AMOS: Analytical Methods for Optimal Vibration Reduction on General Rotors

主动磁轴承的引入使人们对转子主动控制的描述和理解有了很大的进步。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还很少。这是因为目前的控制策略都是基于信号理论，对柔性转子的结构特性关注较少。此外，电流控制策略的复杂数学背景阻碍了对潜在的转子动态现象的彻底分析，并且没有给出控制策略是否最优的线索。在过去的几年里，机械工程机械电子系统研究所在描述主动压电轴承方面取得了重大进展。利用分析方法，可以从解析和实际两方面证明，一般转子的不平衡力可以与环境完全隔离。此外，对不同的主动支承技术进行了概括性的描述。然而，分析研究表明，即使在没有力的情况下，在自由转子共振附近也可能发生大的转子变形。该项目同样侧重于转子的隔离，但另外还考虑了转子的变形。这是通过计入转子弯曲能来实现的。因此，可以在每个工作点限制转子位移，并消除所有共振。然而，单独最小化支承力和弯曲能量是不可能的。一个控制目标的性能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。所提出的方法能够达到极限情况下的两种控制目标，并且可以实现两者的加权组合。这是通过最小化系统的弹性能量来实现的，系统的弹性能量由弯曲能量和轴承内的弹性能量组成，弹性能量与支承力成比例。弹性能的计算使用了一个通用的刚度矩阵，该矩阵应用了弯曲能量和支承力的加权。这种方法的优点是只需要一个控制器就可以达到两个控制目标，这使得在操作过程中可以很容易地改变权重。这种方法不同于将减振、绕几何轴旋转转子和隔振相结合的方法，因为弯曲能量与旋转轴的空间位置无关。所提出的方法将在旋翼试验台上进行数值试验和真实世界条件下的试验。所获得的知识将使人们能够对主动压电轴承的结构动力学工作原理进行一般性的阐述。

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.