Permanent Magnet Linear Synchronous Machine Research Articles

Detent Force Reduction in Tubular Permanent Magnet Linear Synchronous Machine Using Particle Swarm Optimization

Compared to rotary machines, tubular permanent magnet linear synchronous machine (TPMLSM) has many advantages, such as simple construction and excellent dynamic performance. In the current paper, an enhanced particle swarm optimization (PSO) algorithm is utilized to minimize the detent force of TPMLSM. The proposed optimization method can automatically determine the number of particles to reduce the number of particles and promote computational efficiency. Specifically, maintaining the number of particles in the exploration phase and alleviating the number of particles in the exploitation stage, and the stage in exploitation or exploration, are determined by the difference between the gbest’s present and past cost values. The algorithm’s efficiency is evaluated on the six-hump camel back, Goldstein-Price, and 3-D Hartman functions. Then, the TPMLSM is optimized using the improved PSO algorithm, aiming at minimizing the detent force. The calculation results indicate that the value of detent force is reduced 56.3 and 64.8% for positive maximum and negative maximum value, respectively. Finally, a prototype was manufactured according to the optimized dimensions and structure, and an experimental platform was constructed to verify the TPMLSM’s electromagnetic performance. The experimental test verifies the feasibility and design validity of the optimization algorithm.

Improvement on Thrust Control for Start-Up and Piston Motion of Free-Piston Linear Generator

Free-piston linear generators (FPLGs) without a crank mechanism are promising to be used in hybrid vehicles due to their unique operation characteristics. However, the FPLG currently still faces challenges in the start-up and piston control. In this paper, the start-up and operation process of FPLG are analyzed deeply and the improved thrust control strategies for the linear electric machine (LEM) are presented accordingly. First, the mechanism that the vibration center shifts under the general constant thrust resonance starting method is revealed, considering the asymmetric potential energy caused by non-linear compression spring effect in the combustion chamber. Then, a compensation thrust iteratively adjusted by the vibration offset is added to stabilize the swing center during start-up. Next, the coupling effect between the dead centers under single-stroke independent thrust control method is analyzed, by modeling the piston motion from the aspect of energy flow. Accordingly, an improved thrust control method for coupling suppression is presented to enhance the accuracy and robustness of piston motion. Finally, the performance of the proposed method is verified by controlling a permanent- magnet linear synchronous machine (PMLSM) in experiments and simulations.

Minimizing detent force of permanent magnet linear synchronous machines by designing mover using mesh-level stochastic shaping

Detent force is an inherent problem of permanent magnet linear synchronous machines (PMLSMs). In this paper, a mesh-level design methodology is proposed to minimize the detent force on PMLSMs. The novelty concerns introducing the inverse-based design to shape the mover ends on PMLSMs, allowing for automatically exploring the ideal mover ends configuration without any pre-given template. To this end, the ON/OFF method is used to express the topology of mover ends, metaheuristics algorithms are used to steer the topological evolution. To clarify the proposed method, two typical PMLSMs are adopted as numerical examples. The resulting mover ends produced by the genetic algorithm and immune algorithm are presented, and the convergence of the two algorithms is discussed. The comprehensive numerical results show that the proposed method is universal and practical as the detent force of the two typical PMLSMs can be suppressed to a low level.

Developments of Prototype Automatic Transportation Lines with a Direct Electric Drive

The increasingly demanding requirements for the production capacity, accuracy and repeatability of industrial production require the development of fully automated transportation lines in which a workpiece is mounted once and passes all stages of the technological process. To solve these problems, the leading manufacturers of machinery construction equipment offer, instead of conveying systems with belt or roller drive, modular automatic transportation lines based on direct drives with permanent-magnet linear synchronous machines. A specific feature of using a linear machine in a transportation line is an inverted mutual layout of the primary part (the armature) and the secondary part (the magnetic way) in which the magnetic way segment moves over a number of modules distributed along the line with a set of armatures and sensors controlled by individual servo amplifiers interconnected by a digital bus. With such solution, a workpiece is attached to the passive moving part that does not require the connection of electrical cables – to ensure its free and independent movement within the entire production line. The modularity of the design provides flexibility of the transportation systems. The article gives a review of solutions offered by various manufacturers, shows the specific features of using linear synchronous machines and sensors in such systems, and proposes the authors’ own developments of prototype transportation lines.

Optimal force control of a permanent magnet linear synchronous motor with multiple shuttles

Using permanent magnet linear synchronous machines for transportation tasks offers a higher flexibility in production plants compared to conventional conveyor solutions. In this context, passive transportation devices (shuttles) with permanent magnets are commonly used. When multiple shuttles are operated in close vicinity, disturbances due to magnetic interaction can occur. To allow for high-speed operation of the motor with high position control accuracy, these coupling effects must be considered. This paper presents a model-based control strategy that is based on a magnetic equivalent circuit model which is able to describe the nonlinear magnetic behavior at low computational costs. A framework is derived for the model calibration based on measurements. An optimal control scheme for the multi-shuttle operation is derived that allows to accurately track the desired tractive forces of the shuttles while minimizing the ohmic losses at the same time. The control concept is experimentally validated on a test bench and compared to a state-of-the-art field-oriented control concept typically used in industry.

A Simple Modified Deadbeat Direct Thrust Control for Permanent Magnet Linear Synchronous Machine Considering Parameter Asymmetry

Permanent magnet linear synchronous machine (PMLSM) has the inherent drawbacks of end effect which would cause phase winding asymmetry, viz., electromagnetic parameter asymmetry (EMPA). In order to achieve fast and precise thrust response, traditional deadbeat direct thrust control (DB-DTC) is suitable for PMLSM, however it cannot be directly applied to PMLSM since it is constructed based on symmetrical machine mathematical model. Moreover, if EMPA is considered in traditional DB-DTC strategy, it is hard to calculate the required change of load angle since the primary flux linkage should be kept constant, especially when the salient-pole effect exists. Based on this, this paper proposed a simple modified DB-DTC strategy for a salient-pole PMLSM considering EMPA. Firstly, the mathematical model with and without considering asymmetrical inductance are derived. Then the influence of EMPA on traditional deadbeat direct thrust control (DB-DTC) is fully investigated. In order to compensate the effect of EMPA, this paper proposes a simple modified DB-DTC by compensating the error in both prediction and deadbeat control processes. Finally, the prototype experiments are carried out to validate the proposed control strategy. The results show that the phase current unbalance that caused by EMPA is largely suppressed controlled with the proposed control strategy. Moreover, both good steady and transient performances can be obtained compared with traditional DB-DTC strategy. The effectiveness of the proposed control strategy is validated.

A Comprehensive Review on the End Effects of Linear Permanent Magnet Machines

This article presents a literature review of relevant contributions found in the literature concerning the end effects with a focus mainly on linear permanent magnet synchronous machines. Additionally, it presents a classification of the obtained information to classify the end effects and provides essential information for understanding, categorization, modeling, mitigation, and control of the end effects. The causes and consequences of the end effects are also addressed according to the geometrical structure of the linear machine, and the main approaches for end effects modeling are discussed. Also, several existing techniques for mitigation of consequences of end effects are presented, considering changes in the machine geometry or the electromagnetic structure and electronic compensation using control techniques. The control of linear machines accounting for end effects and compensation to achieve better performance to mitigate adverse impacts on machine characteristics are also addressed.

Multi-objective optimization design of permanent magnet linear synchronous machine based on stratified strategy

This paper proposes a multi-objective stratified optimization (MOSO) design for a permanent magnet linear synchronous machine (PMLSM) to obtain higher thrust and suppress the thrust ripple. MOSO can combine the advantages of different optimization methods and have fast and efficient optimization characteristics. Based on the parametric analysis of the influence of the auxiliary tooth size and the end-tooth width on the thrust performance, the sensitive variables are quickly filtered by using the Taguchi method. The response surface model (RSM) is built by adopting the central composite design (CCD) based on the sensitive variables. Moreover, the stratified optimization design of the PMLSM is completed by combining with the multi-objective particle swarm optimization (MOPSO) to achieve a balance between local and global search. Finally, a prototype is manufactured, and experiments are implemented to verify the proposed method.

Optimal performance identification of a combined free piston Stirling engine with a permanent magnet linear synchronous machine using dedicated controls

• A Linear Synchronous Machine combined with a Free Piston Stirling Engine. • For the combined system, two different control methods were developed. • Based on the control methods, the performance of the combined system was optimized. • The performance and application of the two control methods were compared. In the present study, to find the optimal performance of a combined RE-1000 Free Piston Stirling Engine (FPSE) with a three-phase Permanent Magnet Linear Synchronous Machine (PMLSM), two different control methods were developed. To convert the produced mechanical power of the FPSE to the electrical one, generally, it should be coupled with a linear generator. Here, a three-phase PMLSM was chosen to convert the linear movement of the FPSE to electricity. The control of the FPSE system was also done through this generator using velocity control. It is possible to obtain the optimal system behavior based on the identification of the adapted velocity reference value. Based on two different methods, the FPSE-PMLSM optimum working point was determined. In the first method, an open-loop sinusoidal wave was assumed as the reference velocity, and its amplitude and frequency were optimized. In the second method, the reference velocity was identified using closed-loop feedback of the electromagnetic force, and the optimal feedback coefficient was found. The results show that apart from the advantages and disadvantages related to each method, the optimized point was almost identical.

An Accurate No-Load Analytical Model of Flat Linear Permanent Magnet Synchronous Machine Accounting for End Effects

This article proposes an improved analytical model of slotted linear permanent magnet synchronous machines (LPMSMs) to fast and accurately obtain the magnetic field distribution and detent force. Considering the secondary end effect can optimize the thrust performance in terms of machine control, while there are few research works focusing on this study. Combined with the periodic extension method, both the primary and secondary end effects are taken into consideration, which is the major contribution of this article. The analytical model containing seven subdomains (SDs) is conducted in Cartesian coordinates. The magnetic distributions in air-gap, slots, and end regions are obtained by solving Maxwell equations with various interface conditions. The thrust and normal forces are subsequently calculated based on the Maxwell stress tensor. The corresponding finite element (FE) model produces numerical results to validate the analytical results. A prototype is manufactured and tested. The experimental results show that the improved analytical model is accurate and efficient in no-load performance calculation. The investigation shows that this proposed method can be applied to all of the LPMSMs with similar structures.

A Phase-Domain Model of Dual Three-Phase Segmented Powered Linear PMSM for Hardware-Assisted Real-Time Simulation

In this article, a hardware-assisted real-time simulation phase-domain (PD) model of a dual three-phase segmented powered linear permanent magnet synchronous machine (SP-LPMSM) used in electromagnetic drive is established. The model is able to consider the end-effect, saturation effect, coupling effect, and open-phase fault conditions, which are specially occurs in the segmented structure in SP-LPMSM. The unbalanced inductances and saturation effect caused by the segmented structure are investigated and a simplified look-up table for inductances is introduced. Additionally, to accurately evaluate the coupling effect, the permanent magnet (PM) flux linkage is decoupled into the product of unit PM flux linkage and coupling coefficient. In order to avoid the numerical impulse caused by the derivative in the progress of calculating back-EMF, sigmoid function is adopted to express the coupling coefficient. Meanwhile, to make the PD-model compatible with the open-circuit fault conditions, incidence matrices and current constraint matrices are introduced to unify the PD-models with different winding connection types and open circuit faults into one general form. The PD-model realized in field-programmable gate arrays (FPGA) based hardware is validated in comparison with finite-element analysis results.

Non-linear and multi-domain modelling of a permanent magnet linear synchronous machine for free piston engine generators

• The motivations for continued FPE and LEM development are established. • A non-linear and multi-domain model of the PMLSM is presented. • Incorporation of the PMLSM in an FPEG multi-domain model is demonstrated. • Model validation with data captured from an experimental FPEG is conducted. • Simulation results indicate the model captures the dominant dynamics of the PMLSM. The Free Piston Engine (FPE) can be considered a viable and promising option in future low-carbon technology development. When coupled to the Linear Electric Machine (LEM) to produce electrical energy, its characteristic non-linear dynamics typically have been described as linear when considering a systems-level modelling approach. This paper presents a multi-domain model of a Permanent Magnet Linear Synchronous Machine (PMLSM) for Free Piston Engine Generators (FPEG) and offers a detailed non-linear mathematical description of the machine dynamics. The model was implemented in a free-piston expander system and validated against experimental data from a test rig that has identical parameters. The simulation results indicate a strong correlation to the experimental data, which captured the dominant dynamics of the PMLSM and prove the satisfactory accuracy and performance of the model, together with a similar voltage and current output trace, indicating a cyclic energy output error of approximately 10 %. This paper aims to extend the current knowledge and literature within FPEG PMLSM design by considering the inherent non-linearity and multi-directional nature of the system dynamics and its interactions with multi-physical domains.

An Improved and Efficient Analytical Model for Magnetic Field Calculation in Linear Permanent Magnet Machines

A simple and improved analytical model (AM) for linear permanent magnet synchronous machine (LPMSM) based on the correction factor is presented in this paper. A slotless linear permanent magnet machine (PLPM) with AM developed in Cartesian coordinate is selected to investigate. Consequently, the fitting equations of curvature factors for the permanent magnet and armature are obtained. The subdomains for LPMSM are simplified from 6 down to 3 domains based on curvature equations. The magnetic flux density and force show that the proposed approach agrees with the finite element (FE) model. Moreover, the reduced calculation domains and harmonic orders make AM proposed in the paper much faster. The main contribution of the work is to present a simple strategy for coordinate transformation and calculation strategy for LPMSM, which provides guideline for designers to investigate the machines developed in Cartesian coordinate.

Detent Force Minimization of Double-Sided Permanent Magnet Linear Synchronous Machine with 120° Phase Belt Toroidal Windings by Slot-Shift Structure

Double-sided permanent magnet linear synchronous machine with 120° phase belt toroidal windings (120°-TWDSPMLSM) suffers from large detent force due to the end effect and slot effect. Many existing methods can reduce the detent force of the 120°-TWDSPMLSM effectively. But they also minimize the back electromotive force (back-EMF) and thrust simultaneously. To alleviate this problem, this paper adopts a method of combining slot-shift structure with rearranging the 120° phase belt toroidal windings (120°-TW) to suppress the detent force and improve the back-EMF and thrust of the 120°-TWDSPMLSM simultaneously. First, the slots on the two sides of the primary part are stagger by an optimal distance to reduce the detent force. The models of the detent force, including the end force and cogging force, is established theoretically, and then verified by finite-element analysis (FA). Then, the 120°-TW are rearranged to improve the back-EMF and average thrust. And the electromagnetic characteristics of the 120°-TWDSPMLSM under different shifted distances are analyzed and compared in detail. Finally, the result shows that the detent force of optimized machine is 70.19% lower than that of the original machine, and the thrust fluctuation reduces 19.21%. Besides, the back-EMF of optimized machine is 6.84% lower than that of the original machine, but 31.86 higher than the machine with shifting slots and without rearranging the 120°-TW. Therefore, the optimal method in this paper is available in the detent force reduction and thrust improvement of the 120°-DSPMLSM.

Thermodynamic modeling and controlling of a combined Free Piston Stirling Engine System (FPSE) with a Permanent Magnet Linear Synchronous Machine (PMLSM)

Converting thermal energy to electricity is one of the most common energy conversions in the field of electricity production. This transformation of energy is essential for both renewable and non-renewable heat sources. One of the main parameters of such a system that is responsible for this conversion is its efficiency. To have an efficient transformation, many improvements have been made to the old methods, and also new techniques were developed. One of these new methods that will be discussed here is a combined system of a Free Piston Stirling Engine (FPSE) with a Permanent Magnet Linear Synchronous Machine (PMLSM). The two purposes of presenting such a system are that firstly, the theoretical efficiency of a Stirling engine is high. Secondly, by eliminating crank-shaft from this system compared to the standard Stirling engine system, some of the losses will be removed. To study this system, a thermodynamic model of a RE-1000 FPSE was presented and validated. Then it was coupled with a PMLSM, and the combined system was controlled. The total efficiency of this system in steady-state is 14.4%.

Modeling and analysis of a multi-segmented linear permanent-magnet synchronous machine using a parametric magnetic equivalent circuit

Modeling and analysis of a multi-segmented linear permanent-magnet synchronous machine using a parametric magnetic equivalent circuit

Transient Analysis of Line-Start Permanent Magnet Linear Synchronous Motors

This paper focuses on the transient modelling of a specific type of permanent magnet linear synchronous machine designed for line-start operation. The machine uses conductive ladders embedded in the mover to realise a permanent-magnet machine capable of line-start operation. Transient modelling of this type of machine under line-start conditions is critical to optimising machine design, and electrical and mechanical performance prediction, which leads us to devise a novel set of matrices of electrical parameters first. These matrices are developed considering both the impact of the conductive ladders and the longitudinal end effect based on electromagnetic field analysis. The model is then suitable for numerical computation in typical simulation environments. This yields a sufficiently accurate transient model that is verified by experimental results. Hence our novel model, that includes the longitudinal end effects and the effects of conductive ladders, is proven effective in predicting the line-start transients and associated electrical and mechanical performance. The novel model assists in the design optimisation stage where a compromise between synchronised performance and line-start operation is required. The novel machine type can then be investigated as a competitive candidate topology in various applications including electromagnetic launch.

Free Piston Stirling Engine as a new heat recovery option for an Internal Reforming Solid Oxide Fuel Cell

Energy demand increment besides the reduction of fossil fuel resources from one side, and climate issues concerning the conventional power production methods from another side lead humanity to more efficient and cleaner power production methods. One of these methods is polygeneration microgrids based on a renewable energy source. In the present study, a combined cycle of a Free Piston Stirling Engine with a Permanent Magnet Linear Synchronous Machine was proposed as a new heat recovery option for the high-quality thermal energy of an Internal Reforming Solid Oxide Fuel Cell as electricity. Then, a Double Effect Absorption Chiller and a heat exchanger were used to recover the rest of the heat as cooling and hot water, respectively. After modeling and validating all the systems, they were combined. The results of the combined system showed 31.7% (or 40% by including cooling production of Double Effect Absorption Chiller instead of its heat consumption for efficiency calculation) of total efficiency improvement compared to the standalone Internal Reforming Solid Oxide Fuel Cell. Furthermore, the electrical efficiency of the system was improved by 14.1%.

Fault-Tolerance Performance Analysis of a Five-Phase Permanent-Magnet Linear Synchronous Machine

A fault-tolerance control strategy based on the constant magnetomotive force (MMF) is proposed for a five-phase permanent-magnet linear synchronous machine (FP-PMLSM) under one-phase fault condition in this article, which aims to keep steady operation during a short time. First, the mathematical model of FP-PMLSM having one-phase open-circuit fault is analyzed. Based on the analysis, the fault-tolerance strategy is derived under the constraint of constant copper loss. This strategy makes the fault-tolerance currents become unbalanced seriously and the maximum thrust force reduced. Then, the proposed method is introduced and the corresponding fault-tolerance currents are calculated. The fault-tolerance currents of both strategies are optimized in order to reduce the second harmonic component of the thrust force ripple. Finally, the investigation of the electromagnetic performance is carried out in detail. By comparison with the constant copper loss strategy, the proposed strategy is proved to output a steadier thrust force.

Force Ripple Compensation and Robust Predictive Current Control of PMLSM Using Augmented Generalized Proportional–Integral Observer

In this article, an augmented generalized proportional–integral observer (GPIO) is presented to estimate and then compensate for the disturbance/uncertainty both existing in the electrical and mechanical subsystems of the motion stage driven with an air-bearing permanent-magnet linear synchronous machine (PMLSM). First, a modeling method for the two subsystems, considering the disturbance/uncertainty and the integration of the measured outputs as extended states, is proposed. Second, to reduce the coupling effect of the observer gains and the measurement noises on the disturbance estimation dynamics, an augmented GPIO is designed and its convergence theorem is given. Furthermore, with the extended models, the augmented GPIO is developed for both the compensation of parameter mismatch in the predictive current control (PCC) and the force ripple estimation/suppression of the PMLSM. Finally, with the augmented GPIO, an improved PCC robustness test with time-varying parameter mismatch is conducted both in the single-current closed loop and the double-current closed loop with cascade position-current control. A simple and practical parameter-tuning procedure is also analyzed in detail for both the electrical and mechanical subsystems. The position trajectory tracking error is reduced largely with accurate and real-time force ripple compensation. Experimental setup and results are provided to validate the effectiveness of the proposed design method.