Abstract:
Electric tractors can often operate in agricultural environments. Permanent magnet in wheel hub motor drive system is required to deliver high torque, high reliability, and flexible control under extremely low speed and heavy load conditions. However, the motor has limited to severe harmonic distortion and phase delay 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). Conventional sensorless control with band or low pass filters cannot accurately extract the rotor position and speed information, leading to large estimation errors, speed pulsation, and low load capacity. In this study, a distributed cascaded second order generalized integrator (DC SOGI) was proposed for the sensorless control strategy with pulsation suppression. Three components consisted of: (1) In the rotor position feedback loop, a narrow band SOGI was tuned exactly for the injected high frequency signal frequency (
ωh). The high frequency current response was then extracted. A triple cascade SOGI structure was designed to sequentially filter the characteristic harmonics after demodulation: the dominant second order harmonic at 2
ωh, the residual component at
ωh, and the low frequency compound clutter (
ωt with varying amplitude and frequency. Each SOGI module in the cascade was configured with optimal bandwidth. Progressive harmonic suppression was achieved with the minimal phase lag. (2) In the current feedback loop, a dual cascade SOGI was applied into the d axis current, where the high frequency response component was suppressed to reduce the interference with the fundamental current. while a single wide band SOGI was used for the
q axis current. Current distortion and torque ripple were reduced for the electromagnetic torque accuracy. (3) A tracking differentiator (TD) with prediction compensation was introduced into the speed feedback loop. An optimal TD synthesis function was used to track the speed signal and then estimate its derivative. A prediction step was added to compensate for the phase delay of the conventional TD. Speed pulsation was effectively suppressed to fully remove residual compound clutter, compared with the cascade SOGI filters. An experimental platform was built using 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 conducted at 10 r/min with a constant load of 7 N·m. The results show that the DC SOGI with TD strategy was reduced the speed estimation error from 0.60 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 5.0 to 1.3 ms (74% reduction), and the speed pulsation amplitude from 0.38 to 0.30 r/min (21.1% reduction), compared with the conventional filtering. The maximum load capacity increased by 33.4% at injection frequencies of 300, 500 and 700 Hz. Dynamic tests were conducted under variable speed and load conditions. Acceleration/deceleration adjustment times were reduced from 1.7/2.1 to 0.9/1.1 s under a speed step from 10 to 20 r/min (and back) at constant 7 N·m load, which was reduced by 47.1% and 47.6%, respectively. The speed drop decreased from 1.9 to 1.5 r/min (21.1% reduction) under a load torque step from 7 to 13 N·m (and back) at 10 r/min, while the speed overshoot from 1.9 to 1.6 r/min (15.8% reduction), and the speed recovery time from 1.5/1.9 to 1.3/1.5 s (13.4% and 21.1% reductions, respectively). DC SOGI dual feedback loop filtering with TD pulsation suppression was significantly enhanced the accuracy, dynamic response, and anti disturbance of sensorless control for the permanent magnet hub motors in the ultra low speed range. The finding can provide a strong reference to fully meet the high demand for electric tractor in fields.