Permanent magnet synchronous linear motor (PMLSM) has great advantages in control accuracy and response speed, and has been widely applied in automatic control systems, automatic precision machine tools and other occasions. However, due to its own structure, PMLSM has thrust ripples, which cause vibration and noise and greatly affect the control accuracy of the motor drive at low speed. The detent force is the main cause of the output thrust ripples of PMLSM, which is composed of the end force and the cogging force. To solve the problem, this paper proposes a PMLSM thrust ripples suppression strategy based on Proportional Resonant Internal Model Extended State Observer (PR-IMESO) to improve the control accuracy and operation performance of the system.
Firstly, the thrust ripples of PMLSM is modeled and analyzed, and the cogging force and end force models are established respectively. Then, the detent force model is obtained. The detent force is a function of the mover position with the motor pole distance τ as the period. And its frequency is twice the frequency of the primary winding phase current. Aiming at the large detent force in the thrust ripples, according to the principle of internal model, the internal model expanded state observer considering the detent force model is studied, which can not only compensate the detent force but also estimate and compensate the other unmodeled thrust ripples in real time. In addition, a resonant term is introduced into the observer to enhance the compensation ability of the fixed frequency detent force. The observer is designed according to the motion equation of PMLSM considering various thrust disturbances, and the parameters are adjusted by the observer bandwidth.
Finally, simulation and experiment are carried out. In order to verify the correctness of the proposed thrust ripple suppression strategy theoretically, verification of simulation is carried out first. Set the motor running speed to 0.06m/s and load tension to 10N. According to the simulation results, the amplitude of velocity fluctuation with PR-IMESO suppression strategy attenuates to 3.4% of the amplitude of velocity fluctuation without PR-IMESO suppression strategy, and the suppression rate is 96.6%. It is theoretically verified that the proposed PR-IMESO thrust ripples suppression strategy has a significant suppression effect on the detent force whose frequency is secondary fluctuation. Further, in order to verify the effectiveness of the proposed suppression strategy, experiment is carried out with a 750W PMLSM experimental platform. The PMLSM thrust ripples suppression strategy based on ESO, IMESO and PR-IMESO was systematically verified by experiments under the operating conditions of motor speed 0.03m/s, 0.06m/s, no-load, load 2kg, 3kg and 4kg. According to the experimental results, the velocity fluctuation under various working conditions is significantly decreased with PR-IMESO suppression strategy and the suppression rate can reach up to 73.5% and the average suppression rate is 68.7%, which verifies the correctness and effectiveness of the proposed suppression strategy. In addition, the dynamic performance of PR-IMESO thrust ripples suppression strategy is demonstrated by experiments in the case of sudden loading of 4kg. When no suppression strategy is adopted, there is a great fluctuation of the mover velocity before and after sudden loading. After adding PR-IMESO suppression strategy, the fluctuation of the mover velocity is significantly reduced during the whole motion process. And in the process of sudden loading, transition of the velocity error and Q-axis current is smooth and rapid.
The feasibility and effectiveness of the proposed suppression strategy are verified by simulation and experiment. The average suppression rate of the mover velocity fluctuation is 68.7%.
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