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A surface permanent magnet-type vernier motor (SPM-VM) generates high torque at low speed. A Halbach array permanent magnet is adopted for the field system of the SPM-VM in order to obtain high torque. The magnetomotive force (MMF) harmonics of the Halbach array are analyzed theoretically, and then the influences of the MMF to the counter the electromotive force (EMF) are explained. This Halbach array is constructed of radially and circumferentially magnetized permanent magnets. Therefore, the MMF components generated by these two types of magnets are analyzed separately. Then, it is explained that the MMF space harmonics components can be decreased by adjusting the permanent magnet width of the Halbach array. As a result, it is revealed that the waveform distortion of the counter EMF can be reduced to 0.6% when the width ratio of the radially magnetized permanent magnet to the circumferentially magnetized permanent magnet is 3:2.

A small PM (permanent magnet) vernier motor, whose rotor diameter is 42 mm, is designed by adjusting the gap size, permanent magnet thickness, and iron core length to obtain high torque. The design method is presented and the torque increase mechanism is described in terms of the counter electromagnetic field and the synchronous reactance. For the designed motor, a maximum output of 183 W (maximum torque: 4.36 N•m), a maximum power factor of 99.8%, and a maximum efficiency of 90.0% are obtained at an operating voltage of 48.5 V and a synchronous speed of 400 min−1.

This work theoretically assessed a PM (permanent magnet) type Vernier generator capable of producing electricity at low rotational rates. The functions of the rotor and stator permanent magnet were examined. In addition, the space harmonics of the air gap magnetic flux density distribution were analyzed while focusing on the magnetomotive force harmonics of the permanent magnets, as calculated based on a connection factor with an equivalent coil. The presence of space harmonic components and the generation of an induced electromotive force were verified using a finite element analysis supported by experimental data. The results of this analysis established the mechanism by which electromotive force is induced in such a device and explained the effective space harmonic components of air gap magnetic flux density distribution.

A PM vernier motor, which has magnets in both the armature and rotor slots, generates a high torque at low-speed rotation. The pull-out torque of this motor can be increased while maintaining the high power factor by increasing the thickness of the permanent magnets in the machine design process. In this study, the mechanism of this torque increase was analyzed using the finite element method in conjunction with the frozen permeability method. The effects of the permanent magnet thickness are discussed with a focus on the induced electromotive force and the synchronous reactance. As a result, it was revealed that the maintenance of the induced electromotive force and the decrease in the synchronous reactance when the magnet thickness is increased produce the high torque and high power factor that provide the superior performance of this type of motor.

A surface permanent magnet-type vernier generator with slots in only the armature side is analyzed theoretically and a calculation method for its output is proposed. The mutual inductance is derived considering the space harmonics of the air-gap magnetic flux density. The generation mechanism for the induced electromotive force is determined. The voltage equation and the output equation under generation operation are derived based on the unified theory. These equations are verified experimentally using an actual generator, with excellent results obtained. The generation mechanism and the equations for the generator design and power generation control are validated.

A design method for PM vernier motors (PM-VMs), which generate high torque at low speed, is proposed. The proposed design method is based on the voltage and torque equations of a PM-VM. According to these equations, the maximum output is proportional to the induced electromotive force and is inversely proportional to the synchronous reactance. Therefore, the output characteristics can be tuned by adjusting the number of armature winding turns and the iron core length. A maximum output of 6.6 kW, a power factor at the rated output of 91.3%, and an efficiency at the rated output of 92.6% were achieved. These values were directly calculated and verified using two-dimensional finite element analysis.

In this paper, the authors designed a surface permanent magnet (SPM)-type vernier motor whose maximum output is more than 5.2 kW, whose power factor at 4 kW is more than 90%, and whose efficiency at 4 kW is 85% under the conditions that the operating voltage, frequency, and synchronous speed are 400 V, 50 Hz, and 100 min−1, respectively.

Surface permanent magnet-type vernier motors with three magnet array-type rotors (parallel magnetized type, repulsion type, and Halbach type) are compared based on the pull-out torque. It was clarified that increasing the rotor radius increases the pull-out torque at a fixed three-phase alternating voltage. The mechanism for the pull-out torque increase on each magnet array type was different, when the effects of the increase were analyzed based on an induced electromotive force and a synchronous reactance. As a result, the design of the Halbach-type rotor was found to be especially effective for achieving high pull-out torque, because this array type achieves a large induced electromotive force E0 and a small synchronous reactance xs.

Recently, various types of vernier motor have been developed. The variable-reluctance vernier motor (VRVM) is a three-phase reluctance motor whose stator has slots and distributed three-phase windings. The rotor is a slotted iron core without windings. The relationship between S, R, and P is S = R ± P, where S and R are the numbers of stator and rotor slots and P is the number of poles. The rotor of the VRVM moves at a sub-multiple of the angular velocity of the stator mmf. The multiplying factor is P/R. The authors previously reported that a VRVM can be analyzed as a three-phase reluctance motor, and obtained the voltage equations on the γ−δ axis and an expression for the torque. However, the loss separation of a VRVM is not yet clear. In this paper, the iron loss of VRVM is analyzed by the finite element method and compared with experimental values.

A Surface Permanent Magnet-type Linear Vernier Motor (SPM-LVM) is developed, and its output characteristics are clarified by calculation in this paper. As a result, a high thrust, high power factor and high efficiency SPM-LVM with a maximum thrust of 1509N, power factor at 970N of 100.0%, and efficiency at 970N of 90.5% is obtained under the conditions that the operating voltage, frequency and synchronous speed are 100V, 50Hz and 0.942m/s, respectively.

A surface permanent magnet (SPM)-type vernier motor whose rotor uses Halbach array magnet is designed in this study. Voltage and torque equations are derived, and an output calculation method and design process based on these equations are proposed. A high-output power motor and a high-power factor, high-efficiency motor are designed using the proposed design process, and the output characteristics are clarified using the proposed calculation method and finite element analysis. A high-output power motor with a maximum output of 11.9 kW is designed. A high-power factor, high-efficiency motor with a maximum output exceeding 6 kW is also designed; the power factor and efficiency of this motor at 4 kW are more than 90% and more than 85%, respectively. The proposed calculation method and the design process are shown to be very effective.

This paper considers the robust stability analysis problem of multidimensional (nD) discrete systems. It is shown that the problems of stability test and stability margin computation for an nD system described by Roesser model can be recast into μ analysis problems in a unified way, thus can be solved effectively by using the commercially available software package. Several numerical examples are presented to illustrate the new methods.

Recently, various types of vernier motor are developed. The VR type vernier motor is a kind of three-phase reluctance motor, and its stator has slots and distributed three-phase windings. The rotor is slotted iron core without windings. Relationship between S, R and P is S = R±2, where S and R are the numbers of stator and rotor slots per pair of poles, and the number of poles P is two. The rotor of the vernier motor moves at a sub-multiple of the angular velocity of the stator mmf. The multiplying factor is P/R.Authors had reported that the VR type vernier motors are analyzed as a three-phase reluctance motor, and have obtained the voltage equations on the γ-δ axis and expression of the torque.However, the asynchronous characteristics of the vernier motor are not clear yet. In this paper, the asynchronous characteristics of the vernier motors are analyzed with the symmetric components transformation and the commutator transformation. The voltage equations on the symmetrical co-ordinates and asynchronous and synchronous torque expression at steady state condition are obtained.The tests were performed on the trial motor. The calculated asynchronous torque has agreed well with the measured values.

This paper describes a surface permanent magnet (SPM)-type vernier motor that can generate high torque at low speeds, and a simple, high-speed method for analyzing its output characteristics is proposed. In this method, if the induced electromotive force, the synchronous reactance, and the iron loss are provided by finite element analysis (FEA), the output characteristics can be calculated immediately using the voltage and torque equations on the γ and d axes. The proposed method is simpler and faster than the general method that uses FEA only. In this paper, the voltage and torque equations of the SPM-type vernier motor are derived, and the proposed analysis method using these equations is presented. Moreover, the agreement of the results calculated using this method with the measured values confirms a high degree of accuracy.

This paper Presents a method for calculating the nonlinear iron loss in an Orthogonal-core. The authors have analyzed the iron loss by using the 3D magnetic circuit of the orthogonal-core on the reluctance network analysis. The magnetic hysteresis is expressed by the inductances connected in series with reluctances in the circuit in accordance with the Chua-type magnetization model. The computed results approximately agree with experimental ones. It was found that the proposed method is very suitable for calculating the iron loss in an orthogonal-core.

The operating characteristics of parametric transformers and dc-ac converters with an orthogonal core depend heavily on the core shape. Accordingly, to obtain the optimal design for such devices, the quantitative relationship between the orthogonal core shape and the operating characteristics of the application device are determined. In this paper, the application characteristics are discussed analytically in terms of the orthogonal core shape, with reference to a magnetic circuit model of the core.

A pole-changing induction motor with pole-amplitude modulation (PAM) has a single-winding system, and has a unique speed ratio other than 1: 2. It provides an excellent energy-saving property when used for the flow control system of pumps and blowers. This, therefore, has attracted considerable attention in a field of flow control design.However the method of conversion from an 8-pole to a 6-pole induction motor by using this PAM becomes complicated compared with the method of conversion to a 10-pole motor. In addition, the induction motor designed by this approach is likely to be affected by large harmonic magnetomotive forces, and therefore needs careful investigation in the design.This paper describes the harmonic torque prevention approach done by using the unified theory of electrical machinery for the case of 8-pole to 6-pole conversion by PAM. From the result of analysis and speed-torque experiment, it is shown that this induction motor is driven by the negative-phase revolving magnetic field due to the 3rd order harmonic, and that there appear 13th harmonic asynchronous crawling torque in motor region and 11th harmonic asynchronous torque in braking region. It is also shown that a long-pitch winding with a machine angle of 8/24 is recommended for the motor design so that the 11th and the 13th harmonic torques are removed.

The operating characteristics of parametric transformers and dc-ac converters with an orthogonal core greatly depend on the core shapes. Accordingly, in the optimal design for the applications, we used to clarify the quantitative relationship between the orthogonal-core shape and the operating characteristics of the application devices. In this paper, the application characteristics in terms of the orthogonal-core shape are discussed analytically with reference to a magnetic circuit model of the orthogonal core.

A pole-changing induction motor with pole-amplitude modulation allows a speed ratio other than 1:2 using a single winding. Furthermore it has a good energy-saving performance when used for the flow rate control of pump or blower, and also it provides a low manufacturing cost. However, the pole-changing induction motor with pole-amplitude modulation has a problem that its simple calculation method of characteristics has not been presented.A purpose of this paper is to derive the calculation method by using an equivalent circuit in when an 8-pole cage type induction motor is changed into a 10-pole motor by pole-amplitude modulation. In this paper, the authors suggest the equivalent circuit in which the space harmonic effects are considered, because the 10-pole motor has large harmonic magnetomotive forces. This paper also describes a simple determination method of equivalent circuit constants.Torque-slip characteristics and output-characteristics are obtained, and it has been confirmed that they agree well with the experimental values. This calculation method of characteristic is practical and useful for the future designing of pole-changing induction motors with pole-amplitude modulation.

The orthogonal-core has various applications such as a parametric transformer and a DC-AC converter. The operating characteristics of the application devices can be calculated based on the measured flux-MMF relationship of the orthogonal-core. For the optimum design of the applications, we have to predict the flux-MMF relationship. However, in order to calculate the relationship, we need to solve the three-dimensional nonlinear problem. In this paper, we calculate the flux-MMF relationship based on the magnetic circuit model of the orthogonal-core. The computed results agree well with the experimental ones. It is obvious that the method on this study is valid for the calculation and useful for the optimum design of the applications.

This paper describes an analysis of the behavior of orthogonal-core type push-pull parametric transformers, taking the iron loss of the orthogonal-cores and the copper loss of the windings into consideration. The analysis was performed for the magnetic circuit of the orthogonal-core under magnetic saturation and with hysteresis. To improve the accuracy of calculations, the saturation characteristic was approximated by a series which includes terms of up to 21st order in the flux, and the hysteresis curve by a series including terms of up to 5th order in the exciting voltage. The calculated results show good agreement with experimental data. The analytical method presented here is useful for optimizing the design of push-pull parametric transformers.

This paper discusses the difficult problem of synthesis of stable stabilizing compensators for linear multidimensional (nD) single-input single-output (SISO) systems by exploiting existing results on stability tests. Firstly, we give an analytic expression for the class of stable stabilizing compensators when the plant is restricted to be a first-order 2D system and the compensator is a constant. We then briefly discuss how to generalize this result to other low order nD systems with low order stable stabilizing compensators. Two examples are illustrated.

The purpose of this paper is to establish a new constructive procedure for realization of 2D systems by Fornasini-Marchesini second (F-MII) local state-space model which can further reduce the order of the resultant realization to about half of that obtained by the procedure given recently by the authors. Nontrivial illustrative examples are given.

Adaptive control is an effective way of controlling unknown dynamical systems. While many results on one-dimensional (1-D) adaptive control are available, little has been accomplished in the area of two-dimensional (2-D) system theory. In this paper, an indirect adaptive controller will be proposed for a class of 2-D systems in the presence of disturbances. Analyses show that the designed adaptive controller, consisting of a parameter estimator and a linear controller, can stabilize the given class of 2-D systems.

The purpose of this paper is to develop an analytic way for designing optimal PI-controllers for interval plant family, in the sense that the coefficient intervals of the plant is maximized. It will be shown that the optimization problem can be formulated in terms of an eigenvalue minimization problem of matrix pairs of the form (H(h 0 , g 0 ), H(δ 1,κ , δ 2,κ )) where κ = 1,2,3,4 and Poth H(h 0 ,g 0 ) and H(δ 1,κ ,δ 2,κ ) are frequency independent Hurwitz-like matrices.

This paper considers the stability analysis problem of nD discrete-time systems. It is shown that the problems of stability test and stability margin computation for an nD system described by Roesser model can be recast into μ analysis problems in a unified way, thus can be solved effectively by using the commercially available software package.

One method for calculating flux-MMF relationship of an orthogonal core is described. The calculation is based on a three-dimensional magnetic circuit model of the orthogonal core. The model is derived by dividing the orthogonal core, inclusive of the surrounding region, into elements comprising a three-dimensional magnetic circuit. Using this model, the flux-MMF relationship of the orthogonal core with arbitrary dimensions can be calculated from the B-H characteristic of the core material. The calculation method presented is useful for optimum design of devices using an orthogonal core. >

The running characteristics of the split-phase capacitor motor in which a triac is connected in series with the motor circuit to control the applied voltage in accordance with the load conditions are studied. Ferrite magnetic wedges are inserted into the slot openings on the motor stator. The wedging effect on the motor characteristics is studied. When the ferrite wedges are inserted into the slot openings, the flux density pulsation in the air gap is decreased greatly to decrease the inner power losses, resulting in the improvement of motor efficiency and characteristics. >

The flux density distribution in the air gap on revolving electric machines is distorted by the presence of slots and teeth to produce rotor pole face eddy current and stator tooth pulsation losses, resulting in the reduction of motor efficiency. When the asymmetric voltage controlled by switching devices such as a triac is applied to the motor, the voltage and current also pulsate to increase power losses. In the present study, ferrite magnetic wedges have been inserted into the stator slot openings of the capacitor motor and some experiments under the triac control have been carried out. It is found that the pulsation of the flux density distribution in the air gap is decreased by wedging the ferrite materials to increase the apparent magnetic permeability. This resulted in decreasing the motor power losses and improving the motor running characteristics. >

The split-phase condenser motor is very useful for driving home electric appliances, but it has low efficiency. In other words, since the condenser motor is operated by two magnetic fields constituting positive phase and negative phase sequences, large electric power losses in light loads and oscillative torque are usually produced. In addition to this, the presence of the slot embedding electric conductors disturbs the flux density distribution in the air gap, producing tooth pulsation and higher harmonic losses. In this study, ferrite magnetic materials have been wedged into the stator slot openings of the condenser motor to smooth the pulsative distribution of the flux density in the air gap, and some experiments have been carried out to discuss the effect of the ferrite wedges on the motor characteristics with various running condenser capacities. As a result, the usefulness of the ferrite magnetic wedge has been verified.

Split-phase capacitor motors are commonly used to drive household electric appliances. The motor has some slots and teeth to embed electric conductors or coils. The presence of the slots and teeth induces the variation of magnetic reluctance through the magnetic circuit to introduce heavy pulsation of the air gap flux. Thus, the voltage, current and torque of the motor become oscillative to increase the electric power loss and finally to reduce the motor efficiency. First, the authors discuss the characteristics of a 3-phase cage-type induction motor in which the ferrite magnetic wedges have been installed into the stator slot openings of the motor to smooth the air gap flux pulsation and to decrease the electric power loss, resulting in improved motor efficiency. If the motor is driven by the voltage source in accordance with the loading condition, more economical operation will be achieved. In this study, a nonsinusoidal voltage controlled by the switching element of a triac has been applied to a capacitor motor with wedges of ferrite magnetic materials. This paper reports on the interesting results obtained.