Permanent magnet synchronous motors are widely used in industrial production and other fields due to their advantages of high power density, high reliability, and high efficiency. Real-time and accurate three-phase current feedback is the key to AC drive system control. Compared with the traditional multi-current sensor drive control, using a single current sensor to achieve three-phase current reconstruction can reduce costs and improve the reliability of the motor system under complex working conditions. Combined with the improved IRTPWM algorithm and the BSPWM algorithm, this paper forms a hybrid pulse width modulation algorithm to solve the low-key brake dead zone and the reconstructed dead zone at the sector boundary. Then, an improved two-point sampling strategy is adopted to eliminate the second type of time-sharing sampling error and simplify the current compensation step, which fixes the sampling time of the two samples and the sampling spacing as the minimum sampling time.

Based on the traditional RTPWM algorithm, the improved IRTPWM algorithm calculates the action time of the other two effective voltage vectors. The action time of the vector is fixed with the least influence on the synthetic reference voltage vector among the three vectors, and the three effective voltage vectors and zero vectors are recorded. It collects the phase current at the beginning and end of the optimal measurement vector.

The traditional RTPWM algorithm cannot achieve medium and high-speed operation alone. The measurement phase backward shift modulation method (BSPWM) is proposed to eliminate the dead zone of current reconstruction by combining the measurement phase backward shift modulation method and the IRTPWM algorithm outside the working area of the IRTPWM algorithm. The mixed pulse width modulation algorithm can complete the current acquisition twice at two fixed particular sampling points, and the first type of time-sharing sampling error only needs to be compensated. Therefore, the current compensation steps of the traditional mixed pulse width modulation algorithm are reduced from four steps to two steps, and the computing burden of the processing unit is reduced.

The simulation and experimental results show that the error between the reconstruction and the actual current is tiny, which proves that the proposed current reconstruction has high accuracy in both steady-state and transient states. Under the dynamic working conditions of fixed load torque of 2 N·m with the rotation speed of 300 r/min and 600 r/min back and forth and fixed speed of 400 r/min with load torque switching back and forth between 1 N·m and 3 N·m, the motor speed, q-axis current, and three-phase current do not cause great disturbance due to the switching of the algorithm.

The following conclusions can be drawn. (1) The combination of the IRTPWM algorithm and BSPWM algorithm effectively eliminates the influence of the dead zone of current reconstruction. (2) The IRTPWM algorithm has higher current reconstruction accuracy and lower current harmonic value than the traditional RTPWM, and the BSPWM algorithm has higher current reconstruction accuracy than the traditional phase-shifting method. (3) The improved two-point sampling strategy can reduce the number of current compensations and current reconstruction errors, simplifying the experimental algorithm and improving the control performance of PMSM.

Permanent magnet linear synchronous motors with section power supply are affected by disturbances like load force, detent force, and friction force. In the field of electromagnetic drive, the stator track is long. Linear motors usually adopt a segmented structure to save inverter capacity. However, it is difficult to ensure that the air gap of each segmented stator is equal during installation. Therefore, the mover is affected by the normal force. In addition, the load is usually accelerated to the target speed in a short time, so electromagnetic drive devices are usually operated under high current and high acceleration conditions, where the motor parameters are prone to change. Due to the lack of intermediate transmission devices in PMLSMs, these disturbances will directly affect the motor drive system and are included in the output of the controller. An SMSC with a novel convergence law is designed to ensure the fast convergence of speed and suppress the chattering. The designed TSMDO observes the disturbance output to ensure the disturbance suppression performance. Then, the acceleration fluctuations are reduced, and the thrust fluctuations are suppressed in the motor output.

Firstly, a mechanical motion model of PMLSM is established based on Newton's second law. It takes the disturbances as the lumped disturbance d(t) caused by load force, detent force, friction force, normal force, and parameter variation. Secondly, the shortcomings of conventional sliding mode control are analyzed, and a new adaptive sliding mode approaching law is proposed. The designed sliding mode approaching law ensures that variables can approach the sliding mode surface at a fast speed. As the state variables of the system gradually approach the sliding mode surface, the designed sliding mode approaching law can reduce the speed to weaken chattering. Then, due to the presence of d(t) in the output of the sliding mode speed controller, the TSMDO is designed to compensate for it. This observer is equivalent to a first-order low-pass filter. Finally, the proposed SMSC strategy is compared with PI control and conventional SMSC.

The experiments show that the PI controller can improve the dynamic tracking performance of speed by increasing h. However, this increases the acceleration fluctuation. At the same time, there is a noticeable overshoot when the rotor enters the constant speed range. The conventional SMSC has better dynamic tracking performance than PI control, resulting in small acceleration fluctuations. However, due to the fixed sliding mode gain, the increasing sliding mode gain increases the overshoot. The proposed SMSC has a faster tracking speed and better dynamic response than the conventional approaching law because of the new sliding mode approaching law. The proposed SMSC can adaptively change its gain when the speed state changes, ensuring good speed-tracking performance and reducing overshoot. The designed TSMDO effectively reduces the impact of thrust disturbances, acceleration fluctuations, and thrust fluctuations.

The main conclusions are as follows. (1) The proposed new sliding mode approaching law has a fast convergence speed due to the adaptive gain function f(x₁, s) for adaptively adjusting the sliding mode gain. It can weaken chattering, ensuring speed dynamic tracking performance and convergence speed. (2) The designed TSMDO has a small chattering phenomenon. The introduction of TSMDO effectively suppresses the total disturbance d(t) in the SMSC output, reduces acceleration fluctuations, and ensures stable thrust output of the motor.

The demagnetization fault of permanent magnet synchronous motors (PMSM) reduces output performance and load capacity, seriously affecting the motor’s service life. Establishing an accurate fault motor analytical model, conducting rapid electromagnetic performance analysis, and obtaining operational data such as current and torque under fault conditions are beneficial for early prediction and diagnosis of demagnetization faults.

A parameter D is introduced for the partial demagnetization fault of the surface-mounted PMSM prototype, representing the spatial angle of the demagnetized region, defined as the ratio of the spatial angle occupied by the demagnetized region to that of one pole arc. The radial and tangential component equations of the residual magnetization Fourier coefficients as a function of parameter D are derived, which reflect the influence of the spatial angle of the demagnetized region on the magnitude and the waveform of the residual magnetization. An analytical model of PMSM under partial demagnetization is established.

In addition, regarding the control system’s circuit interface in practical applications, an analytical model of demagnetization faults in a PMSM driven by a voltage source inverter with magnetic flux linkage as the intermediate variable is established. This model is applied to the vector control circuit. Thus, a co-simulation model combining the analytical model and the control circuit is created.

The load performance of the prototype is calculated under normal conditions and partial demagnetization using the co-simulation model. Compared with the simulation results from the Ansys/Simplorer time-stepping finite element method and the measured results from the prototype on the experimental platform, the conclusions are as follows. (1) The proposed partial demagnetization analytical model reflects the influence of the demagnetized region on the magnitude and the waveform of the residual magnetization. This model is more consistent with actual conditions than the method of equating partial demagnetization to an overall reduction in magnetic flux linkage. (2) The calculation results of the co-simulation model are in good agreement with the time-stepping finite element simulation results, with the relative errors for the stator flux linkage, stator current, and electromagnetic torque less than 1.5% under normal and partial demagnetization conditions. Furthermore, the computation time of the co-simulation model is only 1/20 that of the finite element model, which greatly improves the operation efficiency. (3) The current waveforms of the prototype under the same control strategy are measured on the experimental platform and subjected to spectral analysis. The results are consistent with the co-simulation results, which validate the accuracy of the co-simulation model, combining the analytical model and the control circuit.

Implementing sensorless control is necessary to reduce the system volume of linear oscillatory machines (LOM) used in linear compressors and achieve efficient and reliable operation. The existing piston stroke observers have low observation accuracy and are susceptible to DC components, resulting in a decrease in system compression performance or cylinder collision risk. Therefore, this paper designs an improved high-precision piston stroke observer for linear oscillation machines based on a high-order generalized integrator (HOGI).

Firstly, a theoretical analysis is conducted on traditional back electromotive force integration, low-pass filter (LPF), and second-order generalized integrator (SOGI), elucidating the existence of integral saturation problems in back electromotive force integration, amplitude attenuation, and phase shift problems in LPF. SOGI performs slightly better than the previous two but still cannot eliminate the DC component. When operating at low resonant frequencies or in systems with large DC components, SOGI is no longer applicable. Secondly, in response to the shortcomings of traditional integrators, this paper adopts HOGI as a piston stroke observer. This method can eliminate the DC component, and no DC bias exists in the observed stroke signal. The paper also uses the forward Euler method to derive the digital implementation method of HOGI. Finally, experiments are conducted to compare SOGI and HOGI. The experimental results show that the piston stroke observed by HOGI is more accurate than SOGI without additional DC bias. Furthermore, when an additional 0.2 A DC bias is added, the piston stroke average offset observed by SOGI at the given value of 5 mm, 6 mm, and 8 mm is 1.367 5 mm, 1.365 mm, and 1.351 5 mm, respectively. The piston stroke observed by HOGI is unaffected by DC bias. Therefore, the piston stroke observer with HOGI is suitable for occasions with serious DC disturbance.

The contributions of this paper are as follows. (1) Based on traditional SOGI, an improved HOGI piston stroke observation structure is designed. Multiple filtering feedback characteristics are used to eliminate the influence of DC components on stroke observation results, improving the accuracy of the piston stroke observation. (2) The complex frequency domain method is used to analyze the pure integrator, LPF, SOGI, and HOGI. The superiority of HOGI is theoretically proven. (3) Based on the forward Euler method for discretization and digital implementation of HOGI, this method has the advantages of simple calculation and easy implementation.

The coupling between spatial-harmonic and time-harmonic currents in asymmetric multiphase motors (AMM) increases torque ripple and decreases efficiency, limiting their widespread application. Currently, active harmonic suppression strategies rely on complex filters or observers to extract harmonics and require the construction of numerous proportional resonance (PR) controllers at different frequencies, making the complexity and impracticality of harmonic suppression. Therefore, this paper proposes a single-frequency PR harmonic suppression strategy without filters based on the harmonic mapping law.

Firstly, based on the magnetic electromotive force equivalence principle, the universal space vector decoupling matrixes for AMM are established. Then, a mapping formula for harmonics of different frequency components on the subspaces is established. The general formula is decomposed into two independent components: amplitude and phase. The amplitude and phase mapping law of harmonics on the subspaces is derived according to the characteristics of the two components. Secondly, three criteria are proposed to search for the AMM with the minimum number of phases to ensure the unique mapping of harmonics. Based on the graphical representation of the mapping laws, the mapping trajectories of all harmonics are obtained to optimize the AMM topology and establish the subspaces for harmonic mapping. Then, based on the current phase-shifting method, a virtual AMM is constructed, and harmonics are extracted through the vector decoupling transformation subspaces. Finally, after unifying the frequency through linear space rotation transformation, PR controllers with the same resonant frequency are used to regulate harmonics.

Harmonic extraction and suppression experiments under steady-state and transient conditions are conducted using a dual three-phase motor. The extracted harmonic amplitudes can reach over 92% of the actual harmonics, demonstrating that the proposed algorithm can effectively separate harmonics. In the harmonic suppression experiment, the strategies of no harmonic suppression, current harmonic suppression under multiple synchronous rotating frames, and the proposed harmonic suppression strategy are compared. The proposed strategy decreases the proportions of the 5th, 7th, 11th, and 13th harmonic currents from 13.92%, 5.31%, 4.05%, and 2.96% before suppression to 3.02%, 0.43%, 0.39%, and 1.19%, respectively. The total harmonic distortion (THD) is decreased from 15.36% to 2.86%. Moreover, the harmonic suppression exhibited robustness under various operating conditions across the entire speed range.

The following conclusions can be drawn. (1) There are two harmonic mapping methods: full mapping with equal amplitudes and partial mapping with reduced amplitudes. The phase of mapping components can be divided into the α component leads or lags the β component by π/2. (2) Based on the harmonic mapping law, an optimal AMM topology selection criterion is established, and a virtual AMM is constructed, effectively avoiding the complex and inaccurate problem of harmonic extraction caused by constructing filters or harmonic observers. (3) The features of harmonic pair mapping on the selected subspace are that the difference in frequency order is equal, and the phase sequence is opposite. Thus, linear spatial rotation coordinate transformations are applied to unify frequencies, which enables single-frequency PR controllers with half the number of harmonics to regulate all harmonics.

Electrical isolation in advanced power supply systems typically relies on power frequency transformers or high-frequency isolation DC-DC converters. However, the transformers result in multiple converter stages and increase the system’s complexity and cost. To reduce the cost of advanced traction power supply system, this paper proposes a two-phase to single-phase non-isolated power electronic transformer (NI-PET) topology based on the existing traction transformer and has the advantages of fewer transformation stages and higher system efficiency.

Some switch states can result in short-circuit paths of the DC-link capacitance in NI-PET topology. The traditional modulation strategy fails to avoid the short-circuit paths. A three-dimensional space-vector pulse width modulation (3D-SVPWM) strategy is proposed based on the 3D space vector distribution diagram, taking the vectors of three ports as the coordinate axis. According to the number of available vectors, the 3D space is divided into different ranges. In addition, the proposed strategy determines the range of reference voltage vectors and selects available space vectors to complex the demanded reference vector. Finally, based on the V-v traction transformer, the simulation model and experimental platform are built.

Simulation and experimental results show that compared to the traditional space pulse width modulation (SPWM) strategy, the proposed modulation strategy can realize the stable operation of the system. When the load and grid-side voltage fluctuate repeatedly in a short period, the two-phase to single-phase NI-PET system restores a steady state within 0.2 s, the grid-side power factor remains above 0.99, and the THD of input and output current is less than 3%. With the same load, the three-phase current unbalance degree of the proposed topology is about 45% less than the traditional power supply system. It is verified that the proposed topology and modulation can adapt to harsh conditions such as continuous load and grid-side voltage fluctuations. Compared to PET, NI-PET avoids the loss caused by the isolation stage, thus significantly improving the efficiency. In the low-power experimental platform, the efficiency of NI-PET is about 10% higher than PET.

The following conclusions can be drawn. (1) The proposed two-phase to single-phase NI-PET topology can adapt to the harsh conditions of advanced traction power supply systems. It has the advantages of low cost and good power quality. (2) Compared to the traditional modulation strategy, the proposed one can avoid the short-circuit paths of DC-link capacitance. There is no short-circuit current that is much larger than the load current on the cascade line. (3) The proposed topology can achieve about 10% efficiency improvement in a low-power experimental platform and is expected to increase the efficiency by about 2% in industrial PET.

Regarding the sensorless control system of permanent magnet synchronous motors (PMSM), this paper combines extended Kalman filtering (EKF) and improved inertial active disturbance rejection control (IADRC). By establishing a mathematical model under the new coordinate system and applying the EKF algorithm, the state of the motor is accurately estimated, thus ensuring the accuracy and stability of the control system. Aiming at the current harmonic disturbance caused by the sudden load change, this paper introduces the second-order oscillation function to optimize the traditional linear active disturbance rejection control and proposes an improved IADRC strategy, which significantly attenuates the harmonic disturbances and strengthens the system's immunity to disturbances.

According to the traditional mathematical model of the PMSM motor under the $\gamma \delta $-axis, the mathematical model of the PMSM motor under the estimated rotational coordinate system $\gamma \delta $ is constructed, and the angle ${{e}_{\theta \gamma }}$ between the dq-axis and the $\gamma \delta $-axis is directly estimated, eliminating the influence of the other observers. After that, through the mutual validation of simulation and the mathematical model, the second-order oscillating function is connected in parallel to suppress current harmonics. The 3rd, 5th, and 7th periodic harmonics with high harmonic contents are suppressed. Its effectiveness and stability are proved by Bode's plot and the Nyquist curve plot, respectively.

The EKF's direct estimation method of error angle ${{e}_{\theta \gamma }}$ in $\gamma \delta $ coordinate system is verified Through simulation and experiment, speed step, sudden load addition, and starting with rated load. Meanwhile, compared with the traditional PI control and LADRC control, IADRC plays a role in suppressing the low harmonics when the motor is running stably at 1 000 r/min with rated load. The 5th and 7th harmonic contents are reduced by 50.5% and 77.4% compared to PI. The IADRC algorithm based on the LADRC algorithm can suppress specific harmonics, with a 41.3% reduction in 5th harmonic content compared to the LADRC and a 49.4% reduction in 7th harmonic content compared to the PI. Comparative analysis of the three-phase currents after a sudden change in the rated load shows that compared to PI, the 5th harmonic content of the LADRC is reduced by 70.5%, the 7th harmonic content is reduced by 79.1%, and the 3rd harmonic content is reduced by 54.8%. Meanwhile, compared to LADRC, the 5th harmonic decreases by 44%, the 7th harmonic decreases by 13%, and the 3rd harmonic decreases by 88%.