Active disturbance rejection control of permanent magnet hub motor based on sigmoid filter

Electric tractors have presented promising potential in modern agriculture, due to their energy saving, high efficiency, green and clean. The efficiency and accuracy can be further improved by the distributed drive electric tractors with a simple structure and many control dimensions. Among them, the hub motor drive system of electric tractors also requires high performance of speed tracking and disturbance rejection, when operating on complex roads and in various conditions. Linear active disturbance rejection control (LADRC) can be used to estimate the external disturbance of the drive system using an extended state observer (ESO). The external disturbance can be suppressed using feedforward compensation. Furthermore, the LADRC can be expected to serve as the hub motor drive system, in order to effectively improve the operation performance of electric tractors. However, the high-gain observer, ESO can amplify the high-frequency interference noise, and then enhance the speed detection noise amplitude of the system, thus causing the electric tractor to deviate from the preset trajectory. Fortunately, the low-pass pass filter (LPF) can be used as the common tool to eliminate the high-frequency noise caused by speed disturbance. But the detected speed can be caused to lag behind the actual, thus reducing the dynamic performance of the hub motor drive system. To this end, the LPF can be adjusted to the observation error filtering of ESO, where the detected speed can be synchronized with the actual. But the intermediate-frequency disturbance of the system can also be amplified as well. In this study, a sigmoid function ESO (SFESO) was proposed to realize the active disturbance rejection control of the permanent magnet hub motor. The experimental platform was designed and constructed with the RTU-BOX204 as the core controller. Three control strategies were selected under the speed mutation and load mutation, namely LADRC with the traditional ESO, LADRC with the filtered observation error ESO (FOEESO), and LADRC with the SFESO. The experimental results show that the speed pulsation of FOEESO-based LADRC with the time constant of 2 ms decreased by 16% and 13.33%, respectively, compared with the ESO-based LADRC. While, the quadrature-axis current pulsation increased by 12.5% and 25%, respectively, and the speed drop and overshoot under the load mutation increased by 5.13% and 8.11%, respectively, where the speed recovery time increased by 1.16% and 5.81%, respectively. The variation amplitude of each data increased with the time constant of 10ms in the FOEESO-based LADRC. The speed pulsation decreased by 26% and 33.33%, respectively, whereas, the quadrature-axis current pulsation increased by 18.75% and 45.83%, respectively, and the speed drop and overshoot increased by 15.38% and 13.51%, where the speed recovery time increased by 17.44% and 21.29%, respectively. The speed pulsation of SFESO-based LADRC decreased by 32% and 41.67%, respectively, while the quadrature-axis current pulsation decreased by 6.25% and 4.17%, respectively, compared with the ESO-based LADRC. The speed drop and overshoot under the load mutation increased by 2.56% and 1.35%, respectively, whereas the speed recovery time increased by 1.74% and 1.90%, respectively. The SFESO-based LADRC effectively suppressed the system noise with less impact on disturbance rejection, compared with the ESO- and FOEESO-based LADRC. Therefore, the SFESO-based LADRC significantly improved the noise suppression of the hub motor drive system, while quickly and accurately tracking the given speed. The finding can also provide innovative ideas and technical references to realize the high-precision operation of electric tractors in complex environments.