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轴承的影响。降低所需半导体电子产品的成本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推力轴承的高度动态控制，如在电子。G.现代工具主轴驱动器。设计限制禁止层压磁芯，这就是为什么由涡电流引起的磁集肤效应高度损害力动态的原因。这个问题在第一个项目阶段得到解决，开发了分数阶磁通估计器，以补充传统的分散和级联位置控制。该估计器使用测量的线圈电流来计算力相关的磁通实时，因此补偿的损害源于涡流。第二个项目阶段的目的是扩大应用范围的磁通估计器的状态控制和观察。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，它们的实际意义直到现在才显现出来。在这一新趋势的开始，必须考虑由通量估计器建模的分数系统行为。该估计器的实现是一个有效的双二阶滤波器级联，但前面的离线计算过程是繁琐的。它需要采用任意精度的算法和额外的知识，以避免出现的高阶多项式的系数量化误差。这就是为什么必须开发一种新的计算过程，完全基于数值上的非临界传递函数的因式分解极点-零点形式。使用新的发现和优化的实验装置，磁推力轴承的扩展动态极限应重新定义。

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.