Flux Linkage Model Research Articles

Nonlinear Flux Linkage Observer with Model Reference Adaptive System for Improved Permanent Magnet Synchronous Motor Control

This paper addresses performance degradation in nonlinear flux linkage algorithms, arising from estimation errors in rotor flux linkage due to fluctuations in current and temperature. We introduce a parameter-adaptive flux linkage model using MRAS, which dynamically adjusts the rotor flux linkage, significantly minimizing estimation errors and improving control performance. When the rotor flux linkage of the motor undergoes sudden changes, the nonlinear flux linkage model shows a speed fluctuation of 5%, whereas the parameter-adaptive flux linkage model reduces the error to 0.6%. The algorithm demonstrates strong robustness when the stator resistance undergoes a sudden change. The control effectiveness under conditions such as load start and load mutation is excellent. Simulations and experiments demonstrate that the parameter-adaptive flux linkage model improves the estimation accuracy of the rotor position when motor parameters change.

Improved MTPA and MTPV Optimal Criteria Analysis Based on IPMSM Nonlinear Flux-Linkage Model

The use of interior permanent-magnet synchronous machines (IPMSMs) is prevalent in automotive and vehicle traction applications due to their high efficiency over a wide speed range. Given the high-power-density requirements of automotive IPMSMs, it is imperative to consider the effect of nonlinearities, such as saturation and cross-coupling, on the motor model. The aforementioned nonlinearities render conventional linear motor models incapable of accurately describing the operating characteristics of the IPMSM, including the maximum torque per ampere (MTPA) trajectory, the flux-weakening (FW) trajectory, and the maximum torque per volt (MTPV) trajectory. With respect to the linear motor model, the nonlinear flux-linkage model is gradually receiving attention from researchers. This modeling method represents the nonlinear behavior of the motor through the direct establishment of a bidirectional mapping relationship between flux-linkage and current. It is capable of naturally incorporating the effects of magnetic saturation and cross-coupling factors. However, the analysis of the current trajectory optimal criteria based on this model has not yet been reported. In this paper, the optimal criteria for the MTPA and MTPV current trajectories are analyzed based on the nonlinear flux-linkage model of IPMSMs. Firstly, the nonlinear flux-linkage model of the tested IPMSM is established by the experimental calibration method. The mathematical analytical expressions of the MTPA and MTPV optimal criteria are then analyzed by constructing and solving optimal problems with different objectives. Finally, the current command table applicable to actual motor control is constructed by calculating the current command for different operating conditions according to the optimal criteria proposed in this paper. The validity and feasibility of the optimal criteria proposed in this paper are verified through experimental tests on different operating conditions.

Parameter Identification of Nonlinear Flux-Linkage Model for Switched Reluctance Motor Based on Chaotic Diagonal Recurrent Neural Network

Parameter Identification of Nonlinear Flux-Linkage Model for Switched Reluctance Motor Based on Chaotic Diagonal Recurrent Neural Network

Modeling of nonlinear characteristics of switched reluctance motor based on optimized RBF neuron network

The strong nonlinearity of switched reluctance motor (SRM) makes it difficult to establish an accurate mathematical model of its electromagnetic characteristics. In this paper, an artificial neural network modeling method is adopted to estimate the nonlinear flux linkage characteristics of a four-phase SRM. Based on the samples obtained by experimental measurement, a radial basis function neural network is trained and further optimized using the K-Means algorithm. The modeling accuracy of the optimized flux linkage model is analyzed in detail and also verified by dynamic simulation of a direct instantaneous torque control system of the motor.

A Fixed-Point Position Observation Algorithm and System-on-Chip Design Suitable for Sensorless Control of High-Speed Permanent Magnet Synchronous Motor

In the sensorless control algorithm of permanent magnet synchronous motors (PMSMs), there is a significant research focus on developing a high-performance position observer and a cost-effective, high-performance processor specifically designed for PMSMs. In this paper, we first reviewed the current mainstream position observation algorithms. Subsequently, we proposed a position observation algorithm based on a fixed-point nonlinear flux linkage model that introduces a variable gain model and an observer compensation model. Furthermore, we implemented the improved position observation algorithm in the circuit and designed a System-on-Chip (SOC) suitable for the sensorless control of high-speed permanent magnet synchronous motors using the ARM Cortex-M0 core. The functionality of the proposed SOC was verified on the Field Programmable Gate Array (FPGA) platform. The results demonstrate that the improved algorithm offers an excellent angle observation accuracy and fast convergence speed. The error between the observed angle and the actual angle is less than 0.2 rad. Additionally, the designed SOC balances the high efficiency of hardware implementation with the flexibility of software implementation. When running a sensorless control algorithm for PMSM, it achieves a 30.3% increase in execution efficiency, enabling support for higher frequency output PWM switching and making it suitable for the high-precision control of high-speed PMSM.

PMSM Combination Modeling for Multiparameter Estimation Using Bayesian Learning With Inverter Distortion Cancellation and Temperature Compensation

Permanent magnet synchronous machine (PMSM) drives with better efficiency are highly demanded, and accurate flux linkage and inductance models or maps are critical to achieve such drives. However, precise modeling and estimation of these parameters should employ redundant data and are affected by magnetic saturation and inverter distortion. This paper firstly derives a flux linkage combination model from machine model for flux linkage and inductance estimation, in which inverter distortion is cancelled and thus inverter influence is minimized for performance improvement. To consider magnetic saturation, radial basis functions are employed to model the nonlinear flux linkages with a small number of relevance vectors, which can effectively depict the nonlinear variation. Bayesian learning approach is then explored to estimate the sparse coefficients of the flux linkage model in the context of radial basis functions, which can deal with non-Gaussian noise to improve the estimation accuracy and guarantee flux linkage model with better computation efficiency and less memory occupation. Moreover, temperature effect is considered to ensure the model accuracy under temperature rise. The proposed approach is validated with experiments and comparisons on a laboratory PMSM drive.

Sensorless control of switched reluctance motor based on a simple flux linkage model

Introduction. The operation of switched reluctance motor requires prior knowledge of the rotor position, obtaining from either low resolution photocoupler based position sensor or high resolution shaft encoder, to control the on/off states of the power switches. Problem. However, using physical position sensor in harsh environment will inevitably reduce the reliability of the motor drive, in which sensorless control comes into play. Novelty. In this paper, a sensorless control scheme of switched reluctance motor is proposed. Methodology. The method is based on a simple analytical model of the flux-linkage curves rather than the conventional approach that normally uses a look-up table to store all the data points of the flux-linkage curves. By measuring the phase current, rotor position can be deduced from the analytical model. Practical value. Simulation results are given and the proposed sensorless scheme is verified to provide a moderate position estimation accuracy in a wide speed range in both unsaturated and saturated conditions.

Current Sensor FTC Method for MPTC of Three-Phase Induction Motor Drives Without Speed Measurement

In encoderless Model Predictive Torque Control (MPTC) of three-phase Induction Motor (IM) drives, current sensors can face different electrical or mechanical faults in harsh industrial environments. In this research, single-phase current sensor Fault-Tolerant Control (FTC) method for MPTC of three-phase IM drives without speed measurement using a flux linkage observer and Model Reference Adaptive System (MRAS) algorithm is proposed. In the presented FTC method, Third-Difference operators, logic circuit module, flux linkage observer, and MRAS algorithm are utilized for fault detection, fault isolation, estimation of stator currents and fluxes, and speed estimation, respectively. In comparison with the conventional current sensor FTC methods, the proposed method can be utilized for encoderless three-phase IM drives. In order to confirm the usefulness and possibility of the proposed encoderless FTC method, experimental studies are performed for a 0.75 kW three-phase IM drive system in different situations. The achieved results demonstrate good performances of the proposed technique during both normal and faulty situations.

Current Sensorless Control for a Wound Rotor Synchronous Machine Based on Flux Linkage Model

Reducing manufacturing costs and increasing reliability are two major issues for the automotive industry. The development of sensorless control methods and estimation techniques for synchronous machines are ways to reduce the impact of these constraints. In this article, a control method is applied to a wound rotor synchronous machine (WRSM), often used in HEV applications, to estimate stator currents and control the machine without using any current sensor on the stator side. In this estimator, instead of the electric state model based on the currents, a flux-based model is used, which increases the precision of the estimator, improves the dynamics of stator currents, and has a better behavior in the case of magnetic saturation. Using this model and applying a Luenberger observer, the stator currents are estimated and then used in the current control loop. The performances of the proposed method are studied in a simulation part. Experimental tests are also performed to verify the effectiveness of the proposed control method.

Active Disturbance Rejection and Ripple Suppression Control Strategy With Model Compensation of Single-Winding Bearingless Flux-Switching Permanent Magnet Motor

The speed and radial displacement of the rotor have the obvious ripples due to the strong coupling between torque and suspension force of a single-winding bearingless flux-switching permanent magnet motor, and the traditional PID/PI controller is difficult to suppress the disturbance of the unbalanced magnetic force. A linear active disturbance rejection control method based on model compensation is proposed in this article. First, the topology and operation principle of the motor are described, and then the dynamic model of the rotor and flux linkage model of the motor are analyzed. Accordingly, the integral-series standard mathematical models of the displacement and speed are deduced, and then the mathematical expressions of the controller gain and radial disturbance are obtained. Second, the linear extended state observer with known model perturbation information and the linear feedback control law are designed, and the parameters tuning method is given. Finally, the simulation and experimental results verified that the proposed method can significantly reduce the rotor displacement and torque ripples, and it has better disturbance rejection performance than the traditional PID/PI control method in the same stability margin.

Comparative Investigation of Torque-ripple Suppression Control Strategies Based on Torque-sharing Function for Switched Reluctance Motor

Torque ripple is an inherent property of switched reluctance motor (SRM), which seriously affects the control performance and application of the motor. This paper proposes two torque ripple suppression control strategies based on torque-sharing function (TSF). According to the symmetry characteristics of the flux linkage and rotor position curve family, a fourth-order Fourier series is used to fit the SRM flux linkage analytical model. The coefficient of each harmonic term of the flux linkage model is a function related to current, expressed by a sixth-order polynomial. The torque analytical formula can be derived from the flux linkage model. The torque error is calculated via the identified torque model and is compensated through TSF controller in order to reduce torque ripple. The torque model can also be used to establish the torque loop to achieve accurate tracking of the TSF reference torque to reduce torque ripple. Digital simulation was conducted, followed by the implementation on a SRM test bench using a 28335DSP as the master control chip. The experimental results are consistent with the simulation results, and indicate the effectiveness of the proposed schemes.

Position Sensorless Control of Switched Reluctance Motor Drives Based on a New Sliding Mode Observer Using Fourier Flux Linkage Model

This paper proposes a new position sensorless method for switched reluctance motor (SRM) drive control based on a sliding mode observer using nonlinear Fourier flux linkage model. First, to obtain an accurate mathematical model of SRM for establishment of sliding mode position observer (SMPO), an analytical method based on Fourier polynomial function is introduced to regress the nonlinear relationship between flux linkage, position and current. Then, a new SMPO is designed in detail to estimate the rotor position, including the establishment of SRM model of sliding mode observer, and analysis of estimation error and convergence conditions of SMPO. Finally, position sensorless control of SRM drive based on SMPO is carried out in terms of accuracy and robustness in simulation. Experiments are also given on a dynamic testing platform to verify the effectiveness of the proposed position sensorless scheme.

Multi-Parameter Estimation of PMSM Using Differential Model With Core Loss Compensation

Accurate parameters are critical to permanent magnet synchronous machine (PMSM) drive. This paper investigates accurate flux linkages, inductances and PM flux linkage estimation for PMSM with core loss compensation. With conventional model, core loss will induce the flux linkage error especially in the deep saturation region. Hence, this paper firstly proposes a novel differential modeling technique to compensate core loss, in which differential measurement is defined as the incremental value calculated from the actual measurements under two different speed conditions. With multiple differential measurements, the flux linkage error due to core loss can be compensated to improve the accuracy of flux linkage estimation. Then, the polynomial based flux linkage model is employed to derive the PM flux linkage and cross-saturation inductances. Self-inductances are estimated from the flux linkage model using least squares method. The proposed approach can accurately estimate parameters without the need of core loss data and can improve the estimation accuracy especially in deep saturation region, which is validated on a laboratory interior PMSM and compared with existing methods under various operating conditions.

An Intersection-Method-Based Current Controller for Switched Reluctance Machines With Robust Tracking Performance

Good current tracking is beneficial to the torque ripple suppression methods like current profiling techniques for the switched reluctance machines (SRMs). An intersection-method-based current controller for the SRM with robust tracking performance is proposed in this article. First, with the aid of the predicted current at the next sampling instant, the prestored reference current, and the flux-linkage information, the required duty cycle for the next control period under specific reference current is estimated through the intersection method. To compensate for the difference between the adopted flux-linkage model and the real ones inside the machine, a Lyapunov-based adaptive flux-linkage observer is presented. Hence, the heavy dependence issue on the accurate flux-linkage model for the current controller is resolved. With the above techniques, robust reference current tracking is achieved in a simple form and only one observer gain. Besides, a balanced switching scheme is presented to reduce the switching frequency requirement of the power transistors and evenly distribute the switching losses. Extensive experimental tests have been carried out on a four-phase 5.1-kW 8/6 SRM setup for the proposed method and conventional current control methods at different operation conditions. These testing results verified the effectiveness of the proposed method.

End Effect Analysis of a Slot-Less Long-Stator Permanent Magnet Linear Synchronous Motor

The implications of the end effect for flux linkage and thrust ripple in a slot-less long-stator permanent magnet linear synchronous motor (LSPMLSM), are analyzed in this paper. Since it is affected by the end effect, the air-gap magnetic field density under the end permanent magnet is different from that under the non-end permanent magnet, leading to asymmetry in the thrust ripple. For this reason, we establish a dynamic permanent magnet flux linkage model, which proves that the end effect leads to sub-harmonics in the permanent magnet flux linkage. The motor’s magnetic field distribution in the left and right parts is symmetrical. A thrust model taking into account the flux linkage sub-harmonics is established, from which the amplitude and period of the thrust ripple caused by the end effect can be calculated. There is no detent force for the slot-less LSPMLSM, and the end effect is the primary origin of the motor thrust ripple. In order to suppress the end effect, a method of increasing the end iron length is proposed, as a result of which the sub-harmonics in the flux linkage and the motor thrust ripple are effectively suppressed. Experimental and simulation results verify the results of this paper.

Global fast terminal integral sliding mode control based on magnetic field measurement for magnetic levitation system

AbstractMagnetic levitation systems are widely applied in many fields. In this paper, a global fast terminal integral sliding mode controller (GFTISMC) based on the second‐order flux linkage model is proposed to improve the response speed and steady‐state error of the maglev system. Firstly, the dynamic model of the maglev system is deduced, and the second‐order flux state model is established. Secondly, to improve the global response speed of the system and reduce the steady‐state error, a GFTISMC is constructed. A position model based on magnetic field measurement is determined to achieve closed‐loop control. Finally, compared with the traditional sliding mode control, the simulation and experimental results show that the proposed controller has better global response speed, stronger robustness, and smaller steady‐state error.

Four-Quadrant Position Sensorless Operation of Switched Reluctance Machine for Electric Vehicles Over a Wide Speed Range

This article focuses on developing a four-quadrant position sensorless technique for switched reluctance machine (SRM) to meet the operating requirements of electric vehicles (EVs). The technique combines two different sensorless schemes and is implemented by the sensorless rules based on the rotor position partition. At startup and low speeds, the zones are identified based on the comparison of unsaturated inductances obtained by pulse current slope difference method, and the segmented Fourier series inductance model or the segmented linear inductance model is selected for position estimation according to the identified zones. At medium to high speeds, the zones are identified based on the comparison of flux linkage generated by excitation current and auxiliary chopping current. Only the segmented linear flux-linkage model is used for position estimation to reduce the computational burden of the processor. The transition methods are also presented to achieve seamless combination between the two sensorless schemes and the smooth transition from motoring to braking. This technique can deliver high-resolution rotor positions in full cycle and is implemented fast and easily. The experimental results on a 1.2-kW 12/8-pole SRM prototype verify the feasibility and correctness of the proposed sensorless control technique.

Evaluation of DC-Link Capacitor RMS Current in Switched Reluctance Motor Drive

In this article, a method to evaluate the dc-link capacitor rms current of a switched reluctance motor (SRM) drive under different operating conditions is presented. Square current reference in both hard and soft chopping modes of pulsewidth-modulated current control is considered. By approximating the current controller response and using a recently proposed flux linkage model, the switching-cycle-average phase voltage and current are evaluated over an electrical cycle. The phase voltage and current are further used to obtain the rms values of dc-link current and capacitor current. The proposed method is also used to determine the capacitor current for low-torque-ripple current reference and single-pulse operation. The analytical predictions pertaining to different control methods under different operating conditions are verified by simulation and experimental results obtained from a 4 kW, 1500 r/min, four-phase SRM drive. While the capacitor current is found to be maximum at the lowest operating speed with hard chopping, the maximum capacitor current is observed at an intermediate speed with soft chopping, both for a given magnitude of square wave current reference. The proposed method is useful to size the dc-link capacitor and evaluate its loss in an SRM drive. Furthermore, closed-form expressions for capacitor rms current are also derived, assuming perfect tracking of square wave current reference at low speeds. These expressions bring out the dependence of capacitor rms current on the machine characteristics.

Bipolar-Voltage-Injection-Based Position Estimation Method of Planar Switched Reluctance Motors Using Improved Flux Linkage Model

This article proposes a new position estimation method based on an unsaturated flux linkage model for planar switched reluctance motors (PSRMs). The bipolar-voltage-injection method is used to measure the flux linkage, and it is found that ripples caused by iron loss and aluminum eddy current with different amplitudes appear at the troughs of the flux curve. The effect of the losses on the flux linkage measurement is revealed in this article, and the loss compensation models are built based on the analysis. The improved flux linkage model is proposed with the loss compensation models. Then, the position estimation method is given with the improved flux linkage model. Flux linkage measurement result shows that the model with loss compensation has higher accuracy than the conventional model. Initial and planar-motion position estimation experiments are carried out for the PSRM. The initial position estimation error is from -0.4 to 0.4 mm. The planar-motion position estimation errors are from -1.1 to 1.1 mm in the X-axis and from -1.2 to 1.0 mm in the {Y-axis, and the effectiveness of the proposed flux linkage model is verified.

Precise non‐linear flux linkage model for permanent magnet synchronous motors based on current injection and bivariate function approximation

Precise non‐linear flux linkage model for permanent magnet synchronous motors based on current injection and bivariate function approximation