Non-sinusoidal Back Electromotive Force Research Articles

Open-Phase-Tolerant Online Current References for Maximum Torque Range and Minimum Loss With Current and Torque-Ripple Limits for n-Phase Nonsalient PMSMs With Nonsinusoidal Back EMF

Multiphase permanent-magnet synchronous machines (PMSMs) with nonsinusoidal back-electromotive force (back-EMF) offer high fault tolerance and torque density for electric vehicles. Most current-reference generation methods either minimize stator copper loss (SCL) or maximize achievable torque. Optimization of both goals is accomplished by full-torque-range minimum-loss (FRML) strategies, but so far just for sinusoidal back-EMF. Thus, FRML for nonsinusoidal back-EMF should be sought. Moreover, many methods are only suitable for healthy conditions or specific machines, harmonics, or open-phase-fault (OPF) scenarios. Additionally, the torque range may be extended by permitting torque ripple or (transiently) greater rms current, but this approach is not general nor FRML yet. This paper proposes online FRML current-reference generation for multiphase PMSMs with nonsinusoidal back-EMF: nonsinusoidal-back-EMF FRML (NSBE-FRML). When the torque reference is feasible, minimum SCL is attained while maximizing the achievable torque (i.e., FRML). For higher torque references, the instantaneous torque deviation is minimized, and the torque reference is saturated in consecutive samples limiting the torque ripple to a pre-specified threshold. Furthermore, the rms current is limited after transient overload by automatically decreasing the torque reference. The NSBE-FRML is suitable for any harmonics, healthy/OPF conditions, and multiphase PMSMs with negligible saliency ratio. Experiments are performed with a six-phase PMSM.

Harmonic Current Suppression for Dual Three-Phase PMSM Based on Deadbeat Control and Disturbance Observer

Harmonic currents always exist in a dual three-phase permanent magnet synchronous machine due to the inverter nonlinearity, nonsinusoidal back-electromotive force, and external disturbances. This article proposes a deadbeat predictive harmonic current control (DPHCC) method to suppress the harmonic currents. The DPHCC method can directly calculate the harmonic control voltage based on the sampled harmonic currents and the machine model. Thus, the steady-state and transient-state performance of harmonic current control can be improved. Further, a disturbance observer is designed to avoid the influence of inaccurate machine parameters and other unmodeled disturbances. The observer is designed based on discrete-time sliding mode theory and an improved sliding mode reaching law. The stability of the observer has been analyzed, and the value range of the observer parameters has been determined theoretically. Finally, experimental results have been presented to verify the effectiveness of harmonic current suppression for the proposed control system.

Decoupled Fault-Tolerant Model Predictive Current Control for Dual Three-Phase PMSMs With Harmonic Compensation

This article proposes a decoupled fault-tolerant model predictive current control for a dual three-phase permanent magnet synchronous motor with harmonic compensation. The harmonics caused by nonsinusoidal back electromotive force can be well controlled under the open-circuit fault scenario by designing a harmonic closed-loop scheme. First, a decoupled predictive model and fault-tolerant voltage vectors are deduced based on a reduced-dimension matrix, which can eliminate the coupling issues between the harmonic and fundamental subspaces. Afterward, a uniform harmonic-free virtual vector is constructed by rearranging the irregular voltage vectors. More importantly, a virtual null vector is designed in the scheme, where the virtual null vector is effective in the harmonic subspace and has no components in the fundamental subspace. So, the harmonics can be further controlled without affecting torque and flux generation. Extensive experimental results verify the effectiveness of the proposed method.

Mathematical Modelling and Torque Ripple Waning in BLDC Motor Using Outgoing-Phase Current Discharge Hysteresis Controlled ANFIS Controller

This study focused on approaches for reducing torque ripples in Permanent Magnet Brushless Direct current motors (PMBLDC) to provide sophisticated performance and reliable machine drives for both industrial and consumer applications. Torque ripples are caused by current ripple, nonsinusoidal Back Electromotive Force (EMF), and cogging torque at the Brushless Direct Current Motor (BLDCM) output. Acoustic emissions are produced when the torque ripple creates vibrations in the mechanical system, which interacts with the motor housing and reduces the life span of the motor. The BLDC’s uses are limited due to these acoustic emissions. Proportional-Integral (PI), Fuzzy Logic Control (FLC), and Adaptive Neuro-Fuzzy Inference System (ANFIS) speed controller approaches were used to construct and analyze the mathematical model of the BLDC motor in the MATLAB environment. The Adaptive Neurofuzzy Inference System (ANFIS) speed control system has solved the shortcomings of the PI and Fuzzy Logic Control (FLC) techniques. Because of FLC interpolation and flexibility, ANFIS is one of the finest trade-offs between neural and fuzzy systems, allowing for smooth control. Model compactness, a smaller training set, and faster convergence are all benefits of the ANFIS approach over traditional feedforward NN. In this research proposal, a simple control approach based on outgoing phase current discharge hysteresis control (OGCDHC) with minimal torque ripple is presented.

Multiple reference frame-based current harmonic control for interior PMSMs considering motional EMF

For permanent magnet synchronous machines (PMSMs), current harmonics need to be controlled under two kinds of conditions. Under the first condition, the current harmonics caused by the non-sinusoidal back-electromotive force (EMF) and the dead time of inverters should be suppressed. Under the second condition, specific current harmonics should be injected to suppress the torque ripple of motors. Therefore, the accurate control of current harmonics is critical. It has been found that the original multiple reference frame (MRF)-based control algorithm cannot effectively achieve the control of current harmonics at high speeds. For the currents in MRFs, motional EMF was dominant rather than induced EMF at higher speeds. As a result, the original MRF-based control algorithm does not work at high speeds. To solve this problem, this paper proposed a novel MRF-based control algorithm that considers motional EMF. Furthermore, this paper achieved decoupling control of the current harmonics in MRFs for interior PMSMs. With the proposed control algorithm, the current harmonics of interior PMSMs can be controlled at both high and low speeds. Under the influence of non-sinusoidal back EMF and the dead time of the inverter, the effect of current harmonic control was verified on a laboratory test bench.

Flux-Weakening Control of Dual Three-Phase PMSM Based on Vector Space Decomposition Control

This article proposes a flux-weakening (FW) control for dual three-phase permanent magnet synchronous machine (DTPMSM) based on vector space decomposition (VSD) control, where the output voltage in αβ subplane is employed for voltage feedback in the FW control loop. As the fundamental components are mapped to αβ subplane while the fifth and seventh harmonics are projected to harmonic z <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> z <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> subplane, the FW current from this new control in αβ subplane is sixth harmonic-free regardless of the fifth and sixth harmonics being resulted from the nonsinusoidal back electromotive force (EMF) or inverter nonlinearity. The proposed control is compared with the conventional FW feedback control extended for DT-PMSM, where the FW control is applied to the two sets of three-phase windings separately. The experimental results show that the proposed FW control based on VSD is superior to the conventional FW control in terms of reduction in current unbalance and harmonic currents.

Real-Time Maximum Torque per Ampere Control of Brushless DC Motor Drive With Minimum Torque Ripple

A nonlinear control scheme is proposed for real-time tracking of maximum torque per ampere trajectory of the surface-mounted brushless dc motor with non-sinusoidal back electromotive force (back-EMF). The strategy employs the Lagrange's Theorem to obtain the optimum stator current, at which both torque ripple and corresponding current magnitude become minimized. A new maximum torque per ampere (MTPA) criterion is introduced. Forcing this criterion to zero guarantees MTPA realization. The input–output feedback linearization (IOFL) control scheme is employed to improve tracking of the applied optimum currents. In the suggested approach, the magnitude of the stator current vector is minimized effectively in each instant. The performance of the control system is validated through experimental results.

Loss-Minimization Strategy of Nonsinusoidal Back EMF PMSM in Multiple Synchronous Reference Frames

Traditional loss-minimization strategies of model-based control, copper loss minimization (CLM), and finite-element-based control suffer from respective problems of iron loss mismatch with a physical view, pseudominimization and amounts of efforts when they are applied to permanent magnet synchronous motor with nonsinusoidal back electromotive force (NS-PMSM). This article combines theories of multiple synchronous reference frames and iron loss resistance to develop a new model of NS-PMSM, based on which the stator iron loss is evaluated to match well with the physical view. Then, a current strategy is proposed to minimize the total stator loss under constraints of ripple-free torque and finite dc supply. The optimal current solution is solved in closed form and implemented effortlessly. A good robustness to phase resistance variation is also achieved. Compared to CLM, the proposed strategy realizes a true minimization with the stator loss reduced by 9% and the motor efficiency enhanced by 0.7% at rated operation of a 3.8-kW NS-PMSM. Precision of the iron loss evaluation and performances of the strategy are validated experimentally on the 3.8-kW motor setup.

Electromagnetic Vibration Analysis of High-Speed Permanent Magnet Synchronous Machines With Amorphous Metal Stator Cores Considering Current Harmonics

This article investigates the electromagnetic vibration characteristics of high-speed (HS) permanent magnet synchronous machines (PMSMs) with amorphous metal stator cores (AMSCs) considering current harmonics. First, an analytical model of radial forces in PMSMs considering current harmonics due to both nonsinusoidal back electromotive force and pulsewidth modulation effects is developed. The cross influences of the two types of current harmonics on vibrations of HS PMSMs in different frequency bands are discussed. Second, the equivalent elasticity modulus parameters of laminated AMSCs are identified by utilizing modal experiment. Third, the influences of slot and pole number combinations on magnetic field harmonic contents and radial force orders for HS PMSMs are investigated by the analytical model. Then, the radial forces of a 15-kW HS PMSM fed by ideal sinusoidal current and experimental current are calculated under different rotational speeds by finite-element method. Finally, the vibrations of the prototype under rated torque and different rotational speeds are tested to verify the theoretical analysis.

Current Harmonics Suppression Strategy for PMSM With Nonsinusoidal Back-EMF Based on Adaptive Linear Neuron Method

In this article, an adaptive linear neuron based current harmonics suppression method for permanent magnet synchronous motors with nonsinusoidal back electromotive force (EMF) is presented, with due account for dead-time effect. The current harmonics can be well-suppressed by feedforwarding a self-tuning compensation voltage. The proposed method does not rely on the knowledge of back-EMF harmonic components and dead-time effect. Moreover, the proposed method is easy to implement, since it does not need the process to extract the current harmonics. The effectiveness of the proposed method is verified by both simulation and experimental results without requiring additional hardware.

A Fault-Tolerant FOC Strategy for Five-Phase SPMSM With Minimum Torque Ripples in the Full Torque Operation Range Under Double-Phase Open-Circuit Fault

This article proposes a fault-tolerant field-oriented control strategy for five-phase surface-mounted permanent magnet synchronous machine with non-sinusoidal back electromotive force under double-phase open-circuit fault, where the failure phases are either adjacent or nonadjacent. Based on the decoupled mathematical model after failure, the optimum current references which satisfy the zero-torque-pulsation constraint at the synchronous frame are presented. However, the torque operation range is small. So a full-range minimum torque ripples post-fault strategy is proposed. This strategy extends the torque operation range by gradually relaxing the zero-torque-pulsation constraint. And it can minimize the torque ripples for each torque reference value in the whole torque operation range. The synchronous frame proportional integral resonant controllers and carrier-based pulsewidth modulation are employed to implement the proposed post-fault strategy. The experimental results are provided to verify that the proposed strategy can achieve wider torque operation range and smaller torque ripples compared with the conventional fault-tolerant strategies.

Fault‐tolerant FOC for five‐phase SPMSM with non‐sinusoidal back EMF

A fault-tolerant field-oriented control (FOC) is proposed for five-phase surface-mounted permanent magnet synchronous motor (SPMSM) with non-sinusoidal back electromotive force under single-phase open-circuit fault. On the basis of the concept of preserving the circular rotation of fundamental magnetic motive force and PM flux linkage, the decoupled model of five-phase SPMSM under single-phase open-circuit fault is derived. To suppress the torque ripples caused by third-harmonic content of PM flux linkage, the closed-form solution of current references with zero-torque pulsation in the synchronous coordinate is presented. Then, the presented solution is used for obtaining optimum current references to achieve minimum stator winding losses and maximum available torque while satisfying the zero-torque-pulsation constraint. The optimal current references generation method is simple and is suitable for real-time implementation. The experimental results confirm that the proposed method can effectively suppress the torque ripples and produce lower stator winding losses as well as wider-torque operation range compared with traditional fault-tolerant FOC method.

Effects of Stator Iron Loss and Current-Loop Delay on Copper-Loss-Minimizing Torque Control of BLDCM: Analysis and Improvements

Copper-loss-minimizing torque control (CLMTC) method has been widely studied to reduce electromagnetic torque ripple and minimize copper loss of a brushless dc motor (BLDCM), but still suffers challenges to improve its performance. This paper presents a quantitative analysis of stator iron loss and current-loop delay effects on CLMTC. In the analysis, the iron-loss-included torque equation that only suits for sinusoidal back electromotive force (EMF) is modified to cover the case of nonsinusoidal back EMF. It is concluded that the iron loss effect brings about significant torque generation error and the delay effect leads to torque ripple that increases linearly with the delay angle. Two improvements are proposed, one of which redefines the condition of an optimal motor current vector to compensate for the iron loss effect. The other one aims to suppress the delay effect by preshaping current reference based on delay characteristic of the loop. The improvements can be performed effectively on a microprocessor to realize a better CLMTC method with reduced torque generation error and torque ripple. Both the analysis and improvements are experimentally validated on a 0.95 kW BLDCM setup.

A Constant Switching Frequency Multiple-Vector-Based Model Predictive Current Control of Five-Phase PMSM With Nonsinusoidal Back EMF

Most of the existing finite-control-set model predictive current control (FCS-MPCC) schemes for multi-phase motor suffer from heavy computational burden, inevitable low-order harmonic currents, and variable switching frequencies. Some virtual voltage vector (V3)-based FCS-MPCC schemes can effectively suppress harmonic current by zeroing the harmonic subspace voltage on average during one sampling period. However, they fail when the motor has a nonsinusoidal back electromotive force. In order to solve the aforementioned issues, this paper proposes a constant switching frequency multiple-vector-based FCS-MPCC scheme. Unlike the traditional FCS-MPCC schemes, the proposed scheme selects optimal V3s and their duty ratios in two orthogonal subspaces. Thus, it can simultaneously track the references in both orthogonal subspaces. In this approach, the optimal V3s and their duty ratios are directly obtained from the principle of deadbeat current control without time-consuming enumeration-based state predictions and cost function calculations. In addition, the obtained optimal V3s and their duty ratios are adopted to rearrange the pulse sequence to obtain constant switching frequency and can be simply synthesized by carrier-based pulsewidth modulation. Furthermore, a discrete time disturbance observer is designed to improve the robustness of the proposed FCS-MPCC against parameter mismatch. Finally, comparative experiments with traditional MPCC schemes for five-phase surface-mounted permanent magnet synchronous machine are carried out to verify the effectiveness of the proposed scheme.

Improved Finite Control-Set Model-Based Direct Power Control of BLDC Motor With Reduced Torque Ripple

This paper deals with active torque ripple compensation based on direct power control of permanent magnet brushless DC (BLDC) motor drive. The torque undulations caused by the mismatch between stator current and its nonsinusoidal back electromotive force (back EMF) waveforms is a well-known issue on BLDC motor drives. In this paper, to remedy this problem, a simple and comprehensive direct power control based approach is proposed. Instead of using conventional field-oriented control or direct torque control schemes, which are widely used in ac machines with sinusoidal flux distribution, an alternative approach is presented to control the mutual torque production through an active and reactive rotor power control loop. As a result, the proposed approach provides a simple way to reduce torque ripple of a permanent magnet synchronous motor with nonsinusoidal back EMF without requiring rotor orientation or back EMF harmonic content estimation method. In order to synthesize the proper input voltages in the context of torque ripple minimization, high bandwidth controllers are required to cope the torque ripple frequencies. In this sense, the power control loop is implemented based on two-vector finite control-set model-based predictive control approach, which provides fast torque response and good steady-state performance. The validity of the proposed control scheme for low torque ripple BLDC motor drive is verified through experimental results, achieving good steady-state performance while maintaining quick dynamic response.

Rotor position estimation scheme with harmonic ripple attenuation for sensorless controlled permanent magnet synchronous motors

To achieve high-performance sensorless control of permanent magnet motors with non-sinusoidal back electromotive force (EMF), an improved sliding mode observer (SMO) adopting synchronous rotating low-pass filter (SRLPF) is proposed. The SRLPF is utilised to reduce the back-EMF harmonics and extract the fundamental component. Different from the traditional rotor position observer, the proposed observer can calculate the rotor position with the back-EMF fundamental component. Owing to the decrease in the influence of non-sinusoidal back-EMF, the estimated rotor position harmonic ripple error can be greatly reduced. Then, the high estimated accuracy and excellent sensorless control performance can be obtained. In addition, the proposed strategy is easy for implementation. With the comparison between the traditional SMO and the proposed observer, the experiments of the system steady-state error, the speed tracking performance, and the disturbance rejection ability in the speed range from 60 r/min to the rated speed 750 r/min are presented. The validity of the proposed method is conformed.

Predictive control of permanent magnet synchronous motor with non‐sinusoidal flux distribution for torque ripple minimisation using the recursive least square identification method

To reduce the torque ripple of permanent magnet synchronous motor with non-sinusoidal flux distribution, a new method is presented in this study. This method is based on model predictive control (MPC). MPC is a model-based control and requires an accurate model of the motor. A sliding mode observer, accompanied with a recursive least square estimator, is utilised to determine the magnitudes of the harmonics of the back electromotive force (EMF) waveforms. The appropriate current harmonics, considering the back EMF harmonics, are injected to shape the motor current. The interaction of non-sinusoidal back EMF and the shaped current leads to torque ripple reduction. The experimental results verify the effectiveness of the proposed method.

A harmonic current injection method for electromagnetic torque ripple suppression in permanent-magnet synchronous machines

Electromagnetic torque model is built in this paper for permanent-magnet synchronous machine (PMSM) with non-sinusoidal back electromotive force (back-EMF) and current. Electromagnetic torque is divided into four parts depending on the different combinations of fundamental and harmonic component. Effects of current harmonic order, amplitude and initial angle on average torque and torque ripple are investigated based on the mathematic model. Desired harmonic parameters are obtained from the analysis, in order to suppress the torque ripple as much as possible. Further, a method for reducing the 5th and 7th harmonic components of torque ripple is proposed, according to the characteristics of back-EMF harmonic distribution. The proposed method is greatly simplified and more feasible by only injecting 5th and 7th harmonic currents. The theoretical analysis validity has been proved by finite element (FE) simulation, and the FE results show that torque ripple would be more effectively reduced by injecting proper harmonic current than weakening it merely.

Adaptive internal model-based suppression of torque ripple in brushless DC motor drives

Permanent-magnet synchronous motors (PMSMs) are widely used as high-performance variable-speed drives. Ripple in the electric torque of such motors is often a source of vibration and tracking errors, especially at low speeds. We study the torque characteristics of PMSMs and propose a method to minimize the torque ripple. First, we establish a detailed model for the motor and present a Fourier analysis of the torque ripple, caused by the non-sinusoidal back electro-motive force (BEMF) and the cogging torque, where the main conclusion is that the frequencies present in the torque disturbance are integer multiples of six times the electric frequency. The resulting model is highly nonlinear. We propose an adaptive controller based on the internal model principle, where the resonant frequencies of the controller and the associated gains change according to the motor speed. This is achieved by replacing the time variable by the motor angle, which simplifies the nonlinear model. Our approach is passivity based and will work also for complex mechanical loads and several resonant frequencies. Simulation and experimental results are given to verify the new controller. We compare the performance of our adaptive algorithm with the well-known one from [Canudas de Wit, C., & Praly, L. (2000). Adaptive eccentricity compensation. IEEE Trans. Control Syst. Technol. 8, 757–766]. We find that it performs similarly in simple configurations, and it works also when the motor is part of a more complex system, for example, when the motor is connected to a load via a very flexible shaft.

Current Control for Dual Three-Phase Permanent Magnet Synchronous Motors Accounting for Current Unbalance and Harmonics

This paper proposes an improved vector space decomposition current control scheme for dual three-phase permanent magnet (PM) synchronous motors having two sets of three-phase windings spatially shifted by 30° electrical degrees. A proportional-integral (PI) and resonant (second) controller is developed for eliminating the current unbalance in αβ subplane, which is effective irrespective of the degree of current unbalance, while PI plus multifrequency resonant (second and sixth) control is employed to eliminate the current unbalance, fifth and seventh current harmonics in z <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> z <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> subplane. Compared with existing methods only accounting for current unbalance in z <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> z <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> subplane, the proposed method has considered the current unbalances in both z <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> z <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> and αβ subplanes and can eliminate them simultaneously at the steady-state of operation. Consequently, the full compensation of current unbalance can be achieved, by which both the current unbalance between two sets and current unbalance between phase windings in each set are eliminated. Meanwhile, the fifth and seventh current harmonics caused by nonsinusoidal back electromotive force and inverter nonlinearity can also be fully compensated. The effectiveness of proposed method is verified by a set of comparative experiments on a prototype dual three-phase PM machine system. It shows that fully balanced currents without the fifth and seventh current harmonics at the steady state of operation can be achieved.