Abstract:
For electric tractors operating in agricultural environments, the in-wheel permanent magnet hub motor drive system is required to deliver high torque, high reliability, and flexible control under extremely low speed and heavy-load conditions. However, when the motor runs in the ultra-low speed range (typically 5–10 r/min, corresponding to a tractor speed of 3–5 km/h during ploughing or rotary tillage), severe harmonic distortion and phase-delay effects arise. Traditional sensorless control methods using band-pass or low-pass filters cannot accurately extract the rotor position and speed information, leading to large estimation errors, speed pulsation, and poor load capacity. To overcome these limitations, this paper proposes a distributed cascaded second-order generalized integrator (DC-SOGI) based sensorless control strategy with pulsation suppression. The proposed method consists of three main components. First, in the rotor position feedback loop, a narrow-band SOGI tuned exactly to the injected high-frequency signal frequency (ω
h) is used to extract the high-frequency current response. After demodulation, a triple-cascade SOGI structure is designed to sequentially filter the characteristic harmonics: the dominant second-order harmonic at 2ω
h, the residual component at ω
h, and the low-frequency compound clutter (ω
1) with varying amplitude and frequency. Each SOGI module in the cascade is configured with appropriate bandwidth to achieve progressive harmonic suppression without introducing significant phase lag. Second, in the current feedback loop, a dual-cascade SOGI is applied to the d-axis current to suppress the high-frequency response component that interferes with the fundamental current, while a single wide-band SOGI is used for the q-axis current. This arrangement reduces current distortion and torque ripple, thereby improving the electromagnetic torque accuracy. Third, an improved tracking differentiator (TD) with prediction compensation is introduced into the speed feedback loop. The TD uses a optimal synthesis function to track the speed signal and estimate its derivative, and a prediction step is added to compensate for the inherent phase delay of the conventional TD. This effectively suppresses the speed pulsation caused by residual compound clutter that cannot be completely removed by the cascade SOGI filters. An experimental platform was built based on a U-shaped interior permanent magnet hub motor (36 slots/50 poles, rated speed 900 r/min) with an RTU-204 controller, a voltage source inverter, and a composite load simulator (servo motor plus magnetic powder brake). Steady-state tests were carried out at 10 r/min with a constant load of 7 N·m. Compared with the conventional filtering method, the proposed DC-SOGI plus improved TD strategy reduces the speed estimation error from 0.6 r/min to 0.22 r/min (a reduction of 63.4%), the rotor position error from 0.55° to 0.19° (65.5% reduction), the phase-delay error from 5 ms to 1.3 ms (74% reduction), and the speed pulsation amplitude from 0.38 r/min to 0.3 r/min (21.1% reduction). The maximum load capacity is increased by 33.4% across injection frequencies of 300, 500 and 700 Hz. Dynamic tests included variable-speed and variable-load conditions. Under a speed step from 10 r/min to 20 r/min (and back) at constant 7 N·m load, the acceleration/deceleration adjustment times are reduced from 1.7/2.1 s to 0.9/1.1 s, i.e. reductions of 47.1% and 47.6%, respectively. Under a load torque step from 7 N·m to 13 N·m (and back) at 10 r/min, the speed drop decreases from 1.9 r/min to 1.5 r/min (21.1% reduction), the speed overshoot from 1.9 r/min to 1.6 r/min (15.8% reduction), and the speed recovery time from 1.5/1.9 s to 1.3/1.5 s (13.4% and 21.1% reductions, respectively). These results demonstrate that the proposed DC-SOGI dual-feedback-loop filtering strategy with improved TD pulsation suppression significantly enhances the accuracy, dynamic response, and anti-disturbance capability of sensorless control for permanent magnet hub motors in the ultra-low speed range, making it well suited for demanding electric tractor field operations.