Flux Linkage Estimation Research Articles

Position sensorless extended and unscented Kalman filters with permanent magnet flux linkage and load torque estimation for surface-mounted PMSM

In this paper, novel position sensorless state estimators with improved robustness to permanent magnet (PM) flux linkage variations in permanent magnet synchronous machines (PMSMs) are presented. Unlike state estimators using conventional infinite inertia or electromechanical models, the estimators presented here can also estimate the PM flux linkage, so they are not sensitive to its uncertainty. For each models used for state estimation, a detailed observability study is presented. Due to the nonlinear models, extended and unscented Kalman filter algorithms are used for the implementation. To compare the sensitivity of conventional and proposed state estimators to uncertainty in electrical parameters, numerical simulations are carried out. In addition, the computational burden of the estimators is compared by real-time execution.

Improved flux linkage observer for position estimation of permanent magnet synchronous linear motor

Abstract. With the development of motor technology, sensorless control attracts more and more attention. In this paper, an improved flux linkage observer is proposed to overcome issues including inaccurate initial positions and sampling noise. The voltage and current models are combined, and a sliding-mode observer is designed based on the hybrid model to obtain the compensation voltage. Therefore, the estimated flux linkage after compensation can greatly resist the influence caused by inaccurate initial positions or sampling noise. Phase-locked loop technology is used to process the estimated flux linkage to get the stable estimated speed and position. The proposed scheme has a simple structure and only one parameter. It is easy to use and adjust in practice. The simulation and experimental results verify that the proposed algorithm is effective, and the estimated flux linkage and position is accurate with an inaccurate initial position.

Flux Linkage Tracking-Based Permanent Magnet Temperature Hybrid Modeling and Estimation for PMSMs With Data-Driven-Based Core Loss Compensation

Flux Linkage Tracking-Based Permanent Magnet Temperature Hybrid Modeling and Estimation for PMSMs With Data-Driven-Based Core Loss Compensation

Simple and low-cost motion-sensorless control approach for the IPMSM with elimination of DC offset and steady-state error

Voltage type flux observer has attracted much attention because of its less mathematical calculations and ease of implementation. The only issue with the flux estimation approach is the integration mechanism; using a pure integrator may cause integrator saturation and a DC bias issue, whereas using the low pass filter (LPF) and a self-adaptive band-pass filter (SABPF) would result in magnitude and phase angle errors. This work offers an improved flux linkage estimation approach with a proportional integral (PI) DC offset compensator, resolving the DC drift issue associated with the observer’s pure integrator. Compared to the standard voltage type flux observer, the DC offset is removed, the LPF and phase adjustment are eliminated, and low-speed armature position estimate accuracy is improved. The proposed method can reduce calculation. As a result, the control period is reduced. The Matlab Simulink framework findings are presented to validate the performance and effectiveness of the proposed strategy.

Multiple Observers-Based Demagnetization Fault Detection With Inductance Mismatch Impacts Eliminated for PMSMs

This paper proposes to use multiple sliding mode (SM) observers to accurately detect demagnetization fault (DF) for permanent magnet synchronous motors (PMSM). First, relying on the properties of the PMSM, three sequential SM observers including a flux linkage observer (FLO), a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q</i> -axis inductance observer (QIO) and a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</i> -axis inductance observer (DIO) are developed, with their stability discussed. Second, the estimation errors of the proposed SM observers are analyzed, and on this basis, the accurate flux linkage that eliminates the negative impacts of inductance mismatch is calculated. Then, the calculated flux linkage is used to determine whether an DF occurs. Finally, comparative experiment is conducted on two PMSM prototypes to validate the proposed flux linkage estimation and DF detection techniques.

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.

Rotor Speed and Position Estimation Analysis of Interior PMSM Machines in Low and Medium-High Speed Regions Adopting an Improved Flux Observer for Electric Vehicle Applications

This paper proposes a nonlinear flux linkage observer for the PMSM speed controls without motion sensors, introducing the deviation among the real stator flux linkage and an estimated stator flux linkage to suppress feedback and integral flux drift. In the position detection of an interior PMSM without a speed sensor, the traditional back EMF integration method uses a pure integrator, or LPF, to estimate the stator flux. Its inherent defects inevitably lead to inaccurate flux estimation, which directly affects the estimation of the motor mover position, resulting in the decline in motor control operation and the distortion of phase current. This paper uses an improved integrator with adaptive compensation. The projected value of the stator flux linkage has been derived from the estimated value of the rotor permanent magnetic flux linkage position angle and the algebraic model (m-model) of the stator flux linkage, along with a synchronous coordinate system. The IPMSM stator coil flux linkage obtained from the stator coil current and integral voltage models in the static coordinate system is compared to form a feedback closed-loop to suppress the integral drift, and using the cross-product approach of the actual and estimated flux linkage yields the projected value of the IPMSM rotor speed and position through a PLL. Compared with the existing motion-sensorless observers, the methodology proposed in this article is simple and exhibits better dynamic and static estimation performance. Extensive and comprehensive MATLAB computer simulation and experimental findings validate the proposed motion-sensorless control mechanism.

Accurate SM Disturbance Observer-Based Demagnetization Fault Diagnosis With Parameter Mismatch Impacts Eliminated for IPM Motors

This paper proposes a novel sliding mode (SM) disturbance observer-based technique to diagnose demagnetization fault of interior permanent magnet (IPM) motors with stator parameter mismatch impacts eliminated. First, the IPM motor model incorporating the disturbances caused by the PM demagnetization and stator parameter mismatch is established. Then, an SM disturbance observer is constructed to identify the overall disturbance caused by all parameters, with its stability discussed by using the Lyapunov function. Third, a current-analysis-based method is developed to extract the disturbance only caused by flux linkage mismatch from the overall disturbance. Third, the extracted disturbance is adopted to calculate the real flux linkage, achieving demagnetization fault judgment and demagnetization degree calculation. Finally, experiment is conducted on two IPM motors to validate the proposed flux linkage estimation and fault diagnosis methods.

Low-Cost Realization of Feature Position Estimation Scheme for Switched Reluctance Motor

This letter proposes a low-cost feature position estimation scheme for singly excited SRM without using lookup tables. This scheme uses the particular flux linkage versus current curve, corresponding to the commutation angle, to generate a flux-linkage reference. Phase commutation is executed at the instant when the online estimated flux linkage reaches this reference threshold. So, this letter, initially, proposes a novel analytical method to compute the reference flux linkage from phase currents. Then, a new approach is presented that maps the individual measured phase currents and estimated flux linkages into corresponding unified signals to reduce the computational burden. Thereafter, the mutual coupling among phases is shown as a cause of serious error in the thresholding operation, and a design criterion to avoid this error is derived. Performance of the proposed sensorless scheme is experimentally validated on a 1 kW, 3000 r/min, 6/4 SRM-based laboratory prototype.

Phase flux linkage estimation of external rotor switched reluctance motor with NARX neural network

Phase flux linkage estimation of external rotor switched reluctance motor with NARX neural network

A Study of Reduced Torque Compensation Method Under Temperature Variation Based on Single Torque-Current Lookup Table

In permanent magnet motors, the stator resistance and magnetic flux of the magnet change as the temperature increases. These changes result in a change in the maximum torque point per unit ampere (MTPA) of the motor. Without adequate compensation, this leads to a decrease in output torque. For this reason, look-up table (LUTs) are prepared over the temperature range and used for interpolation. This paper proposes a method to compensate for the output torque reduction due to a temperature increase using only a single LUT prepared at a base temperature. First, an estimation of the magnetic flux linkage and the output torque using a single LUT is performed. Second, the problem is modeled as a limited optimization problem to minimize the loss due to the torque reduction. The magnetic flux linkage and output torque are calculated in real time through the fundamental active power. The compensation value is calculated using the Lagrange multiplier method, an optimization technique, using the estimated magnetic flux linkage and output torque. The proposed method is verified by comparing it with other algorithms through simulation and experiment.

Enhanced Torque Estimation in Variable Leakage Flux PMSM Combining High and Low Frequency Signal Injection

Torque measurement/estimation in Variable Leakage Flux Permanent Magnet Synchronous Motors (VLF-PMSMs) is preferred for accurate control. Torque measurement systems are expensive, require extra room, add weight, can introduce resonances into the system and can be sensitive to electromagnetic interference. Alternatively, torque can be estimated, accurate knowledge of machine parameters being often required in this case, which for the case of VLF-PMSMs can be a serious drawback due to the large variation of machine parameters with the operating condition. This paper proposes a torque estimation method for VLF-PMSMs based on stator flux linkage estimation. Machine parameters involved in stator flux linkage estimation are obtained from the response of the machine to a pulsating high frequency current signal and a low-frequency and small-magnitude, square-wave current signal. Both signals are injected on top of the fundamental excitation without interfering with the normal operation of the machine.

Robust Incremental Bayesian Learning Based Online Flux Linkage Estimation for PMSM Drives

For the permanent magnet synchronous machine (PMSM), parameter estimation can be greatly affected by the measurement uncertainty, but few efforts are made to reduce the uncertainty level for estimation performance improvement. Therefore, this article proposes an efficient and robust incremental Bayesian learning approach for PMSM parameter estimation. The measurement uncertainty is evaluated to guide the selection of informative measurements, and the estimation uncertainty is provided to indicate the confidence in using the estimated results. Specifically, a Bayesian learning strategy with a layered noise model is proposed for nonlinear flux linkage estimation. The measurement uncertainty level is estimated from the proposed Bayesian learning model, which is utilized to adaptively select the most informative data and delete the noninformative data for parameter estimation. This contributes to improving estimation accuracy and computation efficiency. Moreover, the estimation uncertainty is also determined by the proposed model, which can be used to indicate if the estimated results can be trusted and utilized in practical applications. The proposed approach is evaluated on a laboratory interior PMSM under various operating conditions.

Polynomial Estimation of Flux Linkage for Predictive Current Control in PMSM

This article presents an automatic parameter identification method based on ordinary least square (OLS) algorithm for deadbeat predictive current control (DPCC) to fulfill the purpose of high steady and dynamic performance in permanent magnet synchronous motor (PMSM) drives. Different from the conventional model, a novel model based on the polynomial estimation of flux linkage is constructed which takes the cross-saturation effects into account. First, the conventional mathematical model of PMSM and the proposed model are presented, respectively, and the inverter considering nonideal factors is also analyzed. Then the parameter identification method is investigated, in which the measurement procedure is delimited in advance and the automatic identification method is developed. Furthermore, a voltage reconstruction algorithm is applied to solve the inverter nonlinearities and the digital time-delay effect, so as to improve the accuracy of the identified parameters. Accordingly, a novel DPCC algorithm is presented based on the proposed model to achieve better performance. Finally, based on the concept and principles mentioned before, a detailed comparison of the DPCC based on the classical model considering the parameters’ variation and the modified model of the proposed method is carried out on a laboratory prototype.

A Compensation Strategy of Flux Linkage Observer in SPMSM Sensorless Drives Based on Linear Extended State Observer

Flux linkage estimation based on the voltage model has been widely employed in surface-mounted permanent magnet synchronous machine (SPMSM) sensorless drives due to its simple implementation. To deal with dc-offset and dc-drift problems, the pure integrator is modified as a programmable low pass filter (LPF)in practice. However, the estimation accuracy of the rotor position is affected by the adopted filter. Although the position deviation is compensated in steady-state based on the frequency characteristics of the filter, the compensation effect deteriorates during a dynamic process which severely degrades the sensorless control performance. In order to effectively tackle this problem, a novel compensation strategy based on the linear extended state observer (LESO) is proposed in this paper. With the constructed LESO in the estimated synchronous rotating reference frame, the position estimation error can be detected and compensated both in the steady and dynamic state. Moreover, the observer is enhanced to improve the estimation accuracy in linear acceleration and deceleration. Finally, the feasibility of the proposed method is verified under various operating conditions with a 5.5 kW SPMSM drive system.

Real-Time Estimation of PMSM Rotor Flux Linkage for EV Application under Steady State and Free-Running Conditions

A method for real-time estimation of rotor flux linkage of permanent-magnet synchronous machines (PMSMs) under both steady state and free-running conditions is proposed in this paper. At steady state, a method for the estimation of rotor flux linkage is proposed based on the injection of variable-period zero-voltage perturbation, of which the accuracy is irrespective of the influence of voltage-source inverter (VSI) nonlinearity. Moreover, for the estimation of rotor flux linkage under free-running condition, due to system inertia after shutdown or fault in the motor driver, an effective approach using history data recorded at different transients of rotor speeds is developed, which has eliminated the influence of VSI nonlinearity during the modeling process. The proposed two methods are experimentally validated on a down-sized PMSM prototyped for electric vehicle application, which shows good performance for the estimation of rotor flux linkage under both steady state and free-running conditions.

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.

A fault-tolerant steer-by-wire system based on angular position estimation

While steer-by-wire (SBW) systems benefit from improved performance and comfort, they require a large number of sensors impacting whole system reliability. In order to address this challenge fault tolerance property against sensor faults has to be improved. Application of redundancy for the sensors is the best solution proposed so far. This paper proposes a novel solution of analytical redundancy based on various position estimation methods for both electrical motor and steering wheel position sensors. Three different estimation techniques including extended programmable cascaded low-pass filter (EPCLPF), stator flux linkage estimator using stator currents, as well as stator flux linkage estimator using stator voltages are proposed for this purpose. The faulty sensors are recognized using a voting technique in which a comparison between the sensors’ outputs with the estimated values is made. In this way, the SBW system reliability is highly improved with no additional cost and space. Simulation and experimental results are presented to confirm the presented fault tolerant SBW system capabilities.

Recent Challenges and Advances in the Sensorless Commutation of Brushless DC Motors

Background: Brushless DC motors are highly efficient motors due to their high torque to weight ratio, compact design, high speed operating capability and higher power density. Conventional Hall sensor based rotor position sensing is affected by the heating, vibration, interference and noise. Objective: The innovative, cost-effective and easily implementable sensorless techniques are essential in order to achieve high efficiency, reduced current and reduced torque pulsations. Furthermore, a delay free, high load fast startup is also an important issue. Methods: In this paper, an extensive review of various techniques based on the detection of freewheeling diode current, phase back EMF zero crossing point detection, back EMF integration method and third harmonic back EMF was done. The effect of various PWM strategies on back EMF detection were studied. Later on, the sensorless schemes based on flux linkage estimation and flux linkage increment were introduced. The load torque observers, unknown input observers, sliding mode observers, L∞ − induced observers, H∞ − deconvolution filter for back EMF estimation were also reviewed. As the brushless DC motors have no back EMF at starting and for back EMF based commutation, minimum speed is required for sufficient back EMF. Therefore various strategies of an open and close-loop reduced current startup have been studied to achieve effective commutation without reverse torque. Initial Position Detection (IPD) schemes, which are mostly based on saliency and current response to inductance variation, are effective where reverse torque is strictly prohibited. A detailed review of these Initial Position Detection techniques (IPD) has also been presented. Results: The detailed mathematical and graphical analysis has been presented here in order to understand the working of the state-of-the-art sensorless techniques. Conclusion: The back EMF detection using direct and indirect methods of terminal voltage filtering has the problem of delay and attenuation. PWM noise, freewheeling diode spikes and disturbance in detected back EMFs are also major drawbacks. The problems such as, parameter detuning, underestimation and overestimation, offset problem, system noise and observer gain variation, etc. limit the applicability of observer based technique. Therefore, a more robust and precise position estimation scheme is essential.

Flux linkage estimation strategies for sensorless field-oriented control of doubly-fed induction motor drive

In this paper authours propose two different strategies of flux linkage estimation for sensorless FOC system of doubly-fed induction motor drive implementation. Possibility to measure currents and voltages of rotor and stator circuits in doubly-fed motor gives place to a simplier flux linkage observers model. Functional scheme of electric drive and two models of flux linkage observers are proposed - a model using the voltage and a model using the rotor current. The stability of the present field-oriented control system when implementing these flux-linkage estimations strategies are investigated using LabView software. The results of theoretical research are confirmed by simulation results in Matlab software.