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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.

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.

The increased use of permanent magnet synchronous motors in small to medium power applications has made it imperative that these motors' performance can be modelled successfully. The accuracy of calculating the synchronous reactances determines the success of the modelling technique. An analytical method and the finite element method are used to calculate the synchronous reactances of two prototype synchronous motors. The calculations are compared with measurement for both motors. The results show that the finite element method is more reliable in obtaining synchronous reactances than the analytical method for rotor designs that are very intricate, although both methods show reasonable accuracy.

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.

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.

The time‐stepping finite method of transient analysis in permanent magnet synchronous machines has been presented. This method has been used for determining the steady‐state and dynamic performance of the permanent magnet self‐starting synchronous motor. The movement of the rotor, the saturation of the ferromagnetic core, the properties of permanent magnet and eddy currents in the solid bars of the cage winding have been taken into account.

This paper aims to apply a two‐axis model for accurate representation of the characteristics of permanent magnet synchronous motors (PMSM) of the interior type.

For a three‐phase PMSM, it uses a voltage source inverter with six power transistors with independent switching and PSIM software with Matlab for checking, by simulation, how some parameters influence the start process.

It was found that pulsating components generate the synchronizing torque.

The paper provides a model for accurate representation of the characteristics of permanent magnet motors.

The paper aims to present the comparison between the performances of the exterior‐rotor permanent magnet synchronous motors with distributed windings and the performances of the exterior‐rotor permanent magnet synchronous motors with concentrated windings.

Finite element method is used for motors performance determination. The BLDC operation mode for the motors with different slot and pole number combination and concentrated windings was accounted for in the comparison.

In the BLDC operation mode motor structures with concentrated windings with similar slot and pole numbers exhibit at the same current density similar or even higher torque capability and lower electromagnetic torque ripple in comparison to the motor structure with distributed windings. Motor structures with 9‐slot/8‐pole, 9‐slot/10‐pole, 12‐slot/10‐pole slot and pole number combinations are the most appropriate for the BLDC operation.

The paper shows which motor structures with distributed or concentrated windings in the BLDC operation mode produce lower torque ripple and higher average torque per ampere.

The purpose of this paper is to compare parameters and properties of optimal structures of a line-start permanent magnet synchronous motor (LSPMSM) for the cage winding of a different rotor bar shape.

The mathematical model of the considered motor includes the equation of the electromagnetic field, the electric circuit equations and equation of mechanical equilibrium. The numerical implementation is based on finite element method (FEM) and step-by-step algorithm. To improve the particle swarm optimization (PSO) algorithm convergence, the velocity equation in the classical PSO method is supplemented by an additional term. This term represents the location of the center of mass of the swarm. The modified particle swarm algorithm (PSO-MC) has been used in the optimization calculations.

The LSPMSM with drop type bars has better performance and synchronization parameters than motors with circular bars. It is also proved that the used modification of the classical PSO procedure ensures faster convergence for solving the problem of optimization LSPMSM. This modification is particularly useful when the field model of phenomena is used.

The authors noticed that to obtain the maximum power factor and efficiency of the LSPMSM, the designer should take into account dimensions and the placement of the magnets in the designing process. In the authors’ opinion, the equivalent circuit models can be used only at the preliminary stage of the designing of line-start permanent magnet motors.

The purpose of this paper is to include thermal analysis in the design process of permanent magnet synchronous motor (PMSM). The additional objective is a comparison of PMSM with induction motor (IM) in terms of thermal phenomena.

Numerical investigation using commercial software MotorSolve was performed. Parameterized models of PMSM and IM were used. Calculations of motor parameters and temperature distribution were made using Finite Element Method.

The results of the calculations show that thermal calculations should be included in the design process because the maximum permissible operating temperature of permanent magnets should not be exceeded. A comparative analysis of PMSM and IM shows that the PMSM has better parameters than the IM which was used as a base of the PMSM construction.

Computational models should be verified experimentally on a physical model or by using more complex numerical models. In the case of IM thermal calculations, a method of air speed calculation should be proposed. Air speed is a parameter that is necessary in thermal analysis of IM, but during the design process it is unknown.

This paper presents modelling methodology of 3D transient thermal field coupled with electromagnetic field applied in a three-phase IM at rated load conditions. This paper presents a design strategy which includes thermal analysis of the designed PMSM. Moreover, the paper shows a comparison between PMSM and IM indicating advantages of PMSM over IM.