Permanent Magnet Linear Motor Research Articles

Design and analysis of ELM-based predefined time sliding mode adaptive controller for PMLM position control under physical constraints

Achieving accurate position tracking for robotics and industrial servo systems is an extremely challenging task, particularly when dealing with control saturation, parameter perturbation, and external disturbance. To address these challenges, a predefined time convergent sliding mode adaptive controller (PTCSMAC) has been proposed for a permanent magnet linear motor (PMLM). A novel sliding mode surface (SMS) with predefined time convergence PDTC has been constructed, which ensures that the error converges to zero within the prescribed time. The system not only meets the expected performance standards but also has a uniformly bounded motor speed. The trajectory tracking error in SMS is proven to converge to zero within the predefined time. This predefined time stability of the closed-loop system has been demonstrated by using the Lyapunov stability criterion with PDTC. The convergence time (CT) can be arbitrarily set, and the upper bound of it is not affected by the initial value and control parameters of the system. A new updated version of extreme learning machine (ELM) is introduced to approximate the uncertain part of the system based on PDTC. The ELM is also provided with the hyperbolic tangent function to estimate the saturation constraint. This is done by converting the function into a linear function concerning the unconstrained control input variable. Then, based on established stability, a novel sliding mode adaptive controller (PTCSMAC) with predefined time convergence is designed. The convergence time (CT) of the controller is unaffected by the initial conditions as well as the control parameters. The rigorous numerical simulations on the PMLM model with complex disturbances verify the strong robustness and high-precision tracking characteristic of the proposed control law.

Data-Driven Indirect Iterative Learning Control.

In this work, a data-driven indirect iterative learning control (DD-iILC) is presented for a repetitive nonlinear system by taking a proportional-integral-derivative (PID) feedback control in the inner loop. A linear parametric iterative tuning algorithm for the set-point is developed from an ideal nonlinear learning function that exists in theory by utilizing an iterative dynamic linearization (IDL) technique. Then, an adaptive iterative updating strategy of the parameter in the linear parametric set-point iterative tuning law is presented by optimizing an objective function for the controlled system. Since the system considered is nonlinear and nonaffine with no available model information, the IDL technique is also used along with a strategy similar to the parameter adaptive iterative learning law. Finally, the entire DD-iILC scheme is completed by incorporating the local PID controller. The convergence is proved by applying contraction mapping and mathematical induction. The theoretical results are verified by simulations on a numerical example and a permanent magnet linear motor example.

A General Control Method for Half-Centralized Open Winding Permanent-Magnet Motor Drive System

In this paper, a general control method based on duty ratio selection for half-centralized open winding primary permanent-magnet linear motor (HCOW-PPMLM) drive system is proposed. The proposed control method is designed from the perspective of single-phase subsystem. The novelty of this paper is the voltage process and modulation, which can realize the expansion from two movers to multi movers. The design of voltage process and modulation contains voltage preprocessor, saturation limiter and duty ratio distributor. In the voltage preprocessor, phase voltages are transferred to phase modulation index. The saturation limiter deals with excessive phase modulation indexes based on the independent over-modulation principle. The duty ratio distributor distributes the voltage demand into inverters by the common-leg-based distribution principle. Compared to existing method, the proposed control method can realize the expansion from two movers to multi movers and has less computation burden. In addition, more mover quantities will not increase the complexity of analysis and design. Finally, the effectiveness of the proposed control method has been verified by experimental results.

Simplified Phase Model Predictive Voltage Control for Half-Centralized Open-End Winding Permanent-Magnet Motor Systems

In order to obtain a wider speed range for the permanent-magnet linear motor drive system, a half-centralized open-end winding (OEW) topology is studied. In this topology, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> movers are supplied by <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> +1 voltage-source-inverters (VSIs), and all these VSIs share a common dc bus voltage. In order to reduce the computation burden, a simplified phase model predictive voltage control (S-PMPVC) is proposed in this paper. For S-PMPVC, the optimal and suboptimal base levels are defined. When the optimal base level cannot be implemented, the suboptimal base level is selected. As a result, S-PMPVC requires smaller computation burden while the performances are not degraded. By taking the advantage of the smaller computation burden, S-PMPVC can adopt higher control frequency to improve performances. The effectiveness of S-PMPVC has been verified by simulation and experimental results.

Robust control and experimental validation of trajectory tracking for permanent magnet linear motors based on constraint-following under uncertainty

AbstractThis paper proposes a robust control approach to achieve high-precision trajectory tracking for permanent magnet linear motor (PMLM) system containing uncertainties by describing the dynamic model of PMLM based on the Udwadia-Kalaba equation combined with constraint-following method. First, the system of PMLM is described as a constraint-following system by adding the generalized constraint force to the unconstrained Udwadia-Kalaba equation of PMLM system. Second, the robust constraint-following controller is designed based on the proposed model after uncertainty analysis. Moreover, the proposed controller is verified to guarantee deterministic performance for uncertain systems: uniformly bounded and uniformly ultimately bounded. Third, the numerical simulation and experimental validation demonstrate the effectiveness of proposed controller. Finally, the design approach of constraint-following can be applied to other systems with uncertainties.

Design and utilization of thrust fluctuation of slotted-tubular permanent magnet linear motor: Mechatronics for low-frequency vibration forming machine

Usually, the conventional low-frequency vibration forming machine has a main transmission mechanism as the driving source to provide forming force and an auxiliary mechanism as the vibration source to generate vibration force. The transmission chain is long and the structure is complex and bloated, which affects the forming process and product quality. This paper presents a novel mechatronics idea of low-frequency vibration forming machine, which uses a slotted tubular permanent magnet synchronous linear motor (slotted-TPMLM) as both the driving source and the vibration source. The key is that the slotted-TPMLM provides sufficient forming force accompanied with a certain low-frequency vibration force. Consequently, this paper focuses on the thrust fluctuation caused by the structure. Firstly, the effect of end force and the influence of cogging force are discussed in detail through Fourier analyses, especially the stator adjustment length and pole-slot combination. Then, the slotted-TPMLM is designed, manufactured, and tested. The results show that the slotted-TPMLM can provide a certain low-frequency vibration force (low frequency of 4.8 Hz at 100 mm/s and 48 Hz at 1000 mm/s), which meets the technical requirements. Consequently, the feasibility of the novel mechatronics idea of a low-frequency vibration forming machine has been verified. This research will contribute to the field of linear motors and metal forming machines.

Hybrid Analytical Model of Permanent Magnet Linear Motor Considering Iron Saturation and End Effect

Hybrid Analytical Model of Permanent Magnet Linear Motor Considering Iron Saturation and End Effect

Double-Sided Single-Set Winding Coordinated Active Levitation Control of Linear Permanent Magnet Motor Considering Mover Air-Gap Offset

Double-Sided Single-Set Winding Coordinated Active Levitation Control of Linear Permanent Magnet Motor Considering Mover Air-Gap Offset

Electromagnetic Vibration Analysis of Transverse Flux Permanent Magnet Linear Submersible Motor for Oil Production

A transverse flux linear motor is a special type of linear motor with a high thrust force density, and it has broad application prospects in the field of linear direct-drive systems. In the process of oil production, the vibration of the linear motor poses a significant amount of harm to the system due to its special slender structure. This paper focuses on the electromagnetic vibration of a transverse flux permanent magnet linear submersible motor (TFPMLSM). Firstly, the no-load air gap flux density is calculated based on the field modulation principle. Secondly, the radial electromagnetic force (REF) of the TFPMLSM is calculated, and the finite element method (FEM) is used to analyze the time-space and spectral characteristics of the REF. Then, the influence of secondary eccentricity on the frequency spectrum of the REF is further concluded. Finally, the natural frequencies of each vibration mode are calculated using the modal superposition method and the influence of the REF on the motor vibration is obtained through magnetic-structural coupling analysis. The research results found that the motor does not cause resonance at low speeds, and the fundamental frequency of REF has the greatest impact on electromagnetic vibration.

A novel robust bounded control with inequality constraints and experimental validation for permanent magnet linear motor

In order to solve the problem that the trajectory of a permanent magnet linear motor may be out of bounds in practice and eliminate the influence of uncertainty on trajectory tracking, we propose a robust bounded control based on inequality constraints. First, the dynamics model of the permanent magnet linear motor is established, and then, the constrained output state variables are converted into unconstrained state variables by state conversion. Secondly, based on the dynamics model after state transformation, a novel control method containing both nominal and robust terms is proposed. Finally, the stability of the PMLM system is proved by the Lyapunov minimax method. Simulations and experiments with different algorithms are carried out on the PMLM system and the CSPACE platform. Based on the analysis of the experimental results, it can be found that robust bounded control based on inequality constraints can significantly improve the dynamic performance of the PMLM system and achieve high accuracy.

A Novel Fault Tolerance Structure of Arc Linear Flux Switching Permanent Magnet Motors Based on Redundant Winding

This paper presents a novel structure of the arc linear flux switching permanent magnet motor based on the redundant winding to inhibit the rises of the motor losses and temperature due to the open circuit fault tolerance. Firstly, the structural characteristic of the arc linear flux switching permanent magnet motor is introduced. Then, the fault tolerance current of single phase open circuit fault is calculated for different winding connection forms. The fault tolerance performances under different conditions are compared from a special view of motor temperature rises. Finally, a novel structure for fault tolerance enhancement is proposed, which can effectively improve the freedom degree of the fault tolerance current by using the redundant winding. This novel structure takes full advantage of the circumferential air gap between the arc stator. The calculation results show that the novel structure can allow the fault tolerance of open circuit fault has little influence on the motor copper losses and temperature rises while maintaining the on-load torque.

Thrust Fluctuation Optimization of Permanent Magnet Linear Motor Based on Composite Slot Wedge

In order to reduce the thrust fluctuation of the linear motor, combined with its structural characteristics, the method of embedding a magnetic slot wedge is adopted. Based on the design of a common slot wedge structure, the genetic algorithm is used to optimize the slot wedge size, select the best size of the slot wedge structure, and then carry out finite element analysis. The results show that the thrust fluctuation of the single-sided linear motor is reduced by 66.42%, and that of the double-sided linear motor is reduced by 61.23%, which effectively reduces the thrust fluctuation. It has certain practical application value.

High precision control of direct-drive permanent magnet linear motor with adaptive friction compensation

To improve the control precision and stability of Direct-Drive Permanent Magnet Linear Motor (DPMLM) with frictional nonlinearity and uncertain disturbances at a low speed, an adaptive robust integral sign error control algorithm based on friction compensation of dual nonlinear observer is proposed in this study. An improved LuGre friction model is established to describe the friction phenomena of the system. The dual nonlinear observer is designed to observe the internal frictional state of the model. A parameter adaptive law is designed to perform parameter estimation of structured uncertainty. Robust integral of the sign of the error (RISE) term is designed to overcome the frictional nonlinear disturbances. The friction nonlinearity and parameter uncertainty are compensated by feedforward compensation. The bounded stability of the proposed controller is proved by Lyapunov stability theory. As suggested by the experimental results, RMSE index decreased by 10.8% and the control precision was improved effectively by the proposed control algorithm at a low speed.

Performance Investigation and Improvement of Linear Vernier Permanent Magnet Motor for Servo Application

With its high thrust density and low force ripple, the linear vernier permanent magnet motor (LVPMM) is regarded as a good competitor for linear servo applications. However, typical LVPMMs have shortcomings, such as phase imbalance, a long distributed-winding end, and low power factor. The goal of this work is to present a thorough analysis-based approach for performance enhancement that addresses all three flaws while enhancing the LVPMMs high thrust density advantage. Thanks to the proper slot/pole-pair combination, Halbach array PM, and a special three-modular structure, the proposed LVPMM improves thrust density by 28%, reduces force ripple to 1.2%, increases power factor by over 40%, and nearly eliminates three-phase imbalance when compared with those of a conventional LVPMM. Manufacturing and testing a 2.2 kW/2200 N prototype has confirmed the viability of the theoretical analysis and improvement process.

An equivalent winding thermal model considering fill factor and void ratio for multiphysics coupling analysis of permanent magnet linear motors

Accurately clarifying thermal characteristics and acquiring thermal limits of permanent magnet linear motors (PMLMs) is significant for system safety, which is often evaluated by computational thermal analysis. However, conventional thermal analysis methods are faced with the contradiction between the complexity of modeling and the accuracy of computation. To fix the problem, a new two-way multiphysics coupling method is developed by proposing an improved equivalent homogeneous winding thermal model. The energy consumption distribution is used as the heat source for thermal field calculation, and the material properties are determined by temperature in the electromagnetic field. To further reduce the complexity of winding region modeling and ensure the accuracy of calculation, an improved equivalent homogeneous winding thermal model is established by considering the fill factor and void ratio. The new coupling method is verified by temperature rise experiments on a single winding sample and a PMLM prototype. The error between the simulation and experiment of the single winding sample is less than 3 %, which indicates the high accuracy of the improved equivalent model. Meanwhile, the low error (less than 6 %) on the PMLM case indicates the high accuracy of the new multiphysics coupling method. Then, the temperature distribution of PMLM is analyzed, and the effect of the fill factor and void ratio on the temperature rise of PMLM is studied with the effect of the void ratio on the limiting temperature and continuous working time of PMLM discussed. It is demonstrated that both fill factor and void ratio affect the temperature rise of winding, and thus impact the temperature rise of the PMLM. The continuous working time decreases rapidly with the increase of the void ratio, and this effect will be more significant with a higher effective current. The results can provide references for improving the precision of temperature estimation and selecting a reasonable current density. This also demonstrates the high accuracy and efficiency of the new coupling method.

Modeling and Analysis of HTS Linear Motors in High-Dynamic Applications

In this paper, high-temperature superconducting (HTS) linear motors are modeled and analyzed for a high-dynamic application requiring a periodic, to-and-fro motion with substantial acceleration. Two topologies of a coreless double-sided HTS linear motor (HLM) are investigated: moving magnet motor (MMM) – a set of three-phase AC commutated HTS coils in the stator with permanent magnets in the mover, and moving coil motor (MCM) – a set of DC operated HTS coils in the stator with three-phase AC commutated normal coils in the mover. A two-step design process is adopted where transport current losses are used to determine feasible HTS coils to operate between 20 and 60 K, subject to requirements on input power for the cryogenic cooling system. Using the homogenized T-A formulation, a computationally fast 2D finite element method (FEM) model of the motor is developed to compute these losses. Additionally, a semi-analytical tool calculates the force produced by the motor. The MCMs with feasible HTS coils are then optimized to minimum volume. An MMM with the same force density is designed from the optimum MCM. The optimized motors are further analyzed using FEM for losses during high-dynamic motion. Results show that an MCM topology can reduce the motor volume by at least a factor of 10 when compared to conventional permanent magnet linear motors. The MCM delivers the required force in the same volume with significantly lower losses than an MMM.

Electromagnetic force ripple suppression strategy of the micro permanent magnet linear motor

In order to make the micro permanent magnet linear motor in this paper have an excellent position response in MEMS application scenarios, an electromagnetic force ripple suppression strategy based on harmonic current injection is proposed. Because of the simulation phenomenon of large force ripple under standard sinusoidal current driving, combined with the non-sinusoidal distribution model of the air-gap magnetic field, it is theoretically verified that the odd harmonic current injection can effectively suppress the force ripple. The electromagnetic force under the fundamental + 3rd/7th harmonic currents and only the fundamental current is compared by simulation. The force ripple coefficient is reduced from 31% to 1.3%, and the position response speed is increased by about 11% in the 4 mm position closed-loop response simulation. The experimental results show that under a current with 200 Hz frequency, the motor can achieve a displacement of 5 mm within 0.11 s, providing a peak velocity of 40 mm/s, which verifies the correctness of the design concept and control strategy of the micro linear permanent magnet motor.

Research on Cogging Force Suppression for Toroidal PMLSM Based on Disturbance Observer

For a new type of toroidal permanent magnet linear motor(TPMLSM), this paper analyzes the thrust fluctuation in the constant acceleration operation of the motor from the Angle of the cogging force of the linear motor. For the motor whose structure has been determined and processed, the structural parameters of the motor cannot be changed, and its performance cannot be improved from the perspective of the motor body. Therefore, this paper tries to consider the influence of the cogging force on the normal operation of the motor from the perspective of control. In this paper, starting from the body structure of motor, first on the annular linear motor of the cogging force characteristics were extracted, and its expression is obtained by Fourier decomposition, then investigated considering the cogging force and does not consider the cogging force control of motor model, it can be seen that the control performance deteriorates significantly after considering cogging force of the motor, and the acceleration fluctuation increases significantly during the operation of the motor. On this basis, disturbance observation algorithm is introduced, and feedforward compensation is carried out by extracting the characteristic values of the disturbance model. The results show that the disturbance observer can suppress the thrust fluctuation caused by the motor cogging force to a large extent, and it can reduce the peak-to-peak value of the thrust fluctuation by more than 85% during the motor acceleration operation.

Optimal Learning Control Scheme for Discrete-Time Systems With Nonuniform Trials.

In reality such as a rehabilitation training, a repetitive control is necessary but the operational lengths may be iteration varying due to health condition. For the issue, this article investigates an intermittent optimal learning control scheme that considers the partially available information for the learning processing. The performance index is to minimize the summation of the quadratic timewise tracking error and the amplified adjacent-iteration timewise inputs drift while the argument is assigned as the iteration-time-varying learning gain. By adopting the latest captured historical timewise input and the tracking error, the optimal learning gain is achieved. Theoretical analysis conveys that the timewise tracking error is asymptotically convergent along the iteration direction. In particular, the tracking error may vanish at some finite iteration if the amplifier is null. Numerical simulations for a permanent magnet linear motor model testify the validity and effectiveness of the proposed scheme.

Adaptive backstepping control of primary permanent magnet linear motor via radial basis function neural network and command filter

This paper studies the displacement and speed control of primary permanent magnet linear motor (PPMLM) under the influence of unmodelled load interference, time-varying parameters and end effects. Adaptive backstepping control is first proposed to ensure system stability in the presence of time-varying parameters during motor movements. Then, radial basis function (RBF) neural network is used to compensate for the effect of the unmodeled load disturbance of the system. Furthermore, the command filter is implemented in the backstepping control to counteract the differential expansion phenomenon. The compensation signal is set to reduce the filtering error induced by the filter. Simulation results are given to verify the good performance of the proposed control in comparison with the adaptive backstepping controller and the command filter adaptive backstepping controller.