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A model of permanent magnet synchronous machine (PMSM) including the electromagnetically originated torque ripple is presented in this paper. This unique representation of such equivalent circuit is highly critical to understand the torque ripple content and to develop an appropriate mitigation scheme for low torque ripple applications requiring four quadrant operations. This research proposes a method to quantify the various sources of torque ripple and modifies the existing DQ-model to enhance the modeling capabilities for both surface-mount and interior PMSMs. The study also presents the effect of slot/pole combination on torque ripple contents by analytical and finite element modeling. Finite element analysis is used for modeling various PMSMs to verify the lumped circuit model proposed in this research. The theoretical results obtained from analytical and finite element analysis are validated using experimental test.

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... Also, more than that numerical methods are usually not easy to apply in motor drive applications because it is difficult to obtain the motor geometrical parameters. An enhanced dq-model of PM machines is proposed to include the torque ripple in [13]. However, the approach also uses simulation results obtained from the FEA to calculate the model parameters. ...

Saturation and cross‐coupling effects have a significant impact on the magnetic behaviour of a permanent magnet synchronous motor (PMSM), which cannot be analysed by the conventional linear model in the direct and the quadrature axis. This study introduces a precise two‐axis flux linkage model for PMSMs to offer a better depiction of the relationship between the flux linkages and corresponding currents. A parameter determination methodology is developed to identify the model parameters for a PMSM, and based on these works; the condition of a PMSM can be estimated. The process requires no geometrical parameter of the machine and little computational effort. Once the model parameters are determined, the torque estimation of a PMSM is simple enough to be made in real‐time in a motor drive controller. Finite‐element analysis and experimental results demonstrate the feasibility and accuracy of the improved model. It follows that the proposed non‐linear PMSM model based on current injection and bivariate function approximation can significantly enhance modelling precision of flux linkage and inductance over the entire range of current excitation in the application of PMSM drive.

... Permanent magnet synchronous motors (PMSMs) are widely used in low and medium power applications such as computer peripheral equipment, robotics, adjustable speed drives and electric vehicles [1]. With lots of advantages, such as high torque density, small size and low maintenance cost, the permanent magnet synchronous motors (PMSMs) find wide applications at home and in industries [2,3,4]. The elimination of slip rings and field exciting coils by using permanent magnets in the rotor results in low maintenance requirement, reduced inertia and losses [5]. ...

A simplified sensorless speed control of permanent magnet synchronous motor (PMSM) using model reference adaptive system (MRAS) is presented. The MRAS is designed and incorporated in a complete closed loop PMSM control system fed by a three-phase inverter that utilizes a simplified hysteresis current control (HCC) to generate gating signals. Accurate rotor position, being essential in PMSM control, is estimated using MRAS rather encoders and resolvers which are explicit position sensors thereby eliminating the drawbacks of the traditional speed sensors in drive systems. The performance of this model is compared with an existing model that utilizes encoders and resolvers. Superior performance was obtained from this new model with MRAS. After initial starting transients, it is observed that the rotor speed for the model with MRAS settled to steady state at 0.10 seconds as against the model with speed sensor which attained steady state at 0.31 seconds. Torque response follows the same pattern to return to the load torque of 11Nm at steady state after starting. After speed reversal, the model with MRAS restored to steady state to track the negative speed command at 0.44 seconds. This is a superior performance compared to the model with speed sensor which settled at 0.60 seconds after speed reversal. The results have clearly shown the superiority of sensorless MRAS over traditional drive models with speed sensors. The software used for this research is MATLAB/Simulink 2017 model. K e y w o r d s: PMSM, senesorless, model reference adaptive system (MRAS), hysteresis current controller (HCC)

... Reference [7] proposed a maximum current limit for motor designs to reduce the impact of irreversible demagnetization of the interior and surface-type permanent magnets brushless DC motor. Reference [8] proposed a method to quantify the various sources of the torque ripple and modifies the existing DQ-model to enhance the modeling capabilities for both surfacemount and interior PMSMs. In reference [9], the loss and temperature fields of an SPM and an IPM are compared, but the electromagnetic field and motor performance were not studied. ...

In order to compare the performance difference of the permanent magnet synchronous motors (PMSM) with different rotor structure, two kinds of rotor magnetic circuit structure with surface-mounted radial excitation and tangential excitation are designed respectively. By comparing and analyzing the results, the difference of the motor performance was determined. Firstly, based on the finite element method (FEM), the motor electromagnetic field performance was studied, and the magnetic field distribution of the different magnetic circuit structure was obtained. The influence mechanism of the different magnetic circuit structure on the air gap flux density was obtained by using the Fourier theory. Secondly, the cogging torque, output torque and overload capacity of the PMSM with different rotor structure were studied. The effect mechanism of the different rotor structure on the motor output property difference was obtained. The motor prototype with two kinds of rotor structure was manufactured, and the experimental study was carried out. By comparing the experimental data and simulation data, the correctness of the research is verified. This paper lays a foundation for the research on the performance of the PMSM with different magnetic circuit structure.

... The blue, red and black parts of the torque characteristic are for the healthy mode, ITSC fault and phase to phase fault respectively. Accordingly, it can be noticed that, first the ITSC and phase to phase faults induce ripples on the level of the torque, which negatively affect the performance of the machine [25]. Second, the magnitude of the ripples depends on the quantity of the voltage drop created by the fault and not by the type of fault. ...

This paper proposes an original, simple and fast permanent magnet synchronous generator model, implemented with a new conception on the graphic interface of Matlab/Simulink environment. The obtained physical model suggests a new way to easily carry out different types of stator faults such as inter-turns short circuit faults, phase to phase faults and phase to ground faults as well as simultaneous multi-faults. This is handled by connecting the two desired points in the stator, on the graphic interface of Simulink, exactly as they can be carried out in the experimental tests. This model has the originality to take into account the arrangement of the stator windings of a multi-pole machine by differentiating between the windings under the same pole-pair and those under different pole-pairs. A comparison between the simulated and the experimental results is done to verify the behavior of the proposed model in both healthy and faulty modes under different operating speeds. The good comparison results lead to validate the correct behavior of the proposed model with a satisfactory accuracy.

... The structure of stator and rotor of PMSM resulting in spatial harmonics flux can cause torque ripple. The literatures [16][17][18] studied torque ripple caused by spatial harmonics of the rotor magnetic field, the 6 k order analytical expression of torque ripple was deduced. It is proposed that the non-sinusoidal distributed air-gap magnetic field is the main source of torque ripple of PMSM. ...

Electromagnetic torque ripple of permanent magnet synchronous motor (PMSM) causes electro-mechanical coupling vibration and noise in hybrid electric vehicle (HEV). However, the traditional mathematical model of PMSM cannot absolutely reflect the reason of torque ripple and variation on the different operation performance of the motor for HEV. The purpose lies in the fact that electromagnet factor originated torque ripple and variation have been taken into account in the mathematic model of PMSM. Based on the classical Park's transformation theory and the Fourier series analysis of magnetic field, a general nonlinear mathematical model of PMSM considering saturation and magnetic field spatial harmonics and time harmonics is presented in this paper. The general analytical model cannot only taking into account the variation of electromagnetic parameters caused by electric vehicle operating, but also can explain the frequency and the order of torque ripple theoretically. The model's effectiveness is tested through finite element analysis simulations and some experimental results. The analytical model presented here can be used for the characteristic analysis, the drive system dynamic precise analysis and fault diagnose of PMSM for HEV.

... However, in PMSMs, relative large torque ripple could be produced by spatial harmonics of the air-gap reluctance and magnetic flux linkage, as well as by harmonics in the stator current. Torque ripple leads to acoustic noise and mechanical vibrations [6], the later could reduce the life span of the machine and other mechanical components affixed to the PMSM shaft. ...

This paper presents a new and simple Finite Control Set Model Predictive Control strategy to reduce the torque ripple in Permanent Magnet Synchronous Machines. The method is based on minimising a cost function that considers the flux linkage torque harmonics obtained from a discrete-time model of the machine. The power converter switching state that minimizes this cost function is selected and applied during a whole sampling period. Additionally it is proposed to mitigate the other source of torque ripple, known as cogging-torque, using a feed-forward signal applied to the torque control loop. A hybrid method, that uses the output information from an observer and look-up table, is presented to obtain a good cogging-torque estimation and thus an accurate mitigation of this disturbance torque at low rotational speed. Experimental results demonstrate the good performance of the torque ripple compensation methods presented in this paper.

... Indeed, this phenomenon generates undesired speed oscillations leading to a lack of precision in critical applications and causes acoustic noises. Commonly, it is established that the pulsating torque can be owed from various sources [1]-[3], such as structural imperfectness associated with the machine design, the cogging torque, flux harmonics, errors in current measurements, and stator phases unbalance. The pulsating torque can be separated into lowfrequency and high-frequency components. ...

Ensuring torque smoothness is an essential requirement in a wide range of high performance applications based on permanent magnet synchronous machines (PMSM). The reported work proposes a novel technique for the compensation of the torque oscillations essentially caused by the spatial harmonics which can result from the machine design imperfectness or/and the operating uncertainties. The main idea of the proposed method is to modify a conventional PMSM controller by superposing an appropriate compensating signal in the inner current loop. The proposed approach allows minimizing torque ripple through a simple synthesis of the compensating signal and does not require a hard calculation cost. A theoretical analysis and some simulation results are presented to show the effectiveness of the proposed compensating method.

Torque ripple is an important factor affecting the smoothness of permanent magnet synchronous motor. However, for high saturation permanent magnet synchronous motor (HSPMSM), the flux linkage of permanent magnet is nonlinear, which leads to poor effect of traditional torque ripple suppression methods. Therefore, by systematically considering the amplitude and phase changes of the permanent magnet flux link‐age for the first time, this paper analyzes the torque ripple mechanism of high saturation motors and establishes a corresponding mathematical model. To minimize the loss caused by harmonic currents, two torque ripple suppression methods are proposed: one based on the NSGA‐II algorithm and the other based on an analytical method. Finally, the effectiveness of the two algorithms is verified by the experimental comparison. The experimental results show that compared with the traditional methods, the two algorithms can effectively suppress the torque ripple under the premise of considering the influence of the motor magnetic saturation on the flux linkage and inductance, and improve the output torque smoothness of HSPMSM.

A Taguchi‐based robust design strategy is proposed to minimise the torque ripple of a 6‐slot/2‐pole modular high‐speed permanent magnet motor in mass production, accounting for manufacturing tolerances of split gap (Δg), misalignment (Δm), and offset angle (Δα). Firstly, the effects and interactions of manufacturing tolerances are calculated, indicating that Δg has the highest effect followed by Δm, positive Δg and negative Δm have a strengthening effect, and Δα has no effect, and subsequently, the worst‐case scenario of manufacturing tolerances with the highest torque ripple is obtained. Afterwards, tooth circumferential positions are optimised for minimising torque ripple without jeopardising average torque, considering the tradeoff between the cases without manufacturing tolerance and with the worst‐case scenario of manufacturing tolerances. As will be demonstrated, torque ripples are reduced significantly, that is, they are particularly reduced by 40% in the worst‐case scenario. Under hypothetical 100 sets manufacturing tolerances as Gauss distributions, the optimised machines have significantly reduced torque ripples (maximum and average reductions are 33% and 16%, respectively) with more concentrated distribution. The correctness of the methods is verified by experimental validation.

This paper proposes a control strategy to reduce speed ripples at low speed working conditions of Permanent Magnet Synchronous Machines (PMSMs) for Electric Vehicle
Applications. The treated issue is related to the periodic torque ripples which induce speed oscillation that deteriorate the drive performance. To ensure a high-performance control regarding this issue, the reported work proposes an original control
method based on Grey Wolf (GW) algorithm. The key idea of the proposed approach is to incorporate the benefit of fast optimization process of the GW optimizer in order to find input controls which satisfy the speed tracking and minimize speed ripples. The proposed method is described and the speed ripple issue is analyzed. Experimental results show that the proposed control method can be implemented in real-time on embedded
hardware, offering high performance in both steady and transient states of the PMSM drives even at low speed range

The classical feedback control method for the permanent-magnet synchronous motor cannot fulfill the dynamic requirement and anti-interference requirement at the same time. In this paper, an adaptive inverse control method with disturbance elimination is proposed based on the vector control including speed and current loops. It avoids the system instability and the anti-disturbance performance of the system can be enhanced as well. Firstly, the speed loop adopts the adaptive inverse controller possessing a feed forward control structure, and a normalized least-mean square filtering algorithm accelerates the speed error convergence. The inverse model of the approximately linearized system is obtained by modifying the weighting factor online. Secondly, in order to suppress and eliminate the influence of motor parameter perturbation and external disturbance on the control system, an extended state observer is designed to observe and compensate the disturbance of the system. Thus, the dynamic performance and anti-disturbance performance of the system can be improved simultaneously. Finally, the effectiveness of the proposed method is verified by experiment and simulation.

The effects of disruptive harmonic torque disturbances on permanent magnet synchronous motor drives originating at the mechanical load or from cogging can be mitigated by producing a counteracting electric torque. The study proposes using an adaptive feedforward controller (AFC) for this purpose. The AFC is designed to operate as an auxiliary loop in parallel with a field-oriented controller, which provides speed control. The AFC input is the motor speed control error. The loop is tuned at the frequency of the harmonic torque and its output is added to the q-axis current reference as a variation current of the same frequency. The main advantage of the proposed method is that it does not require an estimation of the disturbance torque. The theoretical analysis of the scheme is presented in the study. Experimental results are also presented in the study from a motor drive system where the mechanical load produces harmonic torques. The results demonstrate the effectiveness of the AFC in significantly reducing speed oscillations by cancelling the effect of the torque harmonic disturbance.

This paper develops an advanced analytical model for the interior permanent magnet synchronous motor to represent the average and transient components of the electromagnetic torque. The conventional flux linkage model is extended to include harmonics in dq-reference frame. Furthermore, the effects of cross-magnetization and saturation on these components are analyzed. The electromagnetic torque derived from the proposed flux model is utilized to compute the average and pulsating components of the torque. Experiments and finite element analysis have been carried out on interior permanent magnet synchronous motor with concentrated and distributed winding to validate the proposed model under different load conditions.

For the simulation of electrical machines and drive systems, the abc-model brings benefits in terms of accuracy, efficiency and flexibility. In particular, it allows one to naturally include both geometry-and saturation-induced space harmonics. We propose here a novel nonlinear abc-model using current-flux linkage and electromagnetic torque N-D lookup tables. The current-flux linkage lookup tables are built from the flux linkage-current lookup tables using inversion and N-D interpolation. The abc-model is validated by comparison with the circuit-coupled finite element model, in both steady and transient state, for balanced and unbalanced operation. It gives the same results as the finite element model with a speedup factor of about two orders of magnitude.

A coupled finite element phase-domain model for superconducting synchronous machine is presented. It allows fast and accurate prediction of the transient and steady-state behavior of grid-connected machines. On the one hand, the machine self and mutual inductances as function of rotor angle are obtained from static finite element analysis. On the other hand, the machine is represented by a lumped-parameter phase-domain model. This approach offers two main advantages. Firstly, as opposed to the classical qd model, the phase-domain model takes into account inductance space harmonics. Secondly, it allows easy and efficient simulation of machine transients with the same accuracy as the one that could be obtained with a computationally expensive full finite element model. To show the flexibility of the proposed method, it is applied to an air-cored high temperature superconducting 10 MW class wind turbine generator with double layer distributed three-phase armature windings connected to the grid through an AC/DC/AC converter.

The simultaneous observation of rotor flux and angular speed in induction motor drive is subject to unstability problems, especially in regenerating mode. Many solutions have been proposed in the literature. In this article, an optimal observer design is proposed in order to reduce the unstability region to a simple line in the torque/speed plane

The paper discusses the approach to analytical calculation of the cogging torque in PM brushless motors. Magnetic field energy in the air gap has been used to calculate the torque. Two equations have been derived: with the PM width taken into account, and simplified equation, i.e., without the effect of the finite width of the PM. The effect of eccentricity has been included too. Analytical results have been compared with laboratory test results.

This paper presents an approach for reducing the torque ripple of
permanent magnet brushless DC motors. The technique requires
coordination of an outer speed loop with an inner current loop. The
inner current loop is responsible for shaping the phase currents during
the commutation intervals. The outer speed loop is responsible for
commanding the magnitude of the phase currents. It is shown that the
speed loop must be sufficiently fast that the commanded phase current is
able to respond to potential ripple torque during phase commutation; a
simple direct adaptive controller satisfies this requirement. The inner
current loop must be able to adaptively change the slope of the
commanded current in order to avoid poor current regulation through
inverter saturation in the face of large back EMFs. The composite
control is able to reduce torque ripple to a level which is dictated by
phase ripple currents

Three-phase permanent magnet brushless DC motors are widely used. As a function of the rotor position, the torque produced by these machines has a pulsating component in addition to the DC component. This pulsating torque has a fundamental frequency corresponding to six pulses per electrical revolution of the motor. The shape of the torque waveform and, thus, the frequency content of the waveform can be influenced by several factors in the motor design and construction. This paper addresses the various factors that influence the torque waveshape. It is shown that in addition to the basic induced electromotive force (EMF) waveshape, the magnetic saturation in the stator core, and the accuracy in the skewing are also key factors in determining the torque waveshape. Computer simulation using finite element technique has been conducted to study the torque waveform. Simulation results successfully duplicated the torque waveforms measured in experiments under different excitation currents.

Although adjustable-speed drives (ASDs) with induction machines (IMs) have already evolved as a mature technology, accurate encoderless operation at very low speed range remains to be problematic for all existing control methods, which include nonlinearity compensation, model-reference-adaptive-system (MRAS), various types of observers, high frequency injection leveraging saliency effects, artificial intelligence (AI) or neural network techniques. These encoderless solutions are integrated into either direct torque control (DTC), or stator current regulated pulse-width-modulated (CRPWM) controllers. The DTC solution can have better dynamic responses, while the CRPWM regulator provides superior steady state performances. In the category of observer formulations without signal injection, one promising dual frame sliding mode observer (DFSMO) can achieve a published performance of below 6 revolutions per minute (rpm) (0.2Hz) at full load under a DTC scheme. DFSMO does not need the rotor position or rotor flux angle, thus it increases the estimation accuracy and is tolerable to IM parameter variations and disturbances. Even though DTC schemes have been researched more in recent years, the rotor flux orientated vector control (RFOVC) architecture still dominates industrial applications. In this paper, instead of DTC, a DFSMO is developed under the RFOVC architecture which cannot be found in published literatures to demonstrate its transient and steady-state low speed performances at both motoring and regenerating mode. Analytical, simulation studies are presented and verified through a 3hp (2.2kW), 380V, 50Hz IM ASD experimental system.

Since last decade many novel interior permanent magnets motors' (IPM) have been developed and introduced in a mass production. Such design has many advantages comparing to well known surface motors' designs; especially it is very robust in terms of permanent magnet requirements: a simple block shape and lower quality issue. These factors play very important role particularly if the costs of neodymium magnet (NdFeB) are under high price fluctuation. Utilization of the IPM motor for sensitive application requires a skewing to minimize cogging and torque ripple. Unfortunately, a skewed IPM motor operates in a field weakening area causing increase of a torque ripple and a motor vibration. This phenomenon is caused by the load dependent reluctance within axial motor's length. This paper describes the presented problem and possible solution for an IPM motor used in automotive area.

The main drawback of reluctance machines is a high torque ripple, due to the interaction between the stator magneto-motive force and the rotor structure. Adopting a rotor configuration characterized by several flux barriers per pole, there is a high influence of the rotor geometry on the machine performance, in terms of both average torque and ripple. An optimization is often required to determine the optimal rotor geometry so as to achieve a high and smooth torque. Then, the geometry determined above should guarantee good performance for various operating points (i.e., changing the current amplitude and phase), as well as for small variations of the geometry. This paper investigates this aspect, showing the results of optimizations carried out on various machines. The impact of the geometry parameters is taken into account and the sensitivity of the optimal solution to the geometry variation is pointed out. The paper highlights the difficulty to get a robust geometry as far as the torque ripple reduction is concerned. Finally, a few experimental results on a Synchronous Reluctance motor prototype will be presented, compared with Finite Element Analysis simulations for validation.

In this paper, three calculation methods of torque for Surface-Mounted Permanent Magnet Synchronous Machines (SPMSMs) are performed, and the results including the average torque and the torque ripple from each method are compared. This is in order to enable one to choose an effective torque estimation technique for further torque ripple minimization in these machines. Accordingly, a vector controlled motor-drive model, including torque ripple minimization techniques, was developed. In this paper, a current harmonics injection and an adaptive internal model algorithm were developed for the torque ripple minimization in the vector control drive system. The corresponding simulation results are given and compared in this paper. An equivalent circuit model coupled to a Time-Stepping Finite Element (TSFE) model of the motor-drive system built in Ansoft-Maxwell V14.0 was developed to verify the above mentioned torque ripple minimization control techniques, which reduce the torque pulsations as well as eliminate the need for skewing the stator windings or the rotor permanent magnet (PM) mounts in SPMSMs.

In this paper two algorithms for sensorless control of induction machines, linear reduced-order and sliding mode observer will be discussed and compared. The linear reduced-order method is a third order disturbance observer which is very simple to design and execute, while the sliding mode observer is complicated. It will be shown by the simulation results that the estimated speed by the two methods are very well, but proposed reduced order observer is sensitive to the stator and rotor resistance parameters while the sliding mode observer is robust against parameter variation.

A permanent magnet motor with power semiconductor supply and shaft position sensing can be constructed using radially- directed high energy magnets on its rotor. This paper presents equivalent circuit models for such motors. The model parameters are related to the motor structure and dimensions. Computed values of parameters are compared with those measured from two experimental motors with different rotor construction.

A new family of speed-sensorless sliding-mode observers for induction motor drives has been developed. Three topologies are investigated in order to determine their feasibility, parameter sensitivity, and practical applicability. The most significant feature of all schemes is that they do not require the rotor speed adaptation, i.e., they are inherently sensorless observers. The most versatile and robust is a dual-reference-frame full-order flux observer. The other two schemes are flux observers implemented in stator frame and rotor frame, respectively. These are simpler than the first one and make use of the sliding-mode invariance over a specified range of modeling uncertainties and disturbances. Main theoretical aspects, results of parameter sensitivity analysis, and implementation details are given for each observer in order to allow the comparison. Experimental results with the dual-reference-frame observer, considered the most adequate for practical applications, are presented and discussed. Sensorless operation with a sliding-mode direct-torque-controlled drive at very low speeds is demonstrated. It is concluded that the new proposed observers represent a feasible alternative to the classical speed-adaptive flux observers.

Permanent magnet synchronous motors feature high power density, high torque to inertia ratio and high conversion efficiency. These characteristics made them advantageous to use in specific applications such as robotics and traction. However, one of the major drawbacks of these motors is the torque ripple, being especially harmful when a high performance position and speed control is required. Usually, this effect can be reduced in the design stage, although several approaches to online reduction have been proposed. In this paper a mathematical model is proposed which calculates the torque based on an energy approach, allowing to incorporate the harmonic components of the torque. Simulation results show the performance of the proposed approach.

Two problems must be solved in the speed sensorless vector control of induction motor drive: the speed estimation and rotor flux observation. Because of the multiplication terms of state variables, the induction motor model is the non-linear state equations. To estimate the state variables of motor model and gain the rotor flux and speed signals, the paper proposes a method to estimate them using extended Kalman filter. Experiment is based on the DSP design system for digital motor control. Software programs carry out extended Kalman filter algorithm to estimate the rotor speed and fluxes. The satisfied experimental results prove that extended Kalman filter algorithm can real time estimate rotor speed and flux very accurately, and based on which the speed sensorless drive system has good static and dynamic performance.

Rotor flux observers can provide an attractive means for achieving direct field oriented control of induction machines. This paper presents a physics-based design methodology and uses it to evaluate open-loop observers and to develop a new closed-loop flux observer. It is shown that the new flux observer is a straightforward structure with properties that combine the best features of known methods. A distinction is made between observers, which use only integration and feedback summation operations, and those estimation methods requiring approximate differentiation which are, in essence, "cancellation" methods. Furthermore, a clear distinction is made between accuracy and dynamic robustness of the observer. This distinction is important because the accuracy of flux observers for induction machines is inherently parameter sensitive, whereas robustness of observers, in a controls sense, is not parameter sensitive. Moreover, it is shown how flux observers can provide robust field oriented control because the flux angle is substantially more correct than the flux magnitude. A distinctive form of frequency response function (FRF) analysis similar to that used in classical control engineering is demonstrated to be a useful and insightful tool even though flux observers are multiple-input, multiple-output systems. Finally, the limits of such flux observers are experimentally evaluated.<
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A neural network based estimator for torque constant and stator resistance in permanent magnet synchronous motors (PMSM) is presented. The neural weights are initially chosen randomly and a model reference algorithm adjusts those weights to give the optimum estimations. The q-axis inductance is modeled offline according to q-axis stator current. The neural network estimator is able to track the varying parameters quite accurately at different speeds with consistent performance. The neural network parameter estimator has been applied to slot and flux linkage torque ripple minimization of the PMSM. The drive system is insensitive to these parameter changes. Simulation results justifying the claim are presented.

This paper focuses on the design and analysis of a direct field orientation (DFO) approach based upon a closed-loop rotor flux observer. The approach is ideally suited for applications requiring both zero and very high (i.e. several times base) speed operation. The observer effectively combines the best accuracy attributes of rotor flux indirect (feedforward) field orientation (IFO) and stator flux DFO. The parameter sensitivity is similar to IFO at low and zero speeds and to stator flux DFO at high speeds. The closed-loop observer provides a smooth transition between two open-loop rotor flux observers referred to as the current and voltage models in a deterministic manner set by the closed-loop eigenvalues. The proposed DFO approach is analytically evaluated in comparison with both IFO and stator flux DFO. Experimental results verify the viability of this approach.< >

Several high-performance motor drive applications require the motor drive to produce smooth torque with very stringent torque-ripple requirement. This paper is focused on various machine design considerations that can be used in reducing the torque ripple of a sinusoidally excited permanent-magnet brushless dc motor. The paper quantifies the various sources of torque ripple, which may be minimized by appropriate design considerations. The paper discusses the factors influencing the harmonic content of the induced voltage, effect of slot/pole combination, winding distribution, and magnetic saturation. Design optimization is directed to minimize cogging torque and the harmonic contents in the back electromotive force, thus reducing the overall torque ripple. Comprehensive finite-element (FE) analysis along with experimental data are provided to validate the theory. The research demonstrates that saturation in the magnetic circuit is another major contributor to the torque ripple and torque nonlinearity as the current increases. A model is developed to study the saturation effect on torque linearity and is verified by FE simulation. Design techniques have been provided to minimize the overall torque ripple and increase the torque linearity.

For pt.I see ibid., vol.25, no.2, p.265-73 (1989). The authors
develop a phase variable model of the BDCM (brushless DC motor) and use
it to examine the performance of a BDCM speed servo drive system when
fed by hysteresis and pulsewidth-modulated (PWM) current controllers.
Particular attention was paid to the motor large-signal and small-signal
dynamics and motor torque pulsations. The simulation included the
state-space model of the motor and speed controller and real-time model
of the inverter switches. Every instance of a power device turning on or
off was simulated to calculate the current oscillations and resulting
torque pulsations. The results indicate that the small- and large-signal
responses are very similar. This result is only true when the timing of
the input phase currents with the back EMF (electromotive force) is
correct. The large-signal and small-signal speed response is the same
whether PWM or hysteresis current controllers are used. This is because,
even though the torque pulsations may be different due to the use of
different current controllers, the average value which determines the
overall speed response is the same

The application of vector control to the PMSM (permanent-magnet
synchronous motor) is described, and complete modeling, simulation, and
analysis of the drive system are presented. State-space models of the
motor and speed controller and real-time models of the inverter switches
and vector controller are included. Performance differences due to the
use of pulsewidth-modulation (PWM) and hysteresis current controllers
are also examined. Particular attention is paid to the motor torque
pulsations and speed response. Some experimental verification of the
drive performance is also given