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The purpose of this paper is to solve the common problems that traditional optimization methods cannot fully improve the performance of electromagnetic linear actuators (EMLAs).

In this paper, a multidisciplinary optimization (MDO) method based on the non-dominated sorting genetic algorithm-II (NSGA-II) algorithm was proposed. An electromagnetic-mechanical coupled actuator analysis model of EMLAs was established, and the coupling relationship between static/dynamic performance of the actuator was analyzed. Suitable optimization variables were designed based on fuzzy grayscale theory to address the incompleteness of the actuator data and the uncertainty of the coupling relationship. A multiobjective genetic algorithm was used to obtain the optimal solution set of Pareto with the maximum electromagnetic force, electromagnetic force fluctuation rate, time constant and efficiency as the optimization objectives, the final optimization results were then obtained through a multicriteria decision-making method.

The experimental results show that the maximum electromagnetic force, electromagnetic force fluctuation rate, time constants and efficiency are improved by 18.1%, 38.5%, 8.5% and 12%, respectively. Compared with single-discipline optimization, the effectiveness of the multidiscipline optimization method was verified.

This paper proposes a MDO method for EMLAs that takes into account static/dynamic performance, the proposed method is also applicable to the design and analysis of various electromagnetic actuators.

The purpose of this paper is to present an algorithm of the optimization of the dynamic parameters of an electromagnetic linear actuator operating in error‐actuated control system.

The elaborated “unaided” software consists of two main parts: optimization solver and numerical model of the actuator. Genetic algorithm has been used for optimization. The coupled field‐circuit‐mechanical model for the simulation of the system dynamics has been applied. Different optimization problems have been considered. The shape of the steady‐state force‐displacement actuator characteristic has been imposed and its deviation has been minimised. Next, the total operation time of the actuator without feedback, and the setup time of the actuator with feedback are minimised. Finally, required trajectory of movement has been imposed and trajectory error is minimised.

The elaborated algorithm and the computer code can be an effective tool for field‐circuit simulation of the dynamics of an electromagnetic linear actuator that operates in an automatic control system. It enables optimal design of the electromechanical system in respect to its dynamic properties.

The elaborated algorithm and the computer code presented in this paper can be an effective tool for the field‐circuit simulation of the dynamics of an electromagnetic linear actuator that operates in an automation control system.

The aim of this study is to investigate the implementation of the sliding-line technique (SLT) in a generic two-dimensional (2D) nonlinear adaptive magnetic equivalent circuit (MEC) model predicting the electromagnetic force evolution of a linear bistable electromagnetic actuator technology.

The developed MEC model considers the saturation effect and the auto-adjustability of the spatial discretisation. The connection between static and mobile zones is ensured by an approach known as “air-gap sliding-line technique”, which is widely used for rotary electric motor models. To the best of the author’s knowledge, that is the first time that the SLT is implemented on an electromagnetic structure with linear motion.

It was found that, in case of a linear actuator with a relatively small working stroke, the implementation of the SLT could lead to some non-negligible inaccuracies.

To solve the above-mentioned problem, it was proposed to investigate the implementation of a single SLT vs double SLT. The results of the MEC models were compared with the 2D finite-element analysis (FEA) as well as with the experimental test results. The developed semi-analytical models can be easily adapted to other topologies of linear electromagnetic machines.

The paper seeks to present an algorithm for a dynamical field‐circuit coupled simulation of an electromagnetic linear actuator operating in automated control systems.

The mathematical model includes: a transient electromagnetic field formulation for a non‐linear conducting and moving medium, equations which describe the electric circuits of the converter and the supply system, the equation of mechanical motion, the equation describing closed‐loop control and models for the sensor and the PID controller. The numerical implementation is based on the finite element method and the step‐by‐step algorithm for time discretization. In order to account for the nonlinearity of the ferromagnetic core the Newton‐Raphson procedure has been applied. The influence of the PID controller settings on the operation of the controlled actuator is shown. Dynamic disturbances, e.g. step change of the set value of mover position or change of loading force, have been analyzed.

The elaborated algorithm and the computer code can be an effective tool for field‐circuit simulation of the dynamics of an electromagnetic linear actuator operating in an automatic control system. Only tapered plunger should be used as multi‐stable actuators.

The study provides information of value in electromagnetic research.

This paper aims to provide an overview of the recent developments and new topologies of single-phase moving magnet linear oscillating actuators (MMLOAs). The key advantage of the MMLOA when compared with conventional LOA is the absence of screws, gears and crankshaft mechanism, which results in fewer mechanical parts, simple structure, easy fabrication, lower noise levels and negligible frictional losses.

The review included papers up to August 2021. The structural designs of alternative topologies are deliberated in detail, and their relative merits and demerits are evaluated. Specific design issues, including pole and tooth number combinations, stroke length, magnet pole ratio and split ratio, are investigated. The imperative phenomena of the resonance, as well as the adjustable stroke, are also discussed in detail.

The electromagnetic performance in terms of thrust force of selected MMLOA topologies is compared. It is observed that the MMLOA with flux bridge topology has the highest thrust force of 365 N because of the large volume of the permanent magnets (PMs) used, which consequently increased the mass of the mover but based on overall performance analysis, single-phase end ferromagnetic Halbach surface-mounted PM LOA has the highest efficiency around 92%.

This review provides a comparative analysis for different tubular MMLOA topologies based on design construction and their electromagnetic performances.

The purpose of this paper is to describe the optimization of a permanent magnet linear actuator with soft magnetic mover for electromagnetic valve. The optimization is carried out with respect to the minimal magnetomotive force ensuring required minimum electromagnetic force on the mover.

Three optimization factors are employed. The value of the electromagnetic force and the objective function – the magnetomotive force – are obtained by caring out a full factorial design of experiment. For obtaining the objective function for each parameter combination, nonlinear equation is solved in order to minimize the flux that creates force in backward direction. Thus, several finite element analyses are carried out for each parameter combination. Then, response surface model is created and optimized. The obtained optimal solution is verified again by finite element analysis.

The paper finds that optimal actuator has been obtained and its force‐stroke characteristics and temperature distribution at steady‐state mode are given.

The valve is optimized by defining optimization function to be the solution of an equation canceling the flux in the nonactive part of the valve.

An algorithm for simultaneous solution of equations describing transient 3D magnetic field coupled to the Kirchhoff’s equations and the equation of motion has been presented. The nonlinearity and anisotropy of the magnetic core have been taken into account. Numerical implementation of the algorithm is based on the finite element method. In order to solve the 3D problem a special iterative procedure, in which the 3D task is substituted with a sequence of 2D problems, has been proposed. The time‐stepping backward difference algorithm for the time‐discretization of the electric circuit equations has been applied. To determine the moving armature position, an implicit procedure, which is unconditionally stable has been proposed. For the sake of example, the calculations of dynamic operation of the E‐type electromagnetic actuator equipped with the shading coil have been performed.

The purpose of this paper is to elaborate the effective method of adaptation of the external penalty function to the genetic algorithm.

In the case of solving the optimization tasks with constraints using the external penalty function, the penalty term has a larger value than the primary objective function. The sigmoidal transformation is introduced to solve this problem. A new method of determining the value of the penalty coefficient in subsequent iterations associated with the changing penalty has been proposed. The proposed approach has been applied to the optimization of an electromagnetic linear actuator, and the mathematical model of the devices contains equations of the magnetic field, by taking into account the nonlinearity of ferromagnetic material.

The proposed new approach of the penalty function method consists in the reduction of the external penalty function in successive penalty iterations instead of its increase as it is in the classical method. In addition, the method of normalization of constraints during the formulation of optimization problem has a significant impact on the obtained results of optimization calculations.

The proposed approach can be applied to solve constrained optimization tasks in designing of electromagnetic devices.

Semi-active suspension systems with electromagnetic dampers allow energy regeneration and the required control strategies are easier to implement than the active suspensions are. This paper aims to address the application of a tubular linear permanent magnet synchronous machine for a semi-active suspension system.

Classical rules of mechanics and electromagnetics were applied to describe a dynamic model combining vibration and electrical machines theories. A multifaceted MATLAB®/Simulink model was implemented to incorporate equations and simulate global performance. Experimental tests on an actual prototype were carried out to investigate displacement transmissibility of the passive case. In addition, simulation results were shown for the dissipative semi-active case.

The application of the developed model suggests convergent results. For the passive case, numerical and experimental outcomes validate the parameters and confirm system function and proposed methodology. MATLAB®/Simulink results for the semi-active case are consistent, showing an improvement on the displacement transmissibility. These agree with the initial conceptual thoughts.

The use of linear electromagnetic devices in suspension systems is not a novel idea. However, most published papers on this subject outline active solutions, neglect semi-active ones and focus on experimental studies. However, here a dynamic mechanical-electromagnetic coupled model for a semi-active suspension system is reported. This is in conjunction with a linear electromagnetic damper.

Linear oscillatory actuators have been used in a wide range of applications because they have a lot of advantages. Additionally, multi-degree of freedom resonant actuators have been developed. The purpose of this paper is to propose a novel three-degree-of-freedom resonant actuator resonant actuator that is driven in three directions. The dynamic characteristics are clarified through finite element analysis and measurement.

A novel three-degree-of-freedom resonant actuator resonant actuator consists of a cross-shaped mover, a stator and five excitation coils. The magnetic structure of this actuator is geometrically similar to that of general permanent magnet synchronous motor. Therefore, vector control is applied to this actuator. The dynamic characteristics are analyzed and measured.

Computed results show that the proposed actuator is able to be independently driven in three directions. However, measured result show that mutual interference is severely observed because of the structure of the mover support mechanism. Therefore, the structure needs to be improved.

The proposed actuator has originality in its structure and operating principle.