System identification and IMC-PID parameter tuning method for a maglev ball system

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Journal of Vibration and Shock ›› 2025, Vol. 44 ›› Issue (10) : 66-75.

VIBRATION THEORY AND INTERDISCIPLINARY RESEARCH

System identification and IMC-PID parameter tuning method for a maglev ball system

FENG Yuexin1，ZHANG Penghui2，ZOU Jinbin2，DENG Zigang*2

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Abstract

As a typical system for electromagnetic levitation, the maglev ball requires an accurate theoretical model for precise control. Therefore, a system identification method based on a revised electromagnetic force formula and an IMC-PID controller is proposed, which effectively improves the accuracy of the theoretical model and the efficiency of parameter tuning. Firstly, the derivation process of the electromagnetic force formula is analyzed, and an electromagnetic simulation model is established. The formula for the electromagnetic force-levitation gap and bias current is revised. Secondly, by collecting the response of the actual current to the sinusoidal target signal, the relationship between the bias current and the levitation gap under the same electromagnetic force is obtained. The above steps are performed using steel balls of different masses, thus the relationship between the levitation gap and the bias current under different electromagnetic forces is obtained. The revised formula is used for fitting, resulting in the specific values of the parameters for the physical system of the maglev ball. Combining the dynamic equations, the levitation gap and bias current at the equilibrium point are defined as displacement and control current, respectively. The displacement stiffness, current stiffness, and precise transfer function of the maglev ball system are derived. Finally, based on the internal model control theory, an IMC-PID controller is designed. All PID parameters are calculated through a single parameter, and control simulation and experimental verification are carried out. The experimental results show that the theoretical model obtained from system identification matches the response of the physical system highly, verifying the accuracy of the system identification results. The IMC-PID controller also significantly improves the efficiency of parameter tuning.

Key words

maglev ball / electromagnetic force formula / system identification / internal mode control

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FENG Yuexin1, ZHANG Penghui2, ZOU Jinbin2, DENG Zigang2. System identification and IMC-PID parameter tuning method for a maglev ball system[J]. Journal of Vibration and Shock, 2025, 44(10): 66-75

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