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PMSM parameters under different current amplitudes and phases (a) Self‐inductance, (b) Mutual inductance, (c) PM flux ψabc, (d) Cogging torque Tcog
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Modelling of the permanent magnet synchronous motor (PMSM) torque ripple and PMSM current harmonics controlling technology are important branches of PMSM research. Based on the existing linear PMSM model derived from magnetic co-energy, this study considers the variation of PMSM parameters (inductance, permanent magnet flux and cogging torque) caus...
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Citations
... Where, F 0 , T 0 is the nominal thrust and nominal torque, A k , B k are linear motor and rotary motor harmonic amplitude components, respectively, d k , f k are linear motor and rotary motor harmonic frequency components, the value is generally an integer multiple of the number of motor pole pairs (pole distance), x, u are linear motor and rotary motor displacement and angle values, respectively. There has been considerable research on the modeling and evolution of each sub-harmonic disturbance in the servo motor operation process, 34,35 and explicit expressions have been developed. For example, the linear motor cogging force can be expressed as equation (11) 36 : ...
The use of mechatronic integrated equipment, such as servo feed drive systems, has become increasingly important in high-end manufacturing, aerospace, and semiconductor industries. However, while advancements in modeling and analysis have improved deterministic feed systems, there is a lack of research into uncertain motion accuracy due to random factors in actual working conditions. This paper aims to address this issue by analyzing the uncertainty of motion accuracy in single-axis feed drive systems. Random factors already impact both positioning accuracy and repeatability, while dynamic errors are reflected in the mean and variance of following errors. The study also considers the impact of disturbance uncertainty, parameter uncertainty, and model uncertainty on motion accuracy. To investigate the impact of these sources of uncertainty on a six-degree-of-freedom linear motor feed system, a simulation example using the Monte Carlo simulation algorithm was utilized. The analysis revealed that uncertainty indeed has an impact on motion accuracy. This research will help identify and improve random errors in servo feed systems, ultimately leading to the development of strategies for reducing motion accuracy uncertainty and enhancing the accuracy and reliability of feed systems in high-end manufacturing, aerospace, and semiconductor industries.
... From Figure 6, although the three controllers have different overshoots, it can be Figure 5 shows the PMSM stator three-phase current waveforms for both controllers. Comparing the current waveforms, it can be seen that the sliding mode controller based on the disturbance observer compensation has a higher sinusoidality for the three-phase currents and contains less harmonic currents, which in turn reduce the losses during PMSM operation [28]. ...
... Figure 5 shows the PMSM stator three-phase current waveforms for both controllers. Comparing the current waveforms, it can be seen that the sliding mode controller based on the disturbance observer compensation has a higher sinusoidality for the threephase currents and contains less harmonic currents, which in turn reduce the losses during PMSM operation [28]. Figure 6 shows the speed and current response waveforms of the three controllers. ...
In this paper, a backstepping sliding mode controller based on a nonlinear disturbance observer (NDO-SMC) is proposed to realize the high-performance speed control of a permanent magnet synchronous motor (PMSM). This paper compares the advantages and disadvantages of the traditional backstepping sliding mode control algorithm (SMC) and integral backstepping sliding mode control algorithm (I-SMC) in the face of mismatched disturbances. In view of the shortcomings of these two algorithms, the idea of using a disturbance observer to observe disturbance and carry out dynamic compensation is proposed, and the composite controller is designed. The overshoot and settling time is improved by 30% and 8 s, respectively, for the proposed NDO-SMC controller compared with the SMC controller. The simulation and experimental results illustrate that the designed controller not only effectively solves the torque jitter problem of SMC, but also improves the overshoot problem caused by the integral module of I-SMC. There is also a better matching degree between the theoretical derivation, the simulation results, and experimental data. It also proves that the composite control algorithm proposed in this paper provides a meaningful solution to the operation disturbance suppression problem of the permanent magnet synchronous motor.
... where, n represents the current harmonic order; N represents natural number; dn u and qn u represent th n d-axis and q-axis voltage component in th n rotating coordinate system in [25]; k can be obtained by the following equation. ...
... The goal of harmonic elimination (the harmonics are controlled to 0) is unified under different fundamental voltage amplitudes and phases, while harmonic injection is different. The voltage (fundament and harmonics) is related with both current and speed [25]. This makes it difficult to calibrate the switching angle MAP. ...
Harmonic injection is commonly used in permanent magnet synchronous motor torque ripple minimization (TRM) of electric vehicle. Traditional inverter switching frequency limits TRM application at high speed due to harmonic modulation accuracy and inverter loss. To achieve TRM in the whole speed range and reduce inverter loss, a novel online calculated low carrier ratio pulsewidth modulation (LCRPWM) is proposed in this article. The carrier ratio determining regular according to the injected harmonics is established first. The relationship between injected harmonics and LCRPWM switching angle is revealed and a set of nonlinear equations is established. Thus, the problem is transformed from solving nonlinear equations into optimization by establishing a cost function. The analytical solutions of nonlinear equations are obtained, which avoids iterative operation and plunging into local minimum. Therefore, the switch angle solution method is suitable for online calculation. The LCRPWM is verified in simulation compared with the traditional regularly sampled space vector PWM, which achieves better results in voltage harmonic injection and flux tracking at a much lower switching frequency. At last, the LCRPWM is used in a test bench experiment that shows good TRM effects. The influence of sideband harmonics on torque ripple is analyzed.
... 6 Compared with induction motor, PMM does not need excitation current, so the power factor can be significantly improved. 7,8 In addition, PMM has no rotor resistance loss in stable operation, and reduces stator current and stator resistance loss. 9,10 In general, the efficiency of PMM is more than 5% higher than that of the induction motor of the same specification. ...
Sound quality (SQ) has become an important index to measure the competitiveness of motor products. To better evaluate and optimize SQ, a novelty SQ evaluation and prediction model of high-speed permanent magnet motor (HSPMM) with better accuracy is presented in this research. Six psychoacoustic parameters of A-weighted sound pressure level (ASPL), loudness, sharpness, roughness, fluctuation strength (FS), and perferred-frequency speech interference (PSIL) were adopted to objectively evaluate the SQ of HSPMM under multiple operating conditions and subjective evaluation was also conducted by the combination of semantic subdivision method and grade scoring method. The evaluation results show that the SQ is poor, which will have a certain impact on human psychology and physiology. The correlation between the objective evaluation parameters and the subjective scores is analyzed by coupling the subjective and objective evaluation results. The average error of multiple linear regression (MLR) model is 7.10%. It has good accuracy, but poor stability. In order to improve prediction accuracy, a new predicted model of radial basis function (RBF) artificial neural network was put forward based on genetic algorithm (GA) optimization. Compared with MLR, its average error rate is reduced by 3.16% and the standard deviation is reduced by 1.841. In addition, the weight of each objective parameter was analyzed. The new predicted model has a better accuracy. It can evaluate and optimize the SQ exactly. The research methods and conclusions of this paper can be extended to the evaluation, prediction, and optimization of SQ of other motors.
... Typically, the influence of the rotor position is neglected. However, some modelling approaches exist in the literature that emphasise the importance of considering the rotor dependence in the machine model, see e.g., [8][9][10][11][12][13]. ...
... Due to the interaction of the nonsinusoidal stator field distribution with both that of the rotor as well as that of the reluctance, only integer multiples of the 6 th fundamental stator frequency f s are present in ψ dθ and ψ qθ . This is due to the interaction of the three phases, see e.g., [11,12,27,31]. For the motor studied in this research, it has turned out that the 18th harmonic and frequencies greater than the 24th harmonic almost vanish. ...
A nonlinear mathematical model for the dynamics of permanent magnet synchronous machines with interior magnets is discussed. The model of the current dynamics captures saturation and dependency on the rotor angle. Based on the model, a flatness-based field-oriented closed-loop controller and a feed-forward compensation of torque ripples are derived. Effectiveness and robustness of the proposed algorithms are demonstrated by simulation results.
... Due to the high power/torque density and high efficiency, permanent magnet synchronous machine (PMSM) has been used widely in the industrial servo drive, renewable energy generation system and electrical vehicle [1,2]. The machine parameters including the stator resistance, rotor flux linkage and d-, q-axes inductances are essential to fault diagnosis and high-performance control of PMSM [3][4][5][6]. However, the multiple-solutions problem exists in solving the steady-state equations of PMSM in the dq-axis reference frame. ...
... Recently, the signal injection is an effective way to estimate machine parameters [18,5,[20][21][22][23][24][25]. This way may not be sufficient to make the estimation model unique-solution if it does not consider changes in motor model, such as dynamic change on the inductance. ...
Online estimation of the machine parameters is essential to fault diagnosis and high‐performance control of permanent magnet synchronous machine (PMSM). The signal injection is an effective way to estimate machine parameters. However, the inductance variation caused by signal injection will result in difficulties for the estimated parameters to converge. At the same time, online parameters estimation brings heavy burden to the operation of control system. To solve these two problems, optimized inductance model is built with the step‐pulse injection to improve the accuracy of estimation. Compared with the existing method, the step‐by‐step parameter estimation method is adopted and orders of feedback matrix are reduced, which improves the computation efficiency. The forgetting factor recursive least square (FFRLS) algorithm is adopted to estimate stator resistance, rotor flux linkage and d‐, q‐axes inductances without acquiring any nominal parameter. The minimum amplitude and appropriate frequency of step‐pulse are determined by the parameter error and convergence analysis. The effectiveness of the proposed method is verified via a 1.5 kW PMSM drive platform.
... Permanent magnet synchronous motor (PMSM) [1][2][3] is widely used by virtue of its high efficiency and high power density. PMSM is divided into interior permanent magnet synchronous motor (IPMSM) and surface permanent magnet synchronous motor (SPMSM) according to the different installation positions of permanent magnets of the motor. ...
—When particle swarm optimization (PSO) is used to identify the parameters of permanent magnet synchronous motor (PMSM), the movement of particles is not selective, which makes the algorithm easy to fall into the local optimum, and the accuracy is poor. The simulated annealing particle swarm optimization (SAPSO) improves the accuracy and evolution speed, but SAPSO has redundant iteration problems. To solve these problems, a motor parameter identification method based on fast backfire double anneal particle swarm optimization (FBDAPSO) is proposed. By reducing the optimization time and quickly tempering and annealing the “misunderstood” difference, the motor adjustable model and fitness function are designed, and the number of iterations is constantly reset to achieve the effect of online identification. Under different working conditions, simulated and experimental results show that the proposed method can quickly and accurately identify the four parameters of the motor’s stator, winding resistance, stator winding d-axis inductance, stator winding q-axis inductance, and permanent magnet flux linkage at the same time, compared with the traditional method of parameter identification, and it has better accuracy, rapidity, and robustness.
... In many applications, the conventional model is considered to be easy to implement and accurate enough for system control [2]. Nevertheless, as mentioned in [3][4][5], inevitable effects such as magnetic saturation and cross-coupling effects may bring about the significant variation of equivalent circuit parameters over the operating range of the machine, especially for the case of either interior PMSMs or large-load conditions. Also that may cause performance degradation of the controller which is based on a conventional linear dq-model. ...
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.
... A genetic approach was used to select the optimal current harmonics for torque ripple minimization in [27]. A torque harmonic coupling model was established in [28]. However, it was not suitable for heavy loads. ...
For permanent magnet synchronous motors (PMSMs) without sufficient design optimization, it is necessary to inject current harmonics to suppress torque ripple. Due to the influence of magnetic saturation, the current harmonics for torque ripple suppression changes with the electrical loads. Based on an existing analytical torque model of a PMSM considering spatial harmonics and magnetic saturation, this paper established a torque harmonic coupling model through a Taylor expansion and a harmonic balance method. Then, based on the torque harmonic coupling model, current harmonic selection for torque ripple minimization was proposed. The validity of the torque harmonic coupling model and current harmonic selection was verified by a finite element analysis (FEA) and experiments on a laboratory PMSM drive system.
... In reference [26], the inductance and PM flux harmonics are considered. For the interior PMSM (iPMSM) with no centre line, the inductance only contains even harmonics (k ∈ 2N) and the PM flux only contains odd harmonics j ∈ 2N + 1 [26]. ...
... In reference [26], the inductance and PM flux harmonics are considered. For the interior PMSM (iPMSM) with no centre line, the inductance only contains even harmonics (k ∈ 2N) and the PM flux only contains odd harmonics j ∈ 2N + 1 [26]. The harmonic orders of cogging torque T cog are determined by the pole slot ratio. ...
... The voltage harmonic waves are thus applied to the motor through the inverter using the SVPWM. The coordinate transformations and inverse coordinate transformations can be found in references [19,26]. ...
Permanent magnet synchronous motors are widely used in electric vehicles. The permanent magnet synchronous motor torque ripple suppression is a research hotspot at present. This study adopts the torque ripple equation based on magnetic co‐energy. Two novel minimum current harmonics torque ripple suppression strategies based on the magnetic co‐energy are proposed. Both methods are suitable for whole current map calculation. One is based on dq‐axis model, which makes the dq‐axis current harmonics fluctuate along gradient direction of the torque equation to dq‐axis currents. The other one is based on the newly proposed torque–current coupling model. The minimum current harmonics obtained by the two methods are basically the same. At last, finite element method and test bench experiment are used to verify the two methods. Both of them can effectively suppress torque ripple.
