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  • Yahui Jia, Fengwei Chen, Zhihui Wang, Yugang Su, Yang Li
    Transactions of China Electrotechnical Society. 2025, 40(12): 3702-3715.

    Wireless power transfer (WPT) technology provides an effective way to solve the problem of stable power supply for rotating equipment. However, in practical applications, the relative misalignment between the rotating side and the stationary side is inevitable. In the practical application of WPT system, due to the presence of ferrite cores, the misalignment of the coupling mechanism will significantly affect the self-inductance and mutual inductance parameters of the coils, resulting in output power fluctuations and efficiency reduction. In order to enhance the anti-misalignment capability of WPT systems under changes in coil parameters, this paper proposes a detuned WPT system anti-misalignment method that considers changes in coil parameters. The detuned WPT system is constructed using changes in coil self-inductance to counteract the output power fluctuations caused by changes in mutual inductance.

    Firstly, using the finite element simulation software, the parameter variation laws of the rotary coupling mechanism under axial and radial offsets were summarized. The study found that the self-inductance and mutual inductance of the coupling mechanism have the same trend of change, and the degree of change is similar within a certain offset range. And based on this, the idea of using self-inductance changes to dynamically adjust the degree of system detuning to offset output fluctuations caused by mutual inductance changes was proposed.

    Secondly, the influence of parameter changes on system operation was obtained through circuit analysis, and the constant voltage output conditions for the degree of receiver detuning and mutual inductance changes were derived, providing a theoretical basis for the coupling mechanism design and compensation parameters optimization. The coupling mechanism design revolves around the number of turns on the secondary side, and the compensation parameters optimization is based on the particle swarm optimization (PSO) algorithm. With the goal of constant output and efficiency improvement, the compensation topology parameters of the inductor-capacitor-capacitor-series (LCC-S) are comprehensively optimized to achieve good axial and radial anti-misalignment capabilities of the rotary WPT system.

    Finally, a 170 W experimental setup was constructed to validate the effectiveness of the proposed method. The experimental results show that within the range of axial offset ±30 mm and radial offset ±5 mm, the maximum mutual inductance change of the rotary coupling mechanism is 74%, the self-inductance change is 48%, and the coupling coefficient is 0.39 to 0.89. The maximum output voltage fluctuation is only 9.5% (axial) and 2.8% (radial), and the maximum efficiency of the system is 93%. This method utilizes the equilibrium characteristic of the parameter changes for the coupling mechanism itself. Its significant advantages lie in simple and effective structure, no DC-DC converter, no communication and closed-loop control, and a more stable and reliable system. It is particularly suitable for WPT system in harsh environments such as high temperature, high voltage, and high-frequency vibration underground, reducing the failure rate of the system and improving power supply reliability.

  • Yun Zhang, Weiyi Huang, Yubo Li, Boyi Hou, Yugang Yang
    Transactions of China Electrotechnical Society. 2025, 40(12): 3692-3701.

    Rotor-unmanned aerial vehicles (R-UAV) have structural irregularities and problems with docking offset. The traditional unipolar CP magnetic structure increases the wind resistance of the R-UAV due to its mechanical structure characteristics, which, in turn, affects the flight stability of the R-UAV. At the same time, the asymmetric characteristics of the original secondary side can generate high stray magnetic fields, affecting the stable operation of the R-UAV. Therefore, applying the wireless charging system to R-UAVs is challenging. In order to build a stable wireless charging system for R-UAVs, it is necessary to conduct a targeted optimization design based on the mechanical structure of the R-UAV. This paper proposes an “I工I” magnetic structure with high anti-offset and low stray magnetic field constraints for the wireless charging system of R-UAVs and designs a multi-stage constant current-constant voltage (MCC-CV) control strategy with soft switching capability based on the characteristics of series-series (S-S) networks.

    Firstly, this paper comprehensively analyzes the characteristics of series-series (S-S) networks, develops an MCC-CV control strategy for wireless charging of lithium batteries, and designs a full-bridge phase-shift soft-switching half-bridge workflow to solve the output current oscillation problem caused by the energy storage characteristics of the resonant network during the multi-stage constant current switching process. By incorporating soft switching capabilities, the system can transition smoothly between different stages of the charging process, minimizing current oscillations and ensuring a stable charging experience. Then, a three-dimensional model of the “I工I” magnetic structure is proposed and established. The transmission structure of this coupling structure is a “I工I” core, while the receiving side structure is an “I” core integrated within the landing gear of the R-UAV. Integrating the magnetic structure within the landing gear allows for zero wind resistance characteristics in wireless charging of R-UAV. Based on the low magnetic resistance characteristics of ferrite cores, the design of the “I” core is completed. Through magnetic circuit analysis and finite element simulations, the magnetic circuit shaping and low stray magnetic field characteristics of the “I” core are determined, and a passive constraint magnetic circuit shaping method for stray magnetic fields is derived. The “I” core distribution is adjusted to increase the anti-offset capability of the “I工I” magnetic structure, thereby achieving a high anti-offset wireless charging system design.

    Finally, a prototype of the “I工I” magnetic structure is built. It is shown that the system can maintain a constant output current under radial offset of 100 mm and rotational offset of 360°, with only a 2% fluctuation in transmission efficiency. At the same time, the distribution characteristics of the stray magnetic field outside the launch platform are measured, and a distribution diagram of the stray magnetic field is drawn. The proposed “I工I” is lightweight and efficient.

  • Xu Liu, Yupeng Cao, Chenyang Xia, Longyue Yang
    Transactions of China Electrotechnical Society. 2025, 40(12): 3828-3841.

    For the wireless charging systems for electric vehicles (EVs), the misalignment phenomenon due to inaccurate parking is the most significant issue, which causes non-negligible negative impacts on the power efficiency and amount. That is because the positional misalignment between coils leads to significant changes in parameters such as mutual inductance, which in turn causes dramatic fluctuations in the system’s output voltage and efficiency. It potentially prevents the system from functioning correctly or even damages it. Therefore, research on the anti-misalignment capability of EV wireless charging systems is crucial. Current research focuses on high-frequency inverter control, coupling mechanism design, and compensation topology design. However, these methods fail to maintain a constant output voltage when both coil misalignment and large variations in load occur. This paper proposes a novel hybrid compensation topology based on the QRQP coil.

    This paper uses finite element simulation software to investigate a QRQP coil and its misalignment and coupling characteristics. To reduce output voltage fluctuations caused by coil misalignment and large variations in load, a novel hybrid topology is introduced based on the QRQP coil. This topology leverages the principle of opposing output characteristics between S-LCC, LCC-S, LCC-LCC, and SS topologies. Detailed design guidelines for the parameters and optimization strategies are proposed. Meanwhile, the system’s anti- misalignment capability under different parameter selections is analyzed. Finally, optimal system parameters are selected and analyzed. The optimized system can maintain a constant output voltage under various misalignment angles and load variations within a specific range. When the receiving coil is removed, the primary-side current can be effectively limited, which ensures the system's safety.

    The proposed topology has been validated through a 1 kW laboratory prototype. Experimental results show that when the load resistance varies from 20 Ω to 100 Ω, the system maintains output voltage fluctuations of less than 5% under X-axis misalignment from -140 mm to +140 mm, Y-axis misalignment from -105 mm to +105 mm, and diagonal misalignment along the XY-axis from -200 mm to +200 mm. When the load resistance varies from 20 Ω to 100 Ω and the coils’ vertical distance changes from -35 mm to 70 mm, the output voltage fluctuation can be kept within 8%. Furthermore, since the system exhibits capacitive behavior after misalignment and has no compensating inductance, it can operate with high efficiency. Analysis under extreme conditions shows that when the receiving coil is removed, the optimized hybrid topology effectively limits the primary-side current surge, preventing system damage.

    The following conclusions can be drawn. (1) The proposed optimization theory for the novel hybrid topology is consistent with the experimental results. (2) The optimized hybrid compensation topology based on the QRQP coil can effectively reduce output voltage fluctuations when coil misalignment and large variations in load occur simultaneously. (3) When removing the receiving coil, the optimized hybrid topology effectively limits the primary-side current surge, preventing system damage.

  • Renwei Deng, Yugang Su, Hongsheng Hu, Xuefeng Yang, Yingjun Fei
    Transactions of China Electrotechnical Society. 2025, 40(12): 3759-3769.

    In underwater applications, such as underwater robots, autonomous underwater vehicles (AUVs), and remotely operated vehicles (ROVs), magnetic-field coupled wireless power transfer (MC-WPT) enables the transmission of electrical energy without electric contact, improving the flexibility and security of power transfer. Underwater electrical devices and base stations must achieve long-distance and high-power wireless power transfer while realizing high-speed bidirectional wireless information exchange to enable command transmission, data feedback, and closed-loop control. Many scholars have researched shared-channel magnetic-field coupled underwater simultaneous wireless power and information transfer (MC-USWPIT) technology. However, there is still a gap between the transmission distance, power transfer capacity, information transfer speed, and the requirements of engineering applications. Therefore, this paper proposes an underwater simultaneous wireless power and information transfer system with a coplanar double-coil coupler. The research focuses on rapid wireless power replenishment and high-speed bidirectional information transmission for AUVs in seawater. The goal is to achieve high-power energy transfer and high-speed bidirectional information transmission over long transmission distances.

    The coupler with a coplanar double-coil and the MC-USWPIT system topology are proposed. Using the relay coil for information transmission reduces the voltage stress on the information transmission circuit and helps mitigate the crosstalk between the power and information transfer channels. By employing an injecting information method with a series of LC circuits in the information transmission channel, the LC circuit is fully compensated at the power transmission frequency. Furthermore, smaller capacitance-blocking capacitors further reduce the crosstalk between the power transmission channel and the information transmission channel, as well as the voltage stress on the information transmission channel, thereby reducing the difficulty of system design.

    Subsequently, the system is analyzed and modeled, and equivalent circuit models for the power and information transfer channels are provided. A parameter design method for the MC-USWPIT system is proposed. The method reduces the eddy current losses induced by the seawater and minimizes the impact of high-power energy transmission on the information transfer speed. It enables the simultaneous improvement of transmission distance, power transfer capacity, and information transfer speed in a frequency-division multiplexed MC- USWPIT system.

    Finally, a 5 kW experimental setup in simulated seawater is constructed. In an environment with a seawater conductivity of 4.15 S/m, the system achieved a transmission distance of 50 cm, an output power of 5.33 kW, and an information transfer speed of 5.68 Mbit/s. Furthermore, under varying seawater conductivities (4, 5, and 6 S/m) and transmission distances (30, 40, and 50 cm), the system still demonstrates good power transfer performance and high information transfer speed. The experimental results confirm that the proposed MC-USWPIT system and method can effectively improve the transmission distance, power transfer capability, and bidirectional information transfer speed in simulated seawater.

  • Bo Feng, Dawei Peng, Yi Yang, Ke Guo, Zeyang Liu
    Transactions of China Electrotechnical Society. 2025, 40(12): 3716-3726.

    Wireless power transfer (WPT) technology has garnered widespread attention in recent years due to its advantages in safety, reliability, and flexibility. However, these benefits are often dependent on the precise alignment of the coupling mechanism. In practical applications, as perfect alignment cannot always be ensured, misalignment leads to a reduction in the coupling coefficient, significantly degrading transmission efficiency and system performance. Traditional flat solenoid coils perform well in resisting longitudinal misalignment, but when lateral misalignment occurs, especially near the coil's edge, the coupling coefficient and efficiency drop rapidly. To address this issue, this paper proposes an improved flat solenoid coil WPT system.

    First, an equivalent model of the LCC/S compensation circuit is established to analyze the effects of circuit parameters on output characteristics, and a method for configuring the parameters of resonant elements is derived, revealing key circuit parameters affecting voltage gain. Then, an equivalent magnetic circuit model is built to analyze the magnetic field distribution characteristics of the coil, demonstrating that core shape and winding configuration significantly influence the coupling coefficient. Consequently, an optimized winding distribution is proposed using an arithmetic progression for the inter-turn spacing, and the specific optimization process is provided. Additionally, the core shape of the transmitter coil in the traditional flat solenoid design is improved to better concentrate the magnetic field lines, enhancing magnetic field uniformity and increasing the misalignment tolerance of the coupling mechanism.

    To verify the optimization effects, multiple simulation models were created with core shape and winding configuration as variables for comparison. Finite element simulation results show that the improved transmitter core achieves more uniform magnetic flux density distribution, significantly reducing the rate of change in the coupling coefficient. Magnetic field uniformity and misalignment tolerance are markedly improved. Finally, a 100 W WPT system prototype was built, and thermal imaging was used to analyze the system’s loss distribution.

    Experimental results show that when the receiver is laterally misaligned within ±50% in both the X and Y directions, the output voltage fluctuation is controlled within 5%, and transmission efficiency reaches 89%. These results validate the effectiveness and feasibility of the proposed system.

  • Jincheng Jiang, Ye Hong, Pengqi Deng, Shiming Fu
    Transactions of China Electrotechnical Society. 2025, 40(12): 3742-3758.

    The magnetic field's compactness can better increase energy's transmission distance in a near-filed wireless power transfer (WPT) system. This paper proposes a non-centrosymmetric excitation unit (NEU) design method for the WPT system with a matrix coupling mechanism to improve the magnetic flux density in the central region. The proposed method enhances the magnetic focusing performance with a flat two-dimensional structure while maintaining its misalignment tolerance without any other auxiliary coil or circuit. The self-inductance value of the transmitting coil in this design method is even smaller than that of the conventional design method under the same size and number of turns. In addition, the proposed method is applicable to all regular matrix coils. Then, a detailed design method of the coupler is given based on the circuit analysis. Finally, taking the LCL-LCC compensation WPT system as an example, the feasibility of the proposed design method is verified. Compared to traditional design methods, the proposed design method can increase the induced voltage by 24.7% at the optimal position.

    The current mobile robot UAV (unmanned aerial vehicle)/AGV (automated guided vehicle) plays an important role in industrial inspection, office logistics, agricultural and forestry plant protection, and military reconnaissance and surveillance fields. A multi-level, multi-modal power supply demonstration application has been designed in intelligent parks and industrial inspections to achieve charging docking between unmanned devices. However, most power supply methods are fixed-point charging, which is complicated in the energy transmission process and faces energy loss problems. In special charging environments such as wilderness and underwater, if there is no suitable parking charging platform condition, UAV hovering charging technology has become the most necessary and perfect charging solution, and it is also the key to building wireless power transmission network environments. Based on the well-established technology of fixed-point hovering and hovering following for unmanned inspection equipment in the air-to-air, ground-to-ground, and air-to-ground scenarios, hovering and alignment energy replenishment is undoubtedly a highly efficient and cutting-edge design concept applied to unmanned inspection equipment. Nowadays, to further enhance the flexibility and reliability of wireless charging systems, more and more wireless charging systems are designed based on matrix coils. The matrix-based multi-excitation wireless charging system has gained more favor in charging applications due to its reconstruction mechanism of the magnetic field at the transmitting end and strong tolerance for voltage and current stress.

    In summary, a matrix coil design method based on non-centrosymmetric excitation units is proposed, combined with an evaluation of the system's spatial field transmission capability to improve the optimization design steps and the focusing ability of the magnetic field. This design method, which has a two-dimensional planar structure, enhances the magnetic flux density at the center position without any auxiliary coils or circuits, avoiding the offset tolerance weakening of the matrix coil itself as much as possible. It reduces the self-inductance of the coil unit to improve mutual inductance utilization.

  • Hu Xiao, Gongping Wu, Zhuo Long, Jian Zheng, Zewen Li
    Transactions of China Electrotechnical Society. 2025, 40(12): 3883-3894.

    Permanent magnet synchronous motor (PMSM) has become a core component of complex electromechanical systems such as electric vehicles, new energy urban rail vehicles, and wind power generation due to its advantages of high efficiency, high power density, and high torque density. The model predictive control strategy based on the mathematical model of the controlled object has been widely applied in PMSMs. However, there is inevitably a mismatch between the actual parameters of the motor system and the application parameters of the model predictive controller, which seriously affects the performance of the predictive control system. This paper proposes a novel model-free stator flux sliding mode control (MF-FSMC) method to achieve high-performance control under parameter mismatch.

    The model-free flux sliding mode controller is adopted to replace the model predictive control algorithm that relies on the controlled object. First, a mathematical model of PMSM is established under parameter mismatch, and an ultralocal stator flux linkage model considering parameter mismatch is constructed under a rotating coordinate system. The novel MF-FSMC method is proposed, a model-free flux sliding mode controller based on a novel reaching law is designed, and a one-beat speed predictive controller is constructed. Finally, the composite integral sliding mode disturbance observer online estimation strategy is proposed, which can effectively observe the unknown disturbance part in the ultralocal model of PMSM under parameter mismatch.

    Simulation and experimental results show that the proposed method can effectively improve the steady-state performance, significantly reduce the stator flux and torque ripple, and enhance the robustness and anti- interference performance of the PMSM system under parameter mismatch. The designed composite integral sliding mode disturbance observer can accurately observe the stator flux values and unknown disturbances on the dq axis. Compared with conventional model predictive control methods, the proposed MF-FSMC method can reduce torque ripple from 75 N·m to 45 N·m in the case of flux linkage parameter mismatch. In addition, with the proposed MF-FSMC method, the distortion of stator current has also been significantly improved, and the static error of stator flux linkage has been reduced from 0.35 Wb to ±0.01 Wb. In the case of inductance parameter mismatch, the proposed MF-FSMC method can reduce torque ripple from 110 N·m to 80 N·m and the fluctuation value of stator flux linkage error from ±0.235 Wb to ±0.02 Wb.

    The MF-FSMC method proposed can obtain the following conclusions: (1) The composite integral sliding mode disturbance observer can accurately observe unknown disturbances and stator flux linkage, effectively enhancing the robustness of predictive control systems under parameter mismatch. (2) The proposed model-free stator flux sliding mode control method designs a model-free flux sliding mode controller in the inner loop of the controller and constructs a one-beat speed predictive controller in the outer loop of the controller. The proposed MF-FSMC method can effectively improve the control accuracy of stator flux, significantly reduce the stator flux/torque ripple of the motor, and ensure the strong robustness of the predictive control system under parameter mismatch.

  • Fu Li, Shuangchen Chen, Zhiyong Lan, Yunze Jiang, Yini Zhao
    Transactions of China Electrotechnical Society. 2025, 40(12): 3895-3904.

    Traditional I-f control for sensorless control of the permanent magnet synchronous motor (PMSM) suffers from poor damping and disturbance rejection, which lead to large speed oscillations at motor startup and long transition time when switching to close-loop control. It is unfavorable for multi-rotor unmanned aerial vehicles and electric vertical take-off vehicles. According to the differentiation of d-axis voltage and transition strategy, this paper proposes an improved I-f control strategy with frequency compensation to increase damping and improve disturbance rejection of the I-f control based on decoupling current dynamics and angle dynamics. Speed oscillations at motor startup are suppressed significantly, and a fast transition from I-f control to closed-loop control is achieved smoothly with less mechanical dynamics.

    Firstly, a small-signal perturbation model of the I-f control is deduced with detailed analyses of its damping characteristics. To increase damping and suppress speed oscillations, differentiation of the open-loop d-axis voltage is used to compensate for the open-loop frequency. Secondly, to improve the load disturbance rejection when switching to closed-loop control, the angle of the reference current vector is rotated via Park transformation. In contrast, the open loop angle is increased to gradually approach the real rotor angle obtained by the angle observer. Since the reference current vector is stationary relative to the real rotor angle during this transition process, no mechanical dynamics are generated. This transition can even be done at zero angle error between the real rotor coordinate and the open-loop coordinate, which indicates no current and angle dynamics at the switching instant. The amplitude of the reference current vector is kept unchanged throughout the whole I-f control. Therefore, the load disturbance is effectively rejected, even during the transition process. Finally, after switching to closed-loop control successfully, the d-axis current is decreased to 0 according to a certain trajectory, and normal closed-loop control takes over.

    Two experiments demonstrate the improvement of system damping and load disturbance rejection. In the first experiment, the proposed strategy is compared with the traditional I-f control and the perturbation of active power in literature. The experimental results show that under traditional I-f control, significant speed oscillations occur during the starting phase, and the peak-to-peak value of speed oscillations is about 80 r/min. With perturbation of active power, speed oscillations rapidly decay in 0.1 seconds, and the peak-to-peak value of speed drops to about 10 r/min in the steady state. The motor attenuates speed oscillations fast, and the peak-to-peak value of speed drops to about 5 r/min in the steady state.

    The second experiment compares the proposed transition strategy and the strategy by reducing the q-axis current in the literature. The experimental results show that reducing the q-axis current generates large mechanical dynamics at the transition stage under sudden load disturbances. The speed decreases by about 260 r/min at the load disturbance of 0.064 N·m, and the motor is out of control at the load disturbance of 0.16 N·m. Mechanical dynamics are much smaller using the proposed method. The speed decreases by about 40 r/min at the load disturbance of 0.064 N·m, and the motor can still maintain normal operation at the load disturbance of 0.512 N·m.

    The proposed improved I-f control strategy has better damping effect on speed oscillations and can transition to closed-loop control with strong rejection of load disturbances.

  • Liangdeng Hu, Cheng Guo, Xiaosong Xu, Xiangyu Luo
    Transactions of China Electrotechnical Society. 2025, 40(12): 3842-3856.

    The multi-phase open-winding induction motor and its adaptive H-bridge multi-phase inverter system have received extensive attention due to their advantages of small torque ripple, strong fault tolerance, and easy power capacity expansion. This paper analyzes the modeling of the multi-phase open-winding motor system and speed sensorless control technology to achieve high degrees of freedom control and low switching frequency characteristics in a twelve-phase, large-capacity, open-winding motor system. The simulation and experimental verification are conducted to enhance the operating performance of the low-switching-frequency multi-phase open-winding motor system.

    The twelve-phase open-winding induction motor system and its equivalent three-phase simplified model are established. The equivalent three-phase full-order observer model and its speed estimation method are presented. The full-order observer used in speed sensorless control has the advantages of low control bandwidth requirements and a wide range of observation speeds. However, the switching frequency of the H-bridge large-capacity inverter supporting the ship’s multi-phase open-winding induction motor is low, which inevitably increases the digital discretization error of the full-order observer. This paper derives the full-order flux observer models based on the forward Euler method, the simplified second-order discretization method, and the proposed Adams fourth-order discretization method. Then, the steady-state error and observer stability are compared using the F-norm and pole diagram. Theoretical analysis reveals that the full-order observer, based on Adams' fourth-order discretization method, achieves the best discrete accuracy and stability of the observation system while minimizing the computational complexity of the digital control system.

    A simulation model and a test platform for a twelve-phase, 25 kW open-winding induction motor with speed sensorless control have been developed. The results show that, compared with the forward Euler method and the simplified second-order discretization method, the observation results for speed, current, and flux based on the Adams fourth-order discretization method are almost consistent with the actual values. Through the speed sensorless closed-loop speed regulation test and load mutation test, it is further verified that the full-order observer based on Adams' fourth-order discretization method exhibits good speed regulation and load-carrying capacity, which can achieve better dynamic and steady-state performance under both extremely low and high-speed conditions. The full-order observer discretization method can provide technical support for applying speed sensorless control technology to low switching frequency multi-phase open-winding motor systems.

  • Qingeng Shi, Junjie Zhu, Yi Han, Xiong Zeng
    Transactions of China Electrotechnical Society. 2025, 40(12): 3868-3882.

    Accurate load torque identification helps to improve the load disturbance resistance of complex nonlinear loaded permanent magnet drive systems. The sliding mode observer (SMO) has become a commonly used algorithm for load torque identification due to its advantages of high robustness to noise, fast response speed, and simple structure. However, the shortcomings of this algorithm, such as high-frequency chattering and slow response speed, limit its application in electric drive systems. This paper proposes a new adaptive sliding-mode load torque observer to solve the problem of the inherent contradiction between the convergence speed and high-frequency chattering of conventional sliding-mode observers.

    Firstly, from the perspective of quasi-sliding mode, the conventional sign function is replaced by the saturation function to suppress the high-frequency chattering of the load torque estimate. The sign function can effectively suppress the chattering phenomenon of SMO, but it still fails to balance the convergence speed and observation accuracy. Second, an adaptive convergence rate is designed to introduce an exponential convergence term based on the conventional isochronous convergence rate. The adaptive gain of the isochronous convergence term is designed to make the sliding-mode observer adaptively adjust the convergence speed along with the change of the system state. Thus, the observer has a short convergence time and strong robustness, and the high-frequency chattering phenomenon of the sliding-mode observer in the steady state is suppressed. Finally, this paper introduces the average estimated value of the load torque in the conventional slip mode identification algorithm and adds it to the feedback loop of the speed observer. The improved load torque observation algorithm can suppress the chattering of the estimated torque by adjusting the feedback gain g. Since the load torque indication signal U can characterize the load torque change without additional delay, it can be directly involved in the speed estimation. Therefore, the proposed algorithm has a fast response speed during transient processes while considering the chattering suppression of the system. Based on the principle of sliding mode variable structure control, the adaptive rate of feedback gain coefficient g is designed.

    Simulation and experimental results show that under varying speed and load disturbances, the proposed adaptive SMO has less chattering than traditional SMO and super-twisting SMO. Additionally, the adaptive SMO converges faster than traditional SMO and performs comparably to super-twisting SMO. In load disturbance experiments at a reference speed of 600 r/min, the speed fluctuations for no torque feedforward, traditional SMO with torque feedforward, and adaptive SMO with torque feedforward are 72.5 r/min, 56 r/min, and 35.5 r/min, respectively, with system recovery times of 0.7 s, 0.65 s, and 0.5 s. To further verify the impact of inertia parameter mismatch on the adaptive SMO, inertia was set to 2, 5, 0.5, and 0.2 times the rated value, with the maximum deviation in load torque observation being 6.7 N·m. The results indicate that the impact of parameter mismatch is not significant.

    The following conclusions can be drawn. (1) The designed adaptive SMO has a simple structure and high stability, is easy to implement, observes the load torque quickly and accurately, and requires fewer parameters. (2) Compared with the conventional SMO, the proposed adaptive SMO has less chattering and faster response speed during the transient change of the load torque. (3) The proposed adaptive SMO is more suitable for the scenario of variable load torque than the conventional SMO. The experimental results show that when the load torque recognized by the adaptive SMO is used as the feedforward term of the reference torque, the response speed and load disturbance resistance of the heavy-duty chain drive system can be effectively improved.