on the edges, faces, and a volume of the tetrahedral element. Lagrange‐type vector basis functions of the subspaces are presented. The effect of the high‐order vector elements is investigated by a cubic conductor model located in AC steady‐state magnetic fields. In the calculations using the fundamental and second‐order elements, no convergent value of the eddy current power loss can be obtained in spite of fine meshes because the eddy current shifts to the surface of the conductor. The higher‐order vector elements give the convergent solutions in the coarse meshes. © 2004 Wiley Periodicals, Inc. Electr Eng Jpn, 147(4): 60–67, 2004; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.10306     

Signal separation using second‐ and high‐order statistics

This paper presents two methods for signal separation. In either method, the fundamental criterion for separation relies on reducing to zero, or at least minimizing, the output cross‐correlation or cross‐cumulant functions of a decoupling multi‐input–multi‐output system that is fed with mixed signals. In one of the approaches used, the parameters of this system are determined through solving — in a least‐squares sense — a linearized set of equations describing the deviations from zero of either the cross‐correlation or cross‐cumulant functions when evaluated for different lags. An alternative rapidly convergent adaptive algorithm is also described for minimizing the cross‐correlation or cross‐cumulant functions. The paper also considers both FIR and IIR representations of the decoupling system. It shows that using IIR functions in the decoupling system does not offer any merit over the FIR case. Illustrative examples are given to show the performance of the proposed algorithms. Copyright © 2000 John Wiley & Sons, Ltd.     

A high‐order discontinuous Galerkin method with time‐accurate local time stepping for the Maxwell equations

We present an explicit numerical method to solve the time‐dependent Maxwell equations with arbitrary high order of accuracy in space and time on three‐dimensional unstructured tetrahedral meshes. The method is based on the discontinuous Galerkin finite element approach, which allows for discontinuities at grid cell interfaces. The computation of the flux between the grid cells is based on the solution of generalized Riemann problems, which provides simultaneously a high‐order accurate approximation in space and time. Within our approach, we expand the solution in a Taylor series in time, where subsequently the Cauchy–Kovalevskaya procedure is used to replace the time derivatives in this series by space derivatives. The numerical solution can thus be advanced in time in one single step with high order and does not need any intermediate stages, as needed, e.g. in classical Runge–Kutta‐type schemes. This locality in space and time allows the introduction of time‐accurate local time stepping (LTS) for unsteady wave propagation. Each grid cell is updated with its individual and optimal time step, as given by the local Courant stability criterion. On the basis of a numerical convergence study we show that the proposed LTS scheme provides high order of accuracy in space and time on unstructured tetrahedral meshes. The application to a well‐acknowledged test case and comparisons with analytical reference solutions confirm the performance of the proposed method. Copyright © 2008 John Wiley & Sons, Ltd.     

Design for testability of high‐order OTA‐C filters

A study of oscillation‐based test for high‐order Operational Transconductance Amplifier‐C (OTA‐C) filters is presented. The method is based on partition of a high‐order filter into second‐order filter functions. The opening Q‐loop and adding positive feedback techniques are developed to convert the second‐order filter section into a quadrature oscillator. These techniques are based on an open‐loop configuration and an additional positive feedback configuration. Implementation of the two testability design methods for nth‐order cascade, IFLF and leapfrog (LF) filters is presented, and the area overhead of the modified circuits is also discussed. The performances of the presented techniques are investigated. Fourth‐order cascade, inverse follow‐the‐leader feedback (IFLF) and LF OTA‐C filters were designed and simulated for analysis of fault coverage using the adding positive feedback method based on an analogue multiplexer. Simulation results show that the oscillation‐based test method using positive feedback provides high fault coverage of around 97%, 96% and 95% for the cascade, IFLF and LF OTA‐C filters, respectively. Copyright © 2016 John Wiley & Sons, Ltd.     

On iterative learning control with high‐order internal models

In this work we focus on iterative learning control (ILC) for iteratively varying reference trajectories, which are described by a high‐order internal models (HOIM) that can be formulated as a polynomials between two consecutive iterations. The classical ILC with iteratively invariant reference trajectories, on the other hand, is a special case of HOIM where the polynomial renders to a first‐order internal model with a unity coefficient. By incorporating HOIM into the ILC law, and designing appropriate learning control gains, the learning convergence in the iteration axis can be guaranteed for continuous‐time linear time‐varying systems. The initial resetting condition, P‐type and D‐type ILC, and possible extension to nonlinear cases are also explored in this work. Copyright © 2010 John Wiley & Sons, Ltd.     

Adaptive finite‐time control for high‐order nonlinear systems with mismatched disturbances

In this paper, adaptive finite‐time control is addressed for a class of high‐order nonlinear systems with mismatched disturbances. An adaptive finite‐time controller is designed in which variable gains are adjusted to ensure finite‐time stabilization for the closed‐loop system. Chattering is reduced by a designed adaptive sliding mode observer which is also used to deal with the mismatched disturbances in finite time. The proposed adaptive finite‐time control method avoids calculating derivative repeatedly of traditional backstepping methods and reduces computational burden effectively. Three numerical examples are given to illustrate the effectiveness of the proposed method.     

Adaptive control for high‐order time‐delay uncertain nonlinear system and application to chemical reactor system

This paper focuses on global adaptive state‐feedback stabilization for a class of high‐order uncertain nonlinear systems with multiple delays. Restriction on system growth is relaxed. Two dynamic gains are introduced to deal with uncertainty and nonlinear growth rate of the system. Without precise information about time‐delay being needed and only by like Lyapunov function, a new control strategy is presented based on homogeneous domination idea and two necessary transformations. As an application, the developed scheme is utilized to control design of a two‐stage chemical reactor with delayed recycle streams. Copyright © 2014 John Wiley & Sons, Ltd.     

High‐precision positioning with strain feedback using piezoelectric element

This paper presents a novel control methodology for robust high‐precision positioning systems. This methodology is based on strain feedback using a piezoelectric element. The mechanical vibration modes at around the control bandwidth cause deterioration of system stability. This prevents the positioning performance from being robust, particularly against variations in the vibration frequency. In this research, therefore, a robust positioning system was designed by applying an additional compensation loop by strain feedback; here, a piezoelectric element that acts as a strain sensor detects the vibration signal. This makes the performance of the system robust. The proposed compensation approach has been verified by numerical analyses and by experiments using a positioning device for industrial galvano scanners. © 2012 Wiley Periodicals, Inc. Electr Eng Jpn, 179(4): 41–50, 2012; Published online in Wiley Online Library ( wileyonlinelibrary.com ). DOI 10.1002/eej.21267     

A new parallelization strategy for solving time‐dependent 3D Maxwell equations using a high‐order accurate compact implicit scheme

With progress in computer technology there has been renewed interest in a time‐dependent approach to solving Maxwell equations. The commonly used Yee algorithm (an explicit central difference scheme for approximation of spatial derivatives coupled with the Leapfrog scheme for approximation of temporal derivatives) yields only a second‐order of accuracy. On the other hand, an increasing number of industrial applications, especially in optic and microwave technology, demands high‐order accurate numerical modelling. The standard way to increase accuracy of the finite difference scheme without increasing the differential stencil is to replace a 2nd‐order accurate explicit scheme for approximation of spatial derivatives with the 4th‐order accurate compact implicit scheme. In general, such a replacement requires additional memory resources and slows the computations. However, the curl‐based form of Maxwell equations allows us to construct an effective parallel algorithm with the alternating domain decomposition (ADD) minimizing the communication time. We present a new parallel approach to the solution of three‐dimensional time‐dependent Maxwell equations and provide a theoretical and experimental analysis of its performance. Copyright © 2006 John Wiley & Sons, Ltd.     

Modeling and design of magnetostrictive vibration‐powered generator using finite element method

This work investigates the design of a vibration‐powered generator with one rod (unimorph) of iron–gallium (galfenol) and compares it with its two‐rod (bimorph) counterpart. Galfenol is a promising magnetostrictive material that combines high magnetic susceptibility and desirable mechanical properties and therefore very suitable for harvesting the vibration energy that involves bending stresses. In this study, an energy‐based magnetoelastic model, so‐called Armstrong model, is employed to predict the behavior of galfenol under multiaxial stresses. The Armstrong model of galfenol is implemented into a static 3D finite element model of the energy harvester by which the performances of the devices are predicted and experimentally observed. Copyright © 2012 John Wiley & Sons, Ltd.     

PML absorbing boundary condition for the integral‐based high‐order FV24 FDTD algorithm

An integral equations‐based perfectly matched layers (PML) implementation is presented for the highly phase‐coherent FV24 finite‐difference time‐domain (FDTD) algorithm. The implementation allows including field values off the grid axes in the split‐field PML formulation conserving in the process the continuity and phase coherency of the FV24 algorithm when modeling absorbing boundary conditions (ABCs). It also eliminates the need for cumbersome subgridded low‐order FDTD subregions that until now were required to model PML ABCs within integral‐based high‐order FDTD simulations. The developed approach was numerically tested and found to match the PML behavior of the standard FDTD method at normal wave incidence on ABC boundaries and exceeds it at highly oblique wave incidence. This development serves to improve the capability and practicality of the computationally efficient FV24 algorithm when modeling electrically large structures in 3‐D space. Copyright © 2010 John Wiley & Sons, Ltd.     

Efficient analysis of planar microwave circuits with mixed‐order prism vector finite macroelements

This paper introduces a new concept of a mixed‐order prism macroelement, suitable for an efficient analysis of three‐dimensional planar microwave circuits, using two‐dimensional meshes and preprocessors. The mixed‐order concept used here implies arbitrary orders of variation in different directions and differs essentially from the well‐known mixed‐order approximation that is an integral part of every Whitney element. It is the existence of a related systematic theory of higher‐order vector finite elements, previously documented, that facilitates the introduction of such a concept. The second‐ and third‐order elements, derived by this approach, are successfully applied in the analysis of planar microwave circuits, rendering the application of finite element method in such problems still a favorable option. Copyright © 2008 John Wiley & Sons, Ltd.     

Adaptive state feedback stabilization of more general stochastic high‐order nonholonomic systems

This paper investigates adaptive state feedback stabilization for a class of more general stochastic high‐order nonholonomic systems. By constructing the appropriate Lyapunov function, skillfully combining parameter separation, sign function, and backstepping design methods, an adaptive state feedback controller is designed to eliminate the phenomenon of uncontrollability and guarantee global asymptotic stability in probability of the closed‐loop system. Two simulation examples are used to demonstrate the effectiveness of this method.     

Adaptive asymptotical tracking controller design for uncertain nonaffine nonlinear system with high‐order mismatched disturbances

In this paper, the problem of anti‐disturbance asymptotical tracking control is studied for nonaffine systems with high‐order mismatched disturbances. The disturbances can be described as polynomial functions, which are first estimated by constructing generalized extended state filter. The nonaffine system is changed into an augmented affine system via introducing an auxiliary integrator. A novel adaptive anti‐disturbance tracking controller is recursively designed, where the disturbance estimation is used for feedforward compensation at each step. A sliding mode differentiator is applied to reduce the computational burden taken by the backstepping method. The boundedness of the closed‐loop system is proved based on Lyapunov stability theory and zero error tracking performance is ensured. Finally, a numerical example is provided to show the effectiveness of the proposed scheme.     

Classical eigenvalue mode‐spectrum analysis of multiple‐ridged rectangular and circular waveguides for the design of narrowband waveguide components

A classical eigenvalue mode‐spectrum analysis of waveguides with multi‐ridged cross sections is presented and applied to the design of narrowband waveguide components in rectangular and circular waveguide technology. Modifications of the modes of the empty waveguide enclosures are used as expansion functions and lead to a classical, real and symmetric eigenvalue problem. A simple yet efficient constraint function is introduced to satisfy boundary conditions for TM modes. The number and locations of ridges positioned in a regular rectangular or circular waveguide enclosure is arbitrary. Measurements and comparisons with results from existing full‐wave modeling tools and commercially available field solvers verify the correctness and flexibility of the approach. Copyright © 2009 John Wiley & Sons, Ltd.     

Comparison between line and surface integral formulations of the hybrid mode‐matching/two‐dimensional finite element method

The hybrid mode‐matching/two‐dimensional‐finite‐element (MM/FEM2D) technique has been proposed for the analysis of discontinuities with waveguides of arbitrary cross section; this technique combines the computational efficiency of modal analysis with the versatility and flexibility of the FEM approach. In this paper, we present in detail a surface‐integrals and a line‐integrals formulation of the hybrid MM/FEM2D technique, in case the ‘Standard Formulation’ is used as FEM2D formulation. Such formulations allow computing analytically both the normalization and the coupling integrals. Furthermore, we compare the accuracy obtained by using the line‐integrals and the corresponding surface‐integrals formulation. To these aims we present several numerical results. Copyright © 2004 John Wiley & Sons, Ltd.     

Adaptive stabilization of a class of high‐order uncertain nonholonomic systems with unknown control coefficients

This paper is concerned with the globally stabilizing control design for a class of high‐order nonholonomic systems. Compared with the existing literature, the high‐order nonholonomic systems under investigations have more uncertainties and unknowns, such as neither lower nor upper bound is known for each control coefficient of the systems. This renders the existing control methods highly difficult to the control problems of the systems or even inapplicable. In this paper, by defining two new unknown parameters whose dynamic updating laws are properly chosen and also by using the discontinuous coordinates transformation and the method of adding a power integrator, a new design approach is given to the adaptive stabilizing controllers for the systems. A numerical simulation is provided to demonstrate the effectiveness of the theoretical results. Copyright © 2012 John Wiley & Sons, Ltd.     

Fourth‐order hybrid implicit and explicit‐FDTD method

A fourth‐order hybrid implicit and explicit finite‐difference time‐domain Method has been presented in this paper. This new method investigates the use of a second‐order accurate in time and a fourth‐order accurate in space. The 2D formulation of the method is presented and the time stability condition of the method is certified. The maximum time step size in this method is only determined by one spatial discretization. The numerical dispersion is discussed. Numerical examples demonstrate that when this method is used to solve electromagnetic problems, higher computational efficiency and less dispersion error can be obtained by comparing with the traditional finite‐difference time‐domain algorithm. Copyright © 2015 John Wiley & Sons, Ltd.     

Extending the enlarged cell and uniformly stable conformal techniques to modeling curved conductors in two‐dimensional high‐order finite‐difference time‐domain algorithms

The critical tool of modeling irregularly shaped perfect conductors is developed for the extended‐stencil high‐order two‐dimensional M24 variant of the finite‐difference time‐domain (FDTD) method. Two standard FDTD conformal approaches are analyzed and successfully extended to work accurately with M24. They both afford higher order convergence with respect to mesh density than a previously developed technique, which better matches M24's characteristics. Both approaches rely on borrowing weighted electromotive forces from nearby extended‐stencil cells to ensure accuracy and numerical stability while the overall algorithm is efficiently operated at the maximum allowable time steps by FDTD and M24 theories. Validation examples demonstrate that M24's amplitude and phase accuracies using coarse numerical meshes were not compromised. Copyright © 2012 John Wiley & Sons, Ltd.     

Krylov model order reduction of finite element approximations of electromagnetic devices with frequency‐dependent material properties

A methodology is presented for the Krylov subspace‐based model order reduction of finite element models of electromagnetic structures with material properties and impedance boundary conditions exhibiting arbitrary frequency dependence. The proposed methodology is a generalization of an equation‐preserving Krylov model order reduction scheme for methodology for second‐order, linear dynamical systems. The emphasis of this paper is on the application of this method to the broadband model order reduction of planar circuits including lossy strips of arbitrary thickness and lossy reference planes. In particular, it is shown that the proposed model order reduction methodology provides for the accurately modelling of the impact of the frequency dependence of the internal impedance per unit length of the thick lossy strip on the electromagnetic response of the stripline structure over a very broad, multi‐GHz frequency band, extending all the way down to frequencies in the DC neighbourhood. In addition, the application of the proposed methodology to the broadband modelling of electromagnetic coupling between strips on either side of a lossy ground plane is demonstrated. Copyright © 2007 John Wiley & Sons, Ltd.