AMOS: Analytical Methods for Optimal Vibration Reduction on General Rotors

主动磁轴承的引入导致了强有力的努力来描述和理解转子的主动控制。尽管有大量不同的控制策略，但如何设计最优控制器的一般论述却很少。原因是当前的控制策略基于信号理论，对柔性转子的结构特性关注较少。此外，当前控制策略的复杂数学背景阻碍了对潜在转子动态现象的深入分析，并且无法给出控制策略是否为最优的线索。近年来，机械工程机电系统研究所在主动压电轴承的描述方面取得了重大进展。利用分析方法，可以在分析和实践上证明，一般转子的不平衡力可以完全与环境隔离。此外，还对不同主动轴承技术进行了广义描述。然而，分析研究表明，即使没有外力，在自由转子共振附近也可能发生较大的转子挠曲。该项目同样侧重于转子的隔离，但也考虑了转子的变形。这是通过包括转子弯曲能量来实现的。因此，有可能在每个工作点保持转子位移有限，并消除所有谐振。然而，一个独立的最小的轴承力和弯曲能量是不可能的。一个控制目标性能的提高会降低另一个控制目标的性能。因此，这是一个帕累托问题。本项目提出的方法能够达到这两个控制目标作为极限情况，并可以执行两者的加权组合。这是通过最小化系统的弹性能量来实现的，由弯曲能量和轴承内的弹性能量组成，这与轴承力成正比。弹性能的计算采用广义刚度矩阵，该矩阵采用弯曲能和承载力的加权。这种方法的优点是只需要一个控制器来达到两个控制目标，这使得在操作过程中可以很容易地改变权重。这种方法不同于减少振动、使转子绕其几何轴旋转和隔振相结合的方法，因为弯曲能量与旋转轴的空间定位无关。所建议的方法将在转子试验台上进行数值和实际条件下的测试。所获得的知识将使有源压电轴承的结构动力学工作原理的一般陈述。

The introduction of Active Magnetic Bearings resulted in strong efforts to describe and understand the active control of rotors. Despite of the large amount of different control strategies, general statements how to design optimal controllers are scarce. The reason is that contemporary control strategies base on signal theory and have only little focus on the structural properties of flexible rotors. Furthermore, the complex mathematical background of current control strategies prevents a thorough analysis of the underlying rotor dynamic phenomena and gives no clues whether or not a control strategy is optimal. In the last years, the Institute for Mechatronic Systems in Mechanical Engineering significantly progressed in the description of active piezoelectric bearings. With analytical methods, it was possible to prove both analytically and practically that unbalance forces of general rotors can be completely isolated from the environment. Furthermore, a generalized description for different active bearing technologies has been found. However, the analytical investigation revealed that even without forces, large rotor deflections may occur in the vicinity of a free rotor resonance. This project likewise focuses on the isolation of rotors but additionally considers the deformation of the rotor. This is achieved by including the rotor bending energy. Thus, it is possible to keep the rotor displacements limited in every operating point and eliminate all resonances. An independent minimization of the bearing forces and the bending energy is, however, not possible. The improvement of the performance of one control objective reduces the other one. Thus, this is a Pareto problem. The proposed approach of this project is capable to reach both control objectives as limit cases and can perform a weighted combination of both. This is achieved by minimizing the elastic energy of the system, comprised of the bending energy and the elastic energy within the bearings, which is proportional to the bearing forces. The calculation of the elastic energy is performed using a general stiffness matrix, which applies the weighting of the bending energy and the bearing forces. The advantage of this approach is that only one controller is required to reach both control objectives, which enables an easy change of the weighting during operation. This approach differs from an approach where vibration reduction, spinning the rotor around its geometrical axis, and vibration isolation are combined because the bending energy is independent of the spatial positioning of the axis of rotation. The suggested approach will be tested numerically and under real world conditions on a rotor test-rig. The gained knowledge will enable general statements on the structural dynamics working principle of active piezoelectric bearings.