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Nowadays, to simplify manufacture process and improve fault-tolerant capability, more and more modular electrical machines are being applied in industrial areas. The purpose of this paper is to investigate a novel modular single-sided flat permanent magnet linear synchronous motor (PMLSM), which adopts segmented armature with the required flux gaps between segments to enhance the performance.

Using 2D finite element analysis, the performances, such as open-flux linkage, back-EMF, average thrust force, thrust ripple, etc., are compared in different values of flux gaps, as well as different slot/pole number combinations (mainly odd numbers of poles). Finally, to show the difference of linear motor from rotary one, the detailed comparison is made between modular PMLSM and rotary PMSM.

Due to flux gaps, it is found the electromagnetic performances are worsened along with flux gap width increasing to modular PMLSMs having slot number higher than pole number, but some aspects of performances such as winding factor, open-circuit flux linkage, back-EMF and average thrust can be improved to those having slot number lower than pole number. Due to the end effect of linear format, the thrust ripple is not significantly improved.

It is concluded the proper flux gaps can be chosen to improve the performance of PMLSM with certain slot/pole combinations. A new structure of 12-slot-13-pole (hereinafter referred to as 12s/13p) PMLSM with fractional slot and alternative-teeth wound winding is designed.

Due to the merits of direct driven, high thrust density and high efficiency, PM linear synchronous motor (PMLSM) is pretty suitable for the long-stroke ropeless lifter. However, the vibration caused by detent force and difficulty of maintenance become the barriers that restrict its application. The paper aims to discuss these issues.

In order to simplify structure and improve driving performance, a novel PMLSM with segmented armature core and end non-overlapping windings is proposed. The analytical formula of detent force is derived based on energy method and harmonic analysis, which is validated by two-dimensional finite element analysis (FEA). Moreover, with erected parametric FEA calculation, the selection principles of slot-pole number combination and interval distance to this novel structure are obtained. Finally, the heat dissipation ability of conventional PMLSM and novel PMLSM are compared through thermal analysis.

In novel PMLSM, it is found that the (3m+1) and (3m+2) order harmonic components of thrust force are eliminated, which leads to a better driving performance in comparison with the conventional structure. Furthermore, the good heat dissipation ability of novel structure makes it possible for higher thrust density, which is crucial for ropeless lifter.

The novel PMLSM has excellent driving performance, simple structure for maintenance, possibility of modular production and high thrust density. It is a strong candidate for long-stroke ropeless lifter.

The purpose of this paper is to investigate the electromagnetic performances of the permanent magnet linear synchronous machines (PMLSM) with sine and third harmonic (SIN + 3rd) shaping mover in comparison with the PMLSM with sine (SIN) shaping mover and conventional shaping mover.

The optimal amplitude of the injected third harmonic to re-shape the SIN + 3rd shaping permanent magnet (PM) for maximizing the thrust force is analytically derived and confirmed by finite element method (FEM). Furthermore, the PM edge thickness, the pole arc to pole pitch ratio and the tooth to slot ratio are optimized. It is found that the optimal amplitude of the injected third harmonic is one-sixth of the fundamental one, the optimal PM edge thickness, the pole arc to pole pitch ratio and the tooth to slot ratio are 0, 0.85 and 0.5 mm, respectively. In addition, the electromagnetic performances are analyzed and quantitatively compared for the PMLSM with SIN + 3rd shaping mover, SIN shaping mover and conventional shaping mover.

The average thrust force and efficiency of the PMLSM with SIN + 3rd shaping mover are improved significantly, while the thrust ripple is not increased, comparing to those of the PMLSM with SIN shaping mover. Meanwhile, the thrust ripple is lower than that of the conventional shaping mover.

The purely sinusoidal currents are applied in this analysis and the influences of harmonics in the current on electromagnetic performances are not considered.

This paper presents a PMLSM with SIN + 3rd shaping mover to improve the thrust force and efficiency without increasing the thrust ripple, considering the effects of the amplitude of the injected third harmonic to re-shape the SIN + 3rd shaping PM, the PM edge thickness, the pole arc to pole pitch ratio and the tooth to slot ratio.

The purpose of this paper is to propose the complementary design rules, give a quantitative comparison and analyze the force production mechanism of two kinds of primary wound field flux-switching linear (PWFFSL) motors.

PWFFSL motors have the merits of no use of rare-earth magnet, low cost and a wide operation range in which the armature windings and the field windings are all located at the short primary mover and the secondary is very robust. Hence, the PWFFSL motor is ideal for rail transportation systems which need a long stator and a wide speed range. To overcome the disadvantages of the existing PWFFSL motors, new complementary design rules will be proposed. Also, to offer a better PWFFSL motor for the rail transportation systems, it is necessary to investigate different structures of PWFFSL motors and give a comprehensive comparison. To predict the force performance of two kinds of PWFFSL motors with different secondary types, their flux density analysis and force production mechanism will be presented and compared.

The comparison result shows that the PWFFSL motor with toothed secondary can offer larger thrust force, higher force density and higher efficiency, whereas the PWFFSL motor with segmented secondary has the merits of lower force ripple, less use of stator iron, higher power factor and less critical saturation.

Many PWFFSL motors with different primary/secondary pole pitches based on the proposed design principle have not been considered in this paper.

This paper has presented the air-gap flux analysis, proposed the complementary design rules for two kinds of PWFFSL motors with different secondary types and compared the electromagnetic performance of the two motors.

The purpose of this paper is to deal with the investigation of no-load operation of tubular linear permanent magnet synchronous machines (T-LPMSMs). It is aimed at the prediction of the phase flux linkages, the back-EMF and the cogging force using a position varying magnetic equivalent circuit (MEC).

This study is based on the elaboration and the resolution of the position varying MEC, and the utilization of its results for the prediction of the phase flux linkages, the back-EMF and the cogging force, considering a general topology of T-LPMSMs. Then, a case study is treated with a position varying MEC-based investigation of its no-load features. These are validated by a 2-D finite element analysis (FEA).

It has been found that the developed position varying MEC can be regarded as an accurate tool that requires a low CPU-time.

Beyond the FEA validation, this work should be extended to an experimental one. Moreover, the position varying MEC validity should be extended to load operation in order to enable the prediction of the force production capability.

The developed position varying MEC could be suitably used for the pre-design of T-LPMSMs. These are currently given an increasing attention in many applications, such as wave energy conversion and free-piston engines.

The paper proposes a position varying MEC for the prediction of the features of T-LPMSMs.

Voltage source inverter-fed permanent magnet synchronous motors (VSI-PMSMs) are widely used in industrial actuation and mechatronic systems in water pumping stations, as well as in the traction of transportation systems (such as electric vehicles and electric trains or ships with electric propulsion). The dynamic model of VSI-PMSMs is multivariable and exhibits complicated nonlinear dynamics. The inverters’ currents, which are generated through a pulsewidth modulation process, are used to control the stator currents of the PMSM, which in turn control the rotational speed of this electric machine. So far, several nonlinear control schemes for VSI-PMSMs have been developed, having as primary objectives the precise tracking of setpoints by the system’s state variables and robustness to parametric changes or external perturbations. However, little has been done for the solution of the associated nonlinear optimal control problem. The purpose of this study/paper is to provide a novel nonlinear optimal control method for VSI-fed three-phase PMSMs.

The present article proposes a nonlinear optimal control approach for VSI-PMSMs. The nonlinear dynamic model of VSI-PMSMs undergoes approximate linearization around a temporary operating point, which is recomputed at each iteration of the control method. This temporary operating point is defined by the present value of the voltage source inverter-fed PMSM state vector and by the last sampled value of the motor’s control input vector. The linearization relies on Taylor series expansion and the calculation of the system’s Jacobian matrices. For the approximately linearized model of the voltage source inverter-fed PMSM, an H-infinity feedback controller is designed. For the computation of the controller’s feedback gains, an algebraic Riccati equation is iteratively solved at each time-step of the control method. The global asymptotic stability properties of the control method are proven through Lyapunov analysis. Finally, to implement state estimation-based control for this system, the H-infinity Kalman filter is proposed as a state observer. The proposed control method achieves fast and accurate tracking of the reference setpoints of the VSI-fed PMSM under moderate variations of the control inputs.

The proposed H-infinity controller provides the solution to the optimal control problem for the VSI-PMSM system under model uncertainty and external perturbations. Actually, this controller represents a min–max differential game taking place between the control inputs, which try to minimize a cost function that contains a quadratic term of the state vector’s tracking error, the model uncertainty, and exogenous disturbance terms, which try to maximize this cost function. To select the feedback gains of the stabilizing feedback controller, an algebraic Riccati equation is repetitively solved at each time-step of the control algorithm. To analyze the stability properties of the control scheme, the Lyapunov method is used. It is proven that the VSI-PMSM loop has the H-infinity tracking performance property, which signifies robustness against model uncertainty and disturbances. Moreover, under moderate conditions, the global asymptotic stability properties of this control scheme are proven. The proposed control method achieves fast tracking of reference setpoints by the VSI-PMSM state variables, while keeping also moderate the variations of the control inputs. The latter property indicates that energy consumption by the VSI-PMSM control loop can be minimized.

The proposed nonlinear optimal control method for the VSI-PMSM system exhibits several advantages: Comparing to global linearization-based control methods, such as Lie algebra-based control or differential flatness theory-based control, the nonlinear optimal control scheme avoids complicated state variable transformations (diffeomorphisms). Besides, its control inputs are applied directly to the initial nonlinear model of the VSI-PMSM system, and thus inverse transformations and the related singularity problems are also avoided. Compared with backstepping control, the nonlinear optimal control scheme does not require the state-space description of the controlled system to be found in the triangular (backstepping integral) form. Compared with sliding-mode control, there is no need to define in an often intuitive manner the sliding surfaces of the controlled system. Finally, compared with local model-based control, the article’s nonlinear optimal control method avoids linearization around multiple operating points and does not need the solution of multiple Riccati equations or LMIs. As a result of this, the nonlinear optimal control method requires less computational effort.

Voltage source inverter-fed permanent magnet synchronous motors (VSI-PMSMs) are widely used in industrial actuation and mechatronic systems in water pumping stations, as well as in the traction of transportation systems (such as electric vehicles and electric trains or ships with electric propulsion), The solution of the associated nonlinear control problem enables reliable and precise functioning of VSI-fd PMSMs. This in turn has a positive impact in all related industrial applications and in tasks of electric traction and propulsion where VSI-fed PMSMs are used. It is particularly important for electric transportation systems and for the wide use of electric vehicles as expected by green policies which aim at deploying electromotion and at achieving the Net Zero objective.

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 input 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, as is the global stability proof for this control method. Comparing with 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 that can be transformed to 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.

This paper aims to develop an analytical approach to validate the finite element analysis (FEA) results. FEA itself is a powerful tool to evaluate the performance of electrical machines but takes more time and requires more drive storage. To overcome this issue, subdomain modeling (SDM) is used for the proposed machine.

SDM is developed to validate the electromagnetic performance of a new linear hybrid excited flux switching machine (LHEFSM) with ferrite magnets. In SDM, the problem is divided into different physical regions called subdomains. Maxwell's governing equation is solved analytically for each region, where the magnetic flux density (MFD) is generated. From the generated MFD, x and y components are calculated, which are then used to find the useful force along the x-axis.

FEA validates the developed SDM via JMAG v. 20.1. The results obtained show excellent agreement with an accuracy of 95.13%.

The proposed LHEFSM is developed for long stroke applications like electric trains.

The proposed LHEFSM uses low-cost ferrite magnets with DC excitation, which offers better flux regulation capability with improved electromagnetic performance. Moreover, the developed SDM reduces drive storage and computational time by modeling different parts of the machine.

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.

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.

The purpose of this paper is to develop an algorithm and software for determining the size of a line-start permanent magnet synchronous motor (LSPMSMs) based on its optimization.

The software consists of an optimization procedure that cooperates with a FEM model to provide the desired behavior of the motor under consideration. The proposed improved version of the genetic algorithm has modifications enabling efficient optimization of LSPMSMs. The objective function consists of three important functional parameters describing the designed machine. The 2-D field-circuit mathematical model of the dynamics operation of the LSPMSMs consists of transient electromagnetic field equations, equations describing electric windings and mechanical motion equations. The model has been developed in the ANSYS Maxwell environment.

In this proposed approach, the set of design variables contains the variables describing the stator and rotor structure. The improved procedure of the optimization algorithm makes it possible to find an optimal motor structure with correct synchronization properties. The proposed modifications make the optimization procedure faster and more

This proposed approach can be successfully applied to solve the design problems of LSPMSMs.