Harmonic Torque Research Articles

Multimotor Drive Control Method of Upper-Retort-Robot Based on Machine Vision

In the cold season, wine aids in maintaining body temperature and is advised for military officers. This paper proposes a study on the multimotor drive control method of the upper-retort-robot based on machine vision for wine brewing automation to meet the demand of military areas located in cold regions, as wine is recommended to keep soldiers’ body temperatures normal in China’s extremely cold regions. Based on machine vision, the target is converted into an image signal by an image pickup device and is sent to the image processing system. Pixel distribution, brightness, color, and other data are transformed to digital signals, and target attributes are retrieved to control the field equipment’s operations. The Monte-Carlo approach is used to generate joint variables at random within each joint’s fluctuation range. The positive aspects of kinematics model are utilized and the working space of the upper-retort-robot is calculated using multimotor drive control method. The multimotor drive compensates the harmonic ripple torque and establishes the fault-tolerant automatic control of the system to maintain quality of the liquor. The results of the experiments reveal that the robot arm can reach any place within the barrel’s set range. To control the quality of the liquor, the robot will function in an automatic manner. The robot’s transmission performance is capable of meeting the requirements for automated liquor quality control during the production of wine from grapes. The results show that the suggested multimotor drive control (MMDCM) approach is robust and viable in terms of robot transmission performance and dexterity.

Six-Step Operation of a Symmetric Dual Three-Phase PMSM With Minimal Circulating Currents for Extended Speed Range in Electric Vehicles

Automotive applications demand high efficiency, good reliability, and a wide operating speed range within limited dc bus voltage constraints. In this article, a zero degree displacement dual three-phase permanent magnet synchronous machines (PMSM) is derived from an original three-phase PMSM to enhance the power rating as well as the operating speed range. The proposed topology can be used as an alternative to the conventional configuration of three-phase PMSM with a bidirectional dc–dc converter for electric vehicles. Even though the commonly used dual three-phase PMSM with split-phase winding eliminates the sixth harmonic torque pulsation, a large circulating current is generated during six-step operation, which results in additional stator copper loss. In this article, six-step operation of the symmetric dual three-phase PMSM with zero degree winding displacement is proposed to achieve maximum inverter utilization. Both harmonic circulating current and torque pulsation were observed to be within satisfactory levels using this configuration. A changeover algorithm is also proposed to enable a smooth transition between closed-loop current vector control during low and medium speed operation to open-loop six-step voltage angle control for high speed operation. The performance of the proposed method is experimentally validated on a 3-kW dual three-phase PMSM drive.

Magnetic Field and Radial Force Analysis of Six-Phase Rotary Machine

Six-phase permanent magnet synchronous machine and the control system are also widely used in industry, precision instruments and aerospace. However, most PMSMs employ magnet patterns either in alternatively radial magnetization or Halbach array, which may constrain the performance improvement in a certain degree. Therefore, a novel six-phase trapezoidal Halbach magnet array (THMA) is proposed in this paper. Six-phase permanent magnet synchronous machines (PMSMs) can reduce the harmonic components of magnetic flux in air gap, and decrease the iron loss and electromagnetic vibration caused by harmonic torque. Thus, it helps to improve the working efficiency and depress the torque ripple of the electrical machine. Dual three-phase windings are employed for the stator design to further improve the power density and reliability of the machine. Six-phase vector model of the machine is built based on dual dq control. It can minimize the electric coupling, magnetic coupling and thermal coupling. The radial electromagnetic force of the machine under load or no load is extracted, then the harmonic decomposition of the radial electromagnetic force for the spatial with time Fourier decomposition is carried out to obtain the force amplitude of different orders which is conducive to analyze the vibration characteristics of the machine.

Iterative Learning Based Torque Ripple Suppression of Flux-Modulation Double-Stator Machine

Due to the double-layer airgap configuration, the even-order harmonic components exist in the phase back electromotive force (EMF) of flux-modulation electrically excitation double-stator synchronous machine (FMEE-DSM), thus resulting in relatively high torque ripples. To promptly and effectively suppress these torque ripples, this article proposes and implements a second-order iterative learning control (ILC) strategy to minimize the main harmonic torque components based on the periodically repetitive characteristic of torque ripples in the FMEE-DSM. Via harmonic analysis on the torque ripples caused by the cogging torque and the nonsinusoidal induced EMFs, the dominative harmonic component, namely, the seventh-order component, can be precisely identified and then involved in the proposed ILC for torque ripple suppression. To verify the feasibility of proposed control strategy, a test bench of the FMEE-DSM control system was built based on dSPACE 1103. Accordingly, both the static and dynamic performances of the FMEE-DSM were investigated under the conditions of no-load and rated load. The theoretical analysis, computer simulation, and hardware experimentation are given to verify the proposed second-order ILC.

A New Robust Method to Investigate Dynamic Instability of FTV for the Double Tripod Industrial Driveshafts in the Principal Parametric Resonance Region

The present work aims to design a robust method to detect and certify the deterministic chaos or ergodic process for the forced torsional vibrations (FTV) of a double tripod industrial driveshaft (DTID) in transition through the principal parametric resonance region (PPRR) which is considered by the researchers in the field as one of the most important resonance regions for the systems having parametric excitations. The DTID’s model for FTV considers the following effects: nonuniformities of inertial characteristics of the DTID’s elements, the harmonic torque excitation induced by the asynchronous electrical motor used for a heavy-duty grain mill, and the harmonic reaction torque generated by different granulation of the substance needed to be milled. Based on these aspects, a model of the FTV for the DTID was designed which was a modified, physically consistent model already used by the authors to investigate the FTV of automotive driveshafts (homokinetic transmission). For the DTID elements, the dynamic instability for nonstationary FTV in the PPRR using time–history analysis (THA) was analyzed—THA represents the phase portraits. Time–history analysis is a detection method for possible chaotic dynamic behavior for the nonstationary FTV (NFTV) in transition through PPRR. If this dynamic behavior was seen, a new robust method LEA–PM was created to certify and confirm the deterministic chaos for the NFTV of DTID. The new method, LEA–PM, is composed of the Lyapunov exponent’s approach (LEA) coupled with the Poincaré Map (PM) applied to the global system of differential equations that describe the FTV of DTID in the PPRR. This new robust method, which embeds LEA and PM, LEA–PM, establishes if the mechanical system has a deterministic chaotic dynamic behavior (strange attractor) or an ergodic dynamic process in this resonant region. LEA represents a new method that includes not only the maximal Lyapunov exponent method (MLEM) but also new mathematical criteria that is “the sum of all Lyapunov exponents has to be negative” which, coupled with MLEM, indicates the presence of deterministic chaos (strange attractors). THA–LEA–PM had been used for the NFTV of DTID computing the phase portraits, the Lyapunov exponents, and representing the Poincaré Maps of the NFTV for the DTID’s elements in transition through PPRR, founding deterministic chaos or ergodic dynamic behavior. Based on the obtained results, numerical simulations revealed the pitting manifestations of the DTID’s elements, typical for the geared systems transmission, mentioned recently in experimental data research for the homokinetic transmissions. Using the new robust method, THA–LEA–PM (time–history analysis coupled with LEA–PM) can be used in future research for chaotic dynamic analysis of DTID’s NFTV transition through superharmonic resonances, subharmonic resonances, combination resonances, and internal resonances. Time–history analysis as a detection method for chaos and LEA–PM as a certifying method for deterministic chaos can be integrated as a design tool for DTID’s FTV control of the homokinetic transmission.

Effects of high-order space harmonics on the operation of five-phase induction machines under unbalance

The paper addresses the effects of high-order space harmonics on the steady-state performance of five-phase induction machines operating under unbalance. We show that the airgap harmonic fields with orders higher than three, although usually disregarded, can produce a significant increase in the torque pulsation and in the Joule losses. We propose a model based on symmetric components which is used to demonstrate that the field produced by each rotor harmonic current is related to two stator sequence currents. Further, the proposed model allows determining additional losses and harmonic torques produced by airgap harmonic fields with orders higher than three, which up to now have not been addressed elsewhere. As a case study, we applied the model to two five-phase induction machines with different designs and assessed the influence of high space harmonics under operation at steady state with one open phase in the stator. The model has been validated by comparing analytical results with results obtained through finite element analysis. Finally, the model validation was also based on experimental results obtained from tests with two prototypes under many different conditions.

Reduction in Selected Torque Harmonics in a Three-Level NPC Inverter-Fed Induction Motor Drive

The reduction or elimination of selected torque and current harmonics is widely used in multilevel inverter fed induction motor drives. A wide range of methods are employed to achieve this goal. Those modes of operation allow the avoidance of certain torque and current harmonics that may lead to disturbance and even mechanical and electrical resonance. In this paper, the selective harmonic elimination technique (SHE-PWM) is employed to reduce the chosen torque harmonics in a three-level NPC inverter-fed induction motor drive. The proposed method is compared with the synchronized carrier pulse width modulation technique (SCPWM). For both schemes of control simulation, a model is proposed using Simulink software. Furthermore, laboratory stand experiments are carried out to verify the correctness of torque harmonics formation.

Correction of Field Orientation Inaccuracy Caused by Resolver Periodic Error and Rotor Time Constant Variation for Indirect Field-Oriented Control Induction Motor Drives

This article proposes an algorithm correcting the field orientation inaccuracy caused by resolver periodic error and rotor time constant variation. It is found that the periodic error brings harmonic current vectors and torque ripples while the rotor time constant variation makes <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">dq</i> currents deviate from the reference values. The cross-product of fundamental and harmonic current vectors contains the information of resolver periodic error. The gradient descent method with a variable step is introduced to compensate the periodic error. During the process, the cross-product is minimized. A new form of cross-product calculation is derived to reduce the computation time. The rotor time constant is identified by the reactive-power based model reference adaptive system (MRAS). Voltages and currents in the stationary reference frame are used in the reference model to avoid the influence of resolver periodic error. Appropriate parameters of the MRAS are selected to guarantee the stability. The algorithm is integrated with an induction motor drive which is based on indirect field-oriented control. The feasibility of the proposed algorithm is verified by simulation results and experiments.

Subharmonic centrifugal pendulum vibration absorbers allowing a rotational mobility

Rotating machines are often subjected to fluctuating torques, leading to vibrations of the rotor and finally to premature fatigue and noise pollution. This work addresses a new design of centrifugal pendulum vibration absorbers (CPVAs), used to reduce the vibrations in an automotive transmission line. These passive devices, composed of several masses oscillating along a trajectory relative to the rotor, are here tuned at a subharmonic of the targeted harmonic torque frequency. Thanks to the inherent non-linearities, a CPVA with two masses oscillating in phase opposition is able to efficiently counteract the input torque, with particular features such as saturation phenomena. This work particularly extends previous works to a new class of CPVA, whose peculiarity is that masses admit a significant rotation motion relative to the rotor, thus adding the benefit of their rotatory inertia. Results on the system’s subharmonic response and its stability are obtained thanks to an analytical perturbation method, and design guidelines are proposed. The validity of those results is also confirmed through comparisons with numerical solutions and the performance of this subharmonic system is compared to that of a classical CPVA tuned at the torque frequency.

Unipolar sinusoidal current excited switched reluctance motor control based on a 3D space vector modulation

This paper reports on a novel unipolar current excited control scheme for the asymmetric bridge converter (ABC)-based switched reluctance drive (SRD), where the 3D space vector modulation under three modes is developed to reduce the total harmonic distribution (THD) and torque ripple. Firstly, two different 3D vector distributions, namely, the small voltage amplitude mode and large mode are presented based on the asymmetric converter. For both distributions, the zero-sequence voltages generated by the effective vectors are considered. Additionally, zero-sequence vectors (1,1,1) and (−1,−1,−1) are no longer treated as null vectors and involved in the control of zero-sequence current. Then, the duty cycles of both two modes are obtained by the combination of the zero-sequence and two adjacent active vectors. Moreover, based on the large modulation mode, a novel method combined with the small mode is proposed to further optimise the switching costs and torque ripples. The effectiveness of the proposed modes is verified through the simulation in MATLAB and the experiment on a dSPACE-1103-based prototype. Compared with the conventional switched reluctance motor vector control, the proposed scheme delivers better performances of THD, efficiency and torque ripple reduction.

Harmonic suppression and road feeling control of steer-by-wire system with permanent magnet synchronous motor

In this paper, a hierarchical control strategy is proposed to improve the quality of road feeling control of a steer-by-wire system. The upper layer proposed a road feeling torque control method of uncertain system, and the lower layer suppresses the current harmonics produced in the road feeling control process. Firstly, the dynamic model of the steer-by-wire system and the vehicle are established. Secondly, considering the influence of uncertain system parameters, uncertain harmonic torque ripple, and uncertain sensor noise on the road feeling torque control, a road feeling torque control strategy based on mixed H2/H∞ robust control theory is designed. Then, a current harmonic suppression strategy based on the extended Kalman filter is proposed in the lower layer to suppress the current harmonics of all frequencies. Finally, the simulation is conducted using MATLAB/Simulink, and the experimental verification is carried out on the steer-by-wire experimental platform. Simulation and experimental results show that the proposed road feeling control strategy is robust to nonlinear system uncertainties, and the proposed current harmonic suppression strategy can suppress current harmonics in all frequency ranges.

Suppression of Torque Ripple of a Flux-Switching Permanent Magnet Motor in Perspective of Flux-Modulation Principle

In this article, the suppression mechanism of torque ripple for the flux-switching permanent magnet (FSPM) motor is investigated. According to the flux modulation principle, the generation principle of torque harmonics is analyzed, which is generated by the interaction between the radial and tangential airgap harmonics. Based on the analysis, a method to suppress the torque ripple of the FSPM motor is proposed, where the airgap harmonics are newly applied to be the bridge to establish the relationship among torque ripple, torque harmonic components, and key design parameters. To confirm the effectiveness of the proposed method, an FSPM motor with the V-shape permanent magnet (VS-FSPM) motor is selected as the research example. The leading torque harmonics and leading airgap harmonics of the VS-FSPM motor are picked out effectively. Some key design parameters are selected according to the flux modulation principle to improve the leading airgap harmonics and reduce the corresponding torque ripple successively. Furthermore, the torque ripples of the initial and improved VS-FSPM motor are calculated and compared in detail. Finally, a prototype motor is built and tested. Both the theoretical analysis and experimental results verify the effectiveness of the proposed new method.

Indirect Space Vector Modeling of Asynchronous Motor for High-Speed Electric Vehicle Propulsion

This paper presents a high performance squirrel-cage asynchronous motor (ASM) drive, proposed for high-speed electric vehicle (EV) propulsion. This is an indirect space vector control (IDSVC) scheme in the rotor flux frame of reference, in which the modeling is based on synchronously rotating coordinate system transformation. Space vector pulse width modulation (SVPWM) inverter fetches the controlled stator direct and quadrature axis responses from the speed and current controllers and supply necessary voltages to stator of ASM. The output voltage waveforms of SVPWM inverter are not sinusoidal in nature, which allows undesired harmonics at high frequency of operation. This due to inconsistent switching frequency. A second-order low-pass (SOLP) RLC filter with Butterworth approximation and was designed and connected in series with SVPWM inverter to grab harmonic free speed and torque profile during high speed operations. Similarly, another SOLP with a quality factor equal to 2 is designed and speed profiles of both filters are compared. The system is developed and simulated in MATLAB/SIMULINK to observe the speed and torque tracking capabilities. Simulation results show that the performance of drive under steady and dynamic states were good with Butterworth filter approximation with robust IDSVC scheme adopted over wide range speed-drive curve.

Cogging Torque Dynamic Reduction Based on Harmonic Torque Counteract

This article presents a method to reduce cogging torque in permanent magnet (PM) machines from dynamic control based on harmonic torque counteract (HTC). We find the possibility of dynamic cancellation of cogging torque and harmonic torque by studying their generation mechanism and period characteristics, and further study the current harmonic injection scheme for cogging torque reduction. Further, two case studies of an integer slot PM machine and a fractional slot PM machine based on finite element analysis well validate the proposed method. Among them, the cogging torque of a 6-slot/2-pole PM synchronous machine is weakened from 932.0 to 56.2 mN.m, with a weakening ratio of 94.0%, and the cogging torque of the other with 6-slot/4-pole is weakened from 1.23 N.m to 44.21 mN.m, with a weakening ratio of 96.4%. The theory of this article can be extended to PM machines with other different pole/slot combinations and topologies.

Harmonic and Vibration Analysis of Dual Three-Phase PMSM with One-Phase Open Circuit Fault

This paper analyzes the harmonics and vibration under different fault-tolerant current control when one-phase winding of dual three-phase permanent magnet synchronous motor (PMSM) is an open circuit fault. Firstly, the dual three-phase load condition subdomain model of breadloaf surface-mounted permanent magnet (PM) PMSM is established. Secondly, the working conditions of an open circuit fault of one-phase winding are set from the perspectives of no fault-tolerant (NFT) control, maximum torque (MT) control, minimum copper loss (MCL) control and single three-phase mode (STPM) control. The torque harmonics and electromagnetic force harmonics of the four working conditions are analyzed. Then, considering the multi-physical field of electromagnetic and structural coupling, the electromagnetic force in the motor air gap acts on the stator core, and the vibration under four different working conditions is calculated and analyzed. Through the comparison between the analytical method and finite element method, the accuracy of the established model is verified. The calculation method is effective and accurate, it can quickly predict the motor performance in case of one-phase open circuit fault of dual three-phase PMSM.

High-Resolution Permanent Magnet Drive Using Separated Observers for Acceleration Estimation and Control.

This paper proposes a high-resolution permanent magnet (PM) motor drive based on acceleration estimation and control. The PM motor is widely implemented in the printed circuit board (PCB) manufacturing process. To achieve the demanded 1 μm drilling resolution, a sine/cosine incremental encoder is usually installed for motion control. In this paper, several improvements are developed to increase the motion control steady-state accuracy balancing transient response. First, the interpolation of every two encoder counts is proposed to increase the position sensing resolution. In this case, the transient response is improved through the high-resolution position feedback. Second, a closed-loop observer with two independent bandwidths is proposed for acceleration estimation. By using the interpolated position for acceleration estimation, the vibration-reflected high-frequency torque harmonics can be compensated through the acceleration closed-loop control. It reduces the steady-state error under the same sensing hardware. According to experimental results, both transient response and steady-state error can be improved on a PM motor using the proposed position interpolation and acceleration control.

An electromagnetic torsion active vibration absorber based on the FxLMS algorithm

Dynamics vibration absorbers are an effective solution to the problem of vibration. However, there are relatively few applications in low-frequency torsional vibration control. Therefore, for low-frequency torsional vibration, this paper proposes an electromagnetic torsional active vibration absorber, and establishes an active control system based on the filter-x least mean square (FxLMS) algorithm. First of all, the electromagnetic torsion actuator structure is designed with an electromagnetic-permanent magnetic hybrid structure, and the theoretical model of electromagnetic torque is established. Moreover, the influence of structural parameters on the linear stable interval of electromagnetic torque is analyzed, and the effective stroke range of electromagnetic torsion actuator is determined. Then, based on the FxLMS algorithm, the control system of the electromagnetic torsion active vibration absorber is established, and the theoretical model of the secondary channel transfer function is obtained. Furthermore, it is verified by simulation analysis, the results show that the electromagnetic torsional active vibration absorber can achieve good low-frequency torsional vibration absorption performance and is significantly better than without control under the excitation of harmonic torque and white noise torque. Finally, an experimental investigation is carried out on the electromagnetic torsion active vibration absorber based on the FxLMS algorithm to verify the feasibility and effectiveness of the electromagnetic torsion active vibration absorber.

Finite element and analytic equivalent circuit models for MSIM feeded by MPI controlled by SVPWM strategy to minimise circulation harmonic current

This article deals with the determination of the multi-stars induction machine (MSIM) equivalent circuit parameters based on the geometrical and electrical data using two methods namely analytic and finite element method (FEM). Additionally, this paper proposes a general dynamic study of MSIM. This latter is fed by a multi-phase inverter (MPI) controlled by a space vector pulse width modulation (SVPWM) and a sinusoidal pulse width modulation (SPWM). However, when this machine is fed by the voltage inverter for the case of 30° electrical shift between stator stars, large harmonic currents are observed. Thus, the main goal of this paper is to reduce the effect of these harmonic currents. Therefore, to overcome these issues, the machine stars number has been increased to three and four and the inverter has been controlled by the SVPWM. The effectiveness of this association and its capability to reduce the effect of the output harmonic current and electromagnetic torque ripple has been proved by simulation results.

Multi-Objective Optimization of Interior Permanent Magnet Machine for Heavy-Duty Vehicle Direct-Drive Applications

In this paper, an interior permanent magnet (IPM) machine is presented and optimized for heavy-duty vehicle direct-drive applications. Since efficiency decrease and serious heating come along with excessive core loss under flux weakening control, a rotor topology with the combination of the eccentricity structure and magnetic barriers is proposed. The key is to achieve the comprehensive optimization of the proposed rotor topology to satisfy the different requirements under diverse operating points. Then, a multi-objective automatic parallel optimization method is applied, which simultaneously analyzes multi-condition operation without weight coefficients defined artificially. The 3D Pareto solution set is generated by using nature inspired evolutionary algorithm based on the high-precision metal-modals of optimal prognosis, which reduce the needed computation cost significantly. Moreover, the back electromotive force total harmonic distortion, torque and core loss of the optimal machine are analyzed at corresponding operating points. Finally, the finite-element results are validated by experiments based on a prototype machine.

Torsional dynamic response of a pipe pile in homogeneous unsaturated soils

This paper proposed an analytical solution for investigating the dynamic response of a pipe pile subjected to a torsional harmonic excitation torque in unsaturated soils. Based on the wave equations of three-phase porous media, the capillary pressure and inertial coupling effect between water and gas phase are taken into account, as well as the influence of saturation degree on soil’s dynamic shear modulus. The pile is modeled using one-dimensional elastic theory. The dynamic governing equations of outer and inner unsaturated soils are derived by virtue of the separation of variables method. Accounting for the boundary and continuity conditions of pile-soil interface, a closed-form solution for the torsional dynamic response of a pipe pile is derived in frequency domain. The proposed analytical solution is verified by comparing with the two existing solutions available in literature. Finally, a parameter study is undertaken to portray the influence on the dynamic response of a pipe pile.