Optimal Pole Research Articles

Design Synthesis of Switched Flux Hybrid-Permanent Magnet Memory Machines

This paper develops a design methodology for switched flux (SF) hybrid permanent magnet memory machines (HPMMMs). The memorable flux is achieved due to the variable magnetization level of low coercive force (LCF) permanent magnets (PMs) Thus, the associated excitation loss is negligible, resulting in high efficiency operation over a wide speed range. A general hybrid PM magnetic circuit is modeled, which is characterized by spoke-array NdFeB PMs and LCF PMs sandwiched between an outer stator ring and an inner stator pole. Based on the magnetic circuit, the design conflicts within the stationary side are unveiled. Thereafter, the machine configuration is introduced, followed by a description of the design procedure. First, the optimal stator pole number is determined based on one-phase machine models. In addition, a simplified permeance function is utilized to analytically optimize the rotor number, accounting for different ratios of the slot opening to NdFeB PM thickness. The electromagnetic performance of the machines with alternate stator/rotor pole combinations are compared. The design guidelines for LCF PMs are presented. Finally, the theoretical analysis is verified experimentally on the prototype machine.

Erratum to: Design of new practical phase shaping circuit using optimal pole–zero interlacing algorithm for fractional order PID controller

Erratum to: Design of new practical phase shaping circuit using optimal pole–zero interlacing algorithm for fractional order PID controller

Design of new practical phase shaping circuit using optimal pole–zero interlacing algorithm for fractional order PID controller

This paper presents the implementation of fractional order PID (FO-PID) controller using hardwired modules of constant phase element (CPE). A new approach of phase shaping by slope cancellation of asymptotic phase plots for zeros and poles within the given bandwidth is realized. Analog circuits, which exhibit analog fractional-order integrator and fractional-order differentiator, are used for building the FO-PID controller. The design procedure is developed to obtain the optimal pole---zero pairs and respective "Fractance" components to realize for any value of fractional differ-integrator. These CPE elements give minimum error tolerance over the set phase value by using commercially available (R---C) components and Op-Amps. The pole---zero location in the root locus plot with constant asymptotic angle under various feed-forward gains is achieved with these analog integrodifferential circuits of the FO-PID. The iso-damping feature of the controller is practically demonstrated. A comparative performance is demonstrated under various settings of feed forward gains, which indicate the constant overshoot with FO-PID against the conventional PID. These circuits are developed and implemented with a DC motor emulator to confirm the designed performance of the controller.

Iterative selection of GOB poles in the context of system modeling

This paper is concerned with the problem of system identification using expansions on generalized orthonormal bases (GOB). Three algorithms are proposed to optimize the poles of such a basis. The first two algorithms determine a GOB with optimal real poles while the third one determines a GOB with optimal real and complex poles. These algorithms are based on the estimation of the dominant mode associated with a residual signal obtained by iteratively filtering the output of the process to be modelled. These algorithms are iterative and based on the quadratic error between the linear process output and the GOB based model output. They present the advantage to be very simple to implement. No numerical optimization technique is needed, and in consequence there is no problem of local minima as is the case for other algorithms in the literature. The convergence of the proposed algorithms is proved by demonstrating that the modeling quadratic error between the process output and the GOB based model is decreasing at each iteration of the algorithm. The performance of the proposed pole selection algorithms are based on the quadratic error criteria and illustrated by means of simulation results.

A Novel Superconducting Magnet Excited Linear Generator for Wave Energy Conversion System

In almost every permanent-magnet linear generator (PMLG), demagnetization would greatly degrade the electricity generation capability over time. This paper proposes a novel electromagnetic linear generator (EMLG) for direct-drive power generation from oceanic waves, which consists of superconducting magnets instead of conventional permanent magnets to create sufficiently strong magnetic field to produce electricity. The proposed generator can avoid the demagnetization problem of the conventional PMLG. To verify the feasibility of the new concept, a generator is designed. Yttrium barium copper oxide is used to make the superconducting magnet. The finite-element analysis is performed by using the commercial software package ANSYS/ANSOFT to analyze the performance of the proposed EMLG, and the genetic algorithm has been used to find the optimal pole size, pole pitch, air gap length, and load variation to maximize the output power. Magnetic pole shoes are designed in such a way that they can effectively minimize force ripples and cogging force. The results are analyzed and discussed. The results demonstrate that the proposed generator almost eliminates the demagnetization problem of the conventional PMLG with some other built-in advantages. The maximum efficiency of the proposed generator is found to be approximately 96% without considering frictional and other mechanical losses. The results demonstrate excellent features of the proposed generator.

FPGA-based optimal robust minimal-order controller structure of a DC–DC converter with Pareto front solution

This paper presents multi-objective optimization-based robust controller design of a DC–DC boost converter, controlled with FPGA (Field Programmable Gate Array). The main aim of the proposed design technique is to obtain a fixed and low-order robust controller which is reliable and easy to implement on a low-cost real-time digital system. The improved proposed control design method with direct closed-loop pole position assessment using metric L2, is based on robust optimal regional closed-loop pole assignment technique. The optimal solution has been obtained using multi-objective Pareto front search genetic algorithm. This paper also presents simulated and practical experimental results with implemented optimized robust controller on FPGA, controlling the DC–DC boost converter. For the sake of comparison with the proposed controller design method, an additional auto-tuned PID controller has been designed along with robust controllers based on mixed sensitivity loop-shaping method.

Optimum Iron Pole Design of a Tubular Linear Synchronous Machine With Double-Sided Axially Magnetized Permanent Magnets Considering Leakage Flux

In this paper, the design optimization of tubular linear synchronous machines (TLSMs) was achieved by minimizing the mass of the iron pole, subject to satisfying the other performance specifications. Furthermore, to optimize the design of TLSMs with axially magnetized permanent magnets, an optimum design of the magnetic circuit of the machine with a reduced mass of ferromagnetic material was proposed while considering leakage flux. The leakage flux density at the iron pole on the surface of each side is an important consideration when choosing a suitable thickness ratio for the iron poles. The machine was optimized by maintaining a constant level of the back electromotive force, and considering the leakage magnetic flux at the iron pole. Finally, the total mass of the flux passing the iron pole of the optimized design is $\sim 39.31$ % of that in the conventional model.

System approximations based on Meixner‐like models

In this study, the authors investigate the parametric complexity reduction of the Meixner-like model for linear discrete-time system representation. The use of the Meixner-like functions is more suitable than the use of Laguerre functions and Kautz functions especially when the system have a slow initial onset or delay. The coefficients of the Meixner-like model can be estimated recursively from input–output data by the new representation. Noting that the selection of an arbitrary pole for the Meixner-like functions can raise the parameter number of the Meixner-like model. However, when the pole is set to its optimal value, an optimal expansion of transfer functions is produced. Therefore an optimisation technique is developed to generate the optimal Meixner-like pole, which is achieved by an iterative method, that consists in minimising the mean square error between the system output and the model output. Theoretical analysis and a numerical simulation show the efficiency of the approach.

Investigation of an integrative transverse-flux linear compressor

Purpose – The purpose of this paper is propose a novel integrative transverse-flux linear compressor (TFLC), which integrates compressor into a single-phase transverse-flux linear oscillating actuator with moving magnet. Its main merit is having similar lamination as rotate motor which is easy to be stacked. Design/methodology/approach – The simple lumped circuit model accounting for magnetic saturation, armature reaction and axial fringing effect is proposed. Based on this model, the magnetic field in air gap is calculated, and then the optimal PM height, PM length, split ratio and pole number are found. The predicted thrust force, stroke and system resonant frequency at no load are validated by prototype measurement. The relation of system resonant frequency and load are also measured. Findings – In this novel TFLC, the optimal split ratio is in area of 0.54∼0.56 and pole number is 6. For designed stroke 10 mm, suitable PM height and length are 3 mm and 63 mm, respectively. By measurement, the predicted thrust force, stroke and system resonant frequency at no load are validated. The measurement also shows that the system resonant frequency can be improved from 30 Hz of no load to 39 Hz at 0.7 Mpa air load. Originality/value – The novel TFLC has excellent driving performance and simple structure for maintenance. It can produce enough pressure to meet the requirement of refrigerator, so it is a strong candidate for refrigerating apparatus.

Investigation of Auxiliary Poles Optimal Design on Reduction of End Effect Detent Force for PMLSM With Typical Slot–Pole Combinations

This paper studies an auxiliary poles technique that is used to reduce the end effect detent force for permanent magnet linear synchronous motor (PMLSM). Based on the lateral force method, the analytical model of the end effect detent force is built. The expressions of the optimal position and the optimal width for the auxiliary poles are derived. Through the use of finite-element calculations, the influence of the position, width, and height of the auxiliary poles on the end effect detent force is obtained. In addition, the detent force characteristics for five PMLSMs with typical slot–pole combinations after adopting the auxiliary poles are analyzed. The inhibitory effect of the auxiliary poles on the end effect detent force is separated from the slot effect detent force using harmonic analysis. The simulation results of the optimal auxiliary poles positions match the analytical expressions well, which proves the correctness of the analytical model. Finally, a prototype of the PMLSM with auxiliary poles, which has a better structure strength and eliminates the installation error, is manufactured and tested.

Root coordinates in the design of SISO control systems

We study pole placement in SISO linear control systems with low-order controllers is studied. A method for finding critical (including optimal and suboptimal) pole placement in closedloop systems is theoretically justified and demonstrated on an example. Using critical root diagrams and root polynomials, it is possible to analytically express the parameters of a suboptimal controller in terms of root coordinates, in particular, the real and imaginary parts of characteristic roots. The resulting algebraic equations and inequalities allow specifying the left-most shift of the pole placement domain and the greatest relative stability (possibly taking into account oscillation) without cumbersome calculations.

Optimal expansions of multivariable ARX processes on Laguerre bases via the Newton–Raphson method

SummaryIn this article, an optimal linear MIMO system approximation by using discrete‐time MIMO autoregressive with exogenous input (ARX) model is proposed. Each polynomial function of the MIMO ARX model associated with the inputs and with the outputs is expanded on independent Laguerre orthonormal basis. The resulting model is entitled MIMO ARX–Laguerre model. The optimal approximation of which is ensured once the poles characterizing each Laguerre orthonormal basis are set to their optimal values. In this paper, a new method to estimate, from input/output measurements, the optimal Laguerre poles of the MIMO ARX–Laguerre model is proposed. The method consists in applying the Newton–Raphson's iterative technique in which the gradient and the Hessian are expressed analytically. The proposed algorithm is tested on a numerical example and on a benchmark system. Simulation results show the effectiveness of the proposed optimal modeling method. Copyright © 2015 John Wiley & Sons, Ltd.

The pole tide and its effect on GRACE time‐variable gravity measurements: Implications for estimates of surface mass variations

AbstractGravity Recovery and Climate Experiment (GRACE) provides monthly solutions for the Earth's gravity field in the form of spherical harmonic coefficients. These can be used to infer changes in mass at the Earth's surface. The pole tide (the response of the Earth and oceans to polar motion) causes gravity signals dominated by harmonics of degree 2, order 1. If the pole tide is not removed from GRACE data, it affects the coefficients of those harmonics (C21, S21) and introduces errors when using those coefficients to determine surface mass variations. The pole tide is partially removed by GRACE processing centers before solving for the gravity field. But long‐period pole tide signals are not usually included in the GRACE pole tide correction, and so those signals are still present in the GRACE coefficients. We discuss this issue from the standpoint of somebody who uses the GRACE gravity fields to infer changes in surface mass. We arrive at a recommendation for an optimal GRACE pole tide correction. We describe how to modify the C21, S21 coefficients provided by the processing centers, so that they conform with our recommendation. We discuss the size of the pole tide contributions to C21, S21, compared to those of the direct load‐induced contributions. As an example, we show how an incompletely removed pole tide can impact GRACE results for the trend in ocean mass. We consider the impact of mantle anelasticity on long‐period pole tide corrections and conclude that it is unlikely to affect those corrections by more than 20%.

Vibroacoustic Analysis of Radial and Tangential Air-Gap Magnetic Forces in Permanent Magnet Synchronous Machines

This paper analyzes Maxwell tensor tangential and radial magnetic forces in permanent magnet synchronous machines in the no-load case. Using matrix notation in the complex domain, a simple expression of the Fourier harmonics of both radial and tangential forces is derived, including all space and time harmonics. These expressions prove that both the frequency content of cogging torque and zeroth-order radial forces are linked to the least common multiple between the stator slot number and the rotor poles number, and that the optimal pole arc to pole pitch ratio to reduce cogging torque is also optimal for the reduction of average radial magnetic forces. It is also shown that both the smallest non-zero spatial order of tangential and radial force harmonics are given by the greatest common divider of the number of slots and the number of poles. These results can be used during the design stage when choosing the pole and slot numbers combination. These analytical results are then compared with calculations using MANATEE vibroacoustic and electromagnetic simulation software. Finally, some variable speed acoustic noise simulations are carried out on three different designs to analyze the efficiency of different vibroacoustic design rules on the slot and pole numbers combination. An attempt to formulate a new vibroacoustic design rule choice is detailed. It is concluded that no simple analytical design rule can be used to evaluate noise and vibrations induced by magnetic forces, and that numerical simulation is necessary.

Optimization of the Sextupole Magnets With Trim Coils for the Collector Ring of the FAIR Project

The collector ring (CR) is a part of the challenging international project facility for antiproton and ion research started in Darmstadt, Germany. The ion optics of the CR includes sextupole magnets with embedded dipole correction coils. To fulfill the requirements of the field quality in the magnet aperture, it is necessary to find an optimal pole tip shape as well as an optimal configuration of the coil system. We used a specially developed optimization procedure for designing the magnet cross section. This procedure consists of two steps. The first one is based on a representation of the pole border line by a superposition of hyperbolic functions corresponding to different Fourier components of the magnetic field expansion. The optimization procedure based on the Newton–Raphson descend algorithm minimizes amplitudes of the undesired field harmonics. At the second step of the magnet design procedure, the parameters of the dipole winding are optimized to provide the required field characteristics in the magnet aperture.

Robust Optimal Regional Closed-loop Pole Assignment over Positivity Conditions and Differential Evolution

The presented paper describes an optimal closed-loop pole assignment for a vast control feedback framework and structure. The main aim of this paper is a regional selection of the closed-loop central polynomial with additional flexibility and leeway for the following optimization procedure. The optimality of the approach is provided through the positivity condition of the quasi-convex spectral polynomial (QSP). The spectral polynomial presents the uncertainty and closed-loop characteristic of the feedback system. The derivation of the QSP is based on the characteristics of the uncertainty models and metrics with norm H∞. The structure of the controller is freely chosen and is also the subject of the optimization procedure. An objective function for the optimization algorithm Differential Evolution (DE) is presented in multi-criteria form and is directly composed of various QSP's. Such optimization of the objective function improves the transparence, computation expense and the regularity of the optimal/suboptimal solution.

遺伝的アルゴリズムを用いた三自由度球面アクチュエータの磁極配置最適化

The development of multiple degree-of-freedom actuators is expected in robotics and industrial machinery fields. There remain, however, some problems in terms of the torque density, control method, and sensing systems. Under the circumstances, we are studying on a 3-degree-of-freedom outer rotor spherical actuator and its control method. We have also confirmed the characteristics employing 3D-FEM. In this paper, genetic algorithm is employed to search for the optimal stator pole arrangement which has the maximum torque constant (Instead, minimum mean current with a constant torque). Then, the effectiveness of the optimization is verified through the comparison of the mean current controlled to generate a constant torque between the optimized and the initial models.

Characteristics of PM synchronous motors according to pole-slot combinations for EPS applications

This paper presents the optimum pole and slot combination of permanent magnet synchronous motors (PMSMs) for electrical power steering (EPS) applications. To do this, the characteristics of three PMSMs, which have the same performance but different pole and slot combinations, are compared. The characteristics such as the cogging torque and radial force of each model are obtained by finite element analysis. The results showed that the pole and slot combination presented in this paper satisfies the performance required in the EPS without rotor or stator skew while minimizing the space harmonics of the radial force with critical with respect to the noise and vibration. The validity of the analysis results is verified by test.

Influence of Stator and Rotor Pole Arcs on Electromagnetic Torque of Variable Flux Reluctance Machines

The influence of stator and rotor pole arcs on electromagnetic torque of variable flux reluctance machines (VFRMs) having different stator and rotor pole combinations is investigated. Different from 6/4 stator/rotor pole switched reluctance machines, which usually employ equal stator pole arc and stator slot opening, unequal stator pole arc and slot opening can boost the torque density of the VFRM. Moreover, the optimal rotor pole arc to rotor pole pitch ratio in VFRMs is \(\sim ~1/3\) and the optimal stator pole arc is equal to or slightly smaller than the optimum rotor pole arc. For a 6-pole stator, the 4-, 5-, 7-, and 8-pole rotor VFRMs with the optimal stator and rotor pole arcs can increase the average torque by 1%, 4%, 30.7%, and 72.9% compared with those having equal stator pole arc and stator slot opening. In addition, the 6/7 stator/rotor pole VFRM exhibits the largest torque density. Prototype machines with optimal stator and rotor pole arcs are manufactured and measured to validate the analysis.

Design Luenberger Observer for an Electromechanical Actuator

In this work we have designed a Luenberger Observer for an Electromechanical Actuator (EMA). We have considered a simple linear model of the Actuator plant with neglecting nonlinearities. The model of the EMA, the Observer and the simulations have been computed in MATLAB®. In our simulation we have examined the dynamics of the planned Observer. With different pole placement proportions and state estimation error conditions, three states have been estimated: Motor current (X1), angular velocity of the throttle plate (X2), and angular position of the throttle plate (X3). Outline of our examination should be to take the conclusions from the influence of the pole placement and error condition on the dynamics of the Observer. Thus determining of an optimal pole values for the proposed Luenberger Observer. Outline of this paper could be used for further research topics (fault detection in Electromechanical Actuator).