磁浮球作为典型的电磁悬浮系统，需要准确的理论模型以进行精密控制，因此提出一种基于修正电磁力公式的系统辨识方法及 IMC-PID 控制器，有效提高理论模型的精确度与参数整定的效率。首先，分析了电磁力公式的推导过程，建立了电磁仿真模型，对电磁力–悬浮间隙、偏置电流公式进行了修正。其次，通过采集实际电流对正弦目标信号的响应，确定了在相同电磁力下偏置电流与悬浮间隙之间的关系。使用不同质量的钢球进行上述步骤，即可得到不同电磁力下悬浮间隙与偏置电流对应关系。采用修正后的公式进行拟合，得到磁浮球实物的参数具体值。结合动力学方程，并定义平衡点处的悬浮间隙与偏置电流为位移和控制电流，推导出磁浮球系统的位移、电流刚度及精确传递函数。最后，基于内模控制理论设计 IMC-PID 控制器，通过单个参数计算出 PID 全部参数，并进行了控制仿真与实验验证。实验结果表明，系统辨识得到的理论模型与实物系统的响应高度吻合，验证了系统辨识结果的准确性，IMC-PID 控制器也大大提高了参数整定效率。
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.
关键词
磁浮球 /
电磁力公式 /
系统辨识 /
内模控制
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Key words
maglev ball /
electromagnetic force formula /
system identification /
internal mode control
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