Fractional Order Flux Observer for Thrust Bearing Control under the Influence of Eddy Currents

目前对可持续工业解决方案的期望进一步增加了免油和免维护磁力轴承的影响。所需半导体电子器件成本的降低提高了该技术的吸引力，并带来了创新的新应用。一个特别的挑战是磁性推力轴承的高动态控制，如用于现代工具主轴驱动。设计限制禁止对磁芯进行层压，这就是涡流引起的磁趋肤效应严重损害力动态的原因。在项目的第一个阶段，通过开发分数阶通量估计器来补充传统的分散和级联位置控制，解决了这个问题。该估计器使用测量线圈电流实时计算力相关磁通，从而补偿涡流造成的损伤。第二个项目阶段的目标是将通量估计器的应用范围扩大到状态控制和观测器。虽然它们在研究中已经存在多年，但由于快速FPGA控制器的可用性越来越高，它们的实际意义现在才显现出来。在这种新趋势的开始，必须考虑由通量估计器建模的分数系统行为。该估计器的实现采用了高效的双滤波器级联，但之前的离线计算过程非常繁琐。它需要使用任意精度算法和额外的技术来避免高阶多项式中出现的系数量化误差。这就是为什么必须开发一种新的计算过程，完全基于因式极点-零形式的数值非临界传递函数。利用新发现和优化的实验装置，重新定义磁止推轴承的扩展动态极限。

The present aspiration towards sustainable industry solutions further increase the impact of oil- and maintenance-free magnetic bearings. Decreasing costs for the required semiconductor electronics boost the technology’s attractiveness and lead to innovative new applications. A particular challenge is the highly dynamic control of magnetic thrust bearings, as used in e. g. modern tool spindle drives. Design restrictions prohibit to laminate the magnetic cores, which is why the force dynamic is highly impaired by the magnetic skin effect caused by the eddy currents. The problem was solved in the first project phase with the development of a fractional-order flux estimator to complement the conventional decentralized and cascaded position control. The estimator uses the measured coil current to calculate the force-related flux in real-time and therefore compensate the impairment originating from the eddy currents.The second project phase aims to extent the range of application of the flux estimator to state controls and observers. Although they are known in research for many years, their practical significance emerges only now due to the increasing availability of fast FPGA controllers. It is essential to consider the fractional system behavior modeled by the flux estimator in the beginning of this new trend. The estimator’s implementation is carried out with an efficient biquad-filter cascade, but the preceding offline calculation process is cumbersome. It requires to employ arbitrary-precision arithmetic and additional know-how to avoid the coefficient-quantization errors in the occurring high-order polynomials. That is why a new calculation process has to be developed, exclusively based on numerically uncritical transfer functions in a factorized pole-zero form. Using the new findings and an optimized experimental setup, the extended dynamic limits of magnetic thrust bearings shall be redefined.