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Permanent magnet synchronous spherical motors can have wide use in robotics and industrial automation. They enable three-DOF omnidirectional motion of their rotor. They are suitable for several applications, such as actuation in robotics, traction in electric vehicles and use in several automation systems. Unlike conventional synchronous motors, permanent magnet synchronous spherical motors consist of a fixed inner shell, which is the stator, and a rotating outer shell, which is the rotor. Their dynamic model is multivariable and strongly nonlinear. The treatment of the associated control problem is important.

In this paper, the multivariable dynamic model of permanent magnet synchronous spherical motors is analysed, and a nonlinear optimal (H-infinity) control method is developed for it. Differential flatness properties are proven for the spherical motors’ state-space model. Next, the motors’ state-space description undergoes approximate linearization with the use of first-order Taylor series expansion and through the computation of the associated Jacobian matrices. The linearization process takes place at each sampling instance around a time-varying operating point, which is defined by the present value of the motors’ state vector and by the last sampled value of the control input vector. For the approximately linearized model of the permanent magnet synchronous spherical motors, a stabilizing H-infinity feedback controller is designed. To compute the controller’s gains, an algebraic Riccati equation has to be repetitively solved at each time-step of the control algorithm. The global stability properties of the control scheme are proven through Lyapunov analysis. Finally, the performance of the nonlinear optimal control method is compared against a flatness-based control approach implemented in successive loops.

Due to the nonlinear and multivariable structure of the state-space model of spherical motors, the solution of the associated nonlinear control problem is a nontrivial task. In this paper, a novel nonlinear optimal (H-infinity) control approach is proposed for the dynamic model of permanent magnet synchronous spherical motors. The method is based on approximate linearization of the motor’s state-space model with the use of first-order Taylor series expansion and the computation of the associated Jacobian matrices. Furthermore, the paper has introduced a different solution to the nonlinear control problem of the permanent magnet synchronous spherical motor, which is based on flatness-based control implemented in successive loops.

The presented control approaches do not exhibit any limitations, but on the contrary, they have specific advantages. In comparison to global linearization-based control schemes (such as Lie-algebra-based control), they do not make use of complicated changes of state variables (diffeomorphisms) and transformations of the system's state-space description. The computed control inputs are applied directly to the initial nonlinear state-space model of the permanent magnet spherical motor without the intervention of inverse transformations and thus without coming against the risk of singularities.

The motion control problem of spherical motors is nontrivial because of the complicated nonlinear and multivariable dynamics of these electric machines. So far, there have been several attempts to apply nonlinear feedback control to permanent magnet-synchronous spherical motors. However, due to the model’s complexity, few results exist about the associated nonlinear optimal control problem. The proposed nonlinear control methods for permanent magnet synchronous spherical motors make more efficient, precise and reliable the use of such motors in robotics, electric traction and several automation systems.

The treated research topic is central for robotic and industrial automation. Permanent magnet synchronous spherical motors are suitable for several applications, such as actuation in robotics, traction in electric vehicles and use in several automation systems. The solution of the control problem for the nonlinear dynamic model of permanent magnet synchronous spherical motors has many industrial applications and therefore contributes to economic growth and development.

The proposed nonlinear optimal control method is novel compared to past attempts to solve the optimal control problem for nonlinear dynamical systems. Unlike past approaches, in the new nonlinear optimal control method, linearization is performed around a temporary operating point, which is defined by the present value of the system's state vector and by the last sampled value of the control inputs vector and not at points that belong to the desirable trajectory (setpoints). Besides, the Riccati equation which is used for computing the feedback gains of the controller is new, and so is the global stability proof for this control method. Compared to nonlinear model predictive control, which is a popular approach for treating the optimal control problem in industry, the new nonlinear optimal (H-infinity) control scheme is of proven global stability, and the convergence of its iterative search for the optimum does not depend on initial conditions and trials with multiple sets of controller parameters. It is also noteworthy that the nonlinear optimal control method is applicable to a wider class of dynamical systems than approaches based on the solution of state dependent Riccati equations (SDRE). The SDRE approaches can be applied only to dynamical systems which can be transformed into the linear parameter varying form. Besides, the nonlinear optimal control method performs better than nonlinear optimal control schemes, which use approximation of the solution of the Hamilton–Jacobi–Bellman equation by Galerkin series expansions. Furthermore, the second control method proposed in this paper, which is flatness-based control in successive loops, is also novel and demonstrates substantial contribution to nonlinear control for robotics and industrial automation.

Taking a 2,000 r/min 10 kW permanent magnet motor as an example, the purpose of this paper is to study the influence of driving modes on the performance of permanent magnet motor at limit conditions, and researched the variation mechanism of motor performance influenced by different driving modes.

A two-dimensional electromagnetic field model of the permanent magnet motor was established, and a rectangular-wave driving circuit was built. By using the finite element method, the electromagnetic field, current, harmonic content and eddy current loss were calculated when the motor operated at rated load and limit load. On the basis of the motor loss calculation, the temperature field of the motor operating at rated condition and limit condition was researched, and the factors that influence motor limit overload capacity were analyzed. By analyzing the motor loss variation at different load conditions, the change mechanism of the motor temperature field was determined further. Combined with the related experiments, the correctness of the above analysis was verified.

Permanent magnet synchronous motor (PMSM) driven by sine wave is better compared with brushless direct current motor (BLDCM) driven by rectangular wave in reducing the magnetic field harmonics, motor losses and optimizing the temperature distribution in the motor. The method driven by sine wave could improve the motor output performance including the motor efficiency and the motor overload capacity. The winding temperature is the most important factor that limits the output capability of PMSM operating for a long time. However, because of the large rotor eddy current losses, the permanent magnet temperature is the most important factor that limits the output capability of BLDCM operating for a long time.

The influence of driving modes on the motor magnetic field, losses and temperature distribution, efficiency and overload capacity was determined, and the influence mechanism was also analyzed. Combined with the analysis of the electromagnetic and temperature fields, the advantages of different driving modes were presented. This study could provide an important basis for the design of permanent magnet motors with different driving modes, and it also provides reference for the application of permanent magnet motor.

This paper presents the influence of driving modes on permanent magnet motors. The limit output capacity of the motor with different driving modes was studied, and the key factors limiting the motor output capability were obtained.

In order to reduce CO₂ emissions of new cars many hydraulic and mechanical systems like e.g.: water pump, oil pump, power steering, clime compressor have been exchanged with pure electromechanical systems, which are driven only on request. This helps to reduce fuel consumption. This trend requires of utilization of modern brushless electric motors, which are controlled from power electronic control unit – ECU. In today's car can be found between 30 to 150 electric motors. Many of them are still simple brush type with ferrite magnets. Also in this area, drift in the direction of brushless motors can bee seen, because of higher efficiency, longer lifetime, lower noise, better EMC and more controllable torque vs speed characteristic. There are different technological solutions, which can been used in the area of brushless motors in order to reduce size and cost of single component. One major factor of BLDC/AC motor is rear earth permanent magnet material used during production. A magnet material cost could be in the range from 30 percent (basis price 2010) up to 90 percent (basis price 2011) of total material motor cost, depends on actual rear earth material price level. In order to reduce magnet cost, the aim of this paper is to find the most robust motor design, which can be resistant against maximum temperature and phase current amplitude for the same magnet material properties, coercive force – Hcj. This behaviour is called demagnetization property.

Analysis was performed based on review of literature, own theoretical and practical research and experience in the area of electromechanical systems for automotive application. During motor analysis computer numerical simulation method, CAD and experiment were used.

As a result, comparison of different motors' topologies with different properties of magnet materials is presented. The worked out methodology shows very good correlation between simulations and measurements. This work can be used in order to reduce test effort and reduce cost of design.

The presented methodology reduces for new designs test effort and development cost and gives an implication of robust motor topology for demagnetization effects.

It is the first paper where demagnetization effects have been studied theoretically and in laboratory in order to find the most robust design, reduce magnet cost by reduction of dysprosium content and develop simulation procedure for analysis of demagnetizations behaviours of interior and surface permanent magnet.

Discusses the 27 papers in ISEF 1999 Proceedings on the subject of electromagnetisms. States the groups of papers cover such subjects within the discipline as: induction machines; reluctance motors; PM motors; transformers and reactors; and special problems and applications. Debates all of these in great detail and itemizes each with greater in‐depth discussion of the various technical applications and areas. Concludes that the recommendations made should be adhered to.

Introduces papers from this area of expertise from the ISEF 1999 Proceedings. States the goal herein is one of identifying devices or systems able to provide prescribed performance. Notes that 18 papers from the Symposium are grouped in the area of automated optimal design. Describes the main challenges that condition computational electromagnetism’s future development. Concludes by itemizing the range of applications from small activators to optimization of induction heating systems in this third chapter.

Early magnetic-geared motors have a high transmission torque density. However, the torque due to the coil is low because the permanent magnets in the stator become a large magnetic resistance when the current is applied to the coil. The purpose of this paper is to propose magnetic-geared motors which have a high transmission torque density and torque due to the coil. In addition, the proposed magnetic-geared motors are compared with past magnetic-geared motors and the effectiveness is verified by using finite element analysis.

A new magnetic-geared motor which has permanent magnets in the stator slot are proposed. The torque due to the coil increases by removing permanent magnets at the tip of the stator of past magnetic-geared motors. The permanent magnets placed in the stator slots are all magnetized to the outward direction and then the stator teeth are all magnetized to the inward direction. The maximum transmission torque and torque constant are compared.

The proposed magnetic-geared motor has a slightly smaller maximum transmission torque than the early magnetic-geared motors. However, the maximum transmission torque of the proposed magnetic-geared motor is high enough for practical uses. The torque due to the coils is higher than the early magnetic-geared motors.

The proposed magnetic-geared motor has originalities in its structure, especially in the permanent magnets in the stator slots.

The purpose of this paper is to present the optimal design of a low-cost interior permanent magnet (IPM) alternating current (AC) motor. It examines the influence of the permanent magnet (PM) materials, and proposes a simple and practical method of optimizing the air-gap field to achieve sinusoidal back electromotive force (EMF), and to reduce the cogging torque.

IPM AC motors with different magnet materials and various topologies are comparatively studied. Finite element method (FEM) is used to predict the performances of these designs. Material costs and manufacture costs are both taken into account. Finally, an optimized design is prototyped and tested, validating the design considerations.

In an IPM AC motor, even if the rotor outer profile is round, the air-gap field distribution can be fined, while the cogging torque can be significantly reduced, by properly shaping the stator tooth tips. Nevertheless, this technique is usually applicable to motor configurations with concentrated windings, but not to those with distributed windings.

While using ferrite magnets for PM AC motors with a kW power, interior magnets are usually inserted in V-shaped slots, and the rotor outer profile is often shaped in order to enhance the air-gap field distribution. However, such a rotor configuration usually increases the manufacture costs, and also deteriorates the consistency of mass production. Therefore, a new motor configuration with a round rotor outer profile and shaped stator tooth tips is proposed. It can not only overcome the aforementioned problems, but also improve the motor performance.

In the present paper the influence of the magnetization patterns of rotor magnets on the performance characteristics of a surface permanent magnet (SPM) motor has been investigated. The purpose of this paper is to show how the electromagnetic and electromechanical characteristics of this type of motor can be significantly changed by applying various magnetization patterns of permanent magnets (PM) on the rotor surface.

First, a survey of possible and most frequently used magnetization patterns for PM motors is presented. The research is focussed on the comparison of performance characteristics and is developed at three levels. The study starts with investigation of a conventional SPM motor having segmented PM, and two magnetization patterns are considered: parallel and radial. As there was no significant difference in motor performance at parallel and radial magnetization, for further investigation only radial magnetization, being more conventional, was considered. In the second step, the counterparts of SPM with two Halbach array configurations, under the constraint of fixed magnet volume, are studied. Finally, detailed comparative analyses of SPM at radial, Halbach 1, and Halbach 2 magnetic patterns are presented. The advantages and drawbacks of the suggested magnetic configurations are then discussed.

The authors have shown how the magnetization pattern of rotor PM can have a substantial impact on the SPM motor performance characteristics. From the analysis of magnetic field properties at various types of magnetization, it is observed that both the shape and the rates of the characteristics, for radial magnetization and Halbach 2 configuration, exhibit similar features. This is because the Halbach 2 array cancels the magnetic flux above the PM – that is, it strengthens the magnetic field in the rotor, and enhances the coupling between the rotor and stator magnetic field. It is worth emphasizing that, because of less saturation of the magnetic core and lower iron loss at Halbach 1 and Halbach 2 magnetization, it is possible to increase the armature current and consequently increase the electromagnetic torque. This finding could be an interesting for further research.

The paper presents an original comparative analysis of the performance characteristics of a surface permanent motor at various magnetization patterns. The novelty of the paper is seen in the introduction of two Halbach magnetization arrays for PM and improvement of the performance characteristics of the analysed motor.

The purpose of this paper is to clarify the electrical loss of an interior permanent magnet (IPM) motor driven by the pulse‐width modulation (PWM) inverter with various carrier frequencies quantitatively.

An IPM motor driven by the PWM inverter was simulated using the three‐dimensional finite‐element method while changing various carrier frequencies of the PWM inverter. The calculated results are compared with the calculated results differing the number of permanent magnet division.

The eddy current loss in the permanent magnets decreases as the carrier frequency increases. In the case of low‐carrier frequency, the eddy current loss greatly decreases as the number of permanent magnet division increases. However, the effect of the eddy current loss decreases by the number of permanent magnet division as the carrier frequency increases.

The paper describes the electrical loss of an IPM motor driven by the PWM inverter with various carrier frequencies.

This paper aims to elaborate the method and algorithm for the analysis of the influence of temperature on back electromotive force (BEMF) waveforms in a line start permanent magnet synchronous motor (LSPMSM).

The paper presents a finite element analysis of temperature influence on BEMF and back electromotive coefficient in a LSPMSM. In this paper, a two-dimensional field model of coupled electromagnetic and thermal phenomena in the LSPMSM was presented. The influence of temperature on magnetic properties of the permanent magnets as well as on electric and thermal properties of the materials has been taken into account. Simulation results have been compared to measurements. The selected results have been presented and discussed.

The simulations results are compared with measurements to confirm the adequacy of this approach to the analysis of coupled electromagnetic-thermal problems.

The paper offers appropriate author’s software for the transient and steady-state analysis of coupled electromagnetic and thermal problems in LSPMS motor.