Three Theoretical Problems in the Control of Rotating Machines

这个项目致力于旋转机械振动控制的理论方面，但它的最终动机是完全实用的。它的三条主要线索中有两条涉及机器的主动控制方法。人们普遍认为，通过主动控制，旋转机械的效率、功率密度和成本将进一步显著提高。这两条线索是不同的，但具有互补性，每一条都有明确的价值。该项目的第三个主要方面涉及对电机/发电机构成整体部件的机器的分析。这三条链由一个基本的数学框架连接，在任何给定的运行条件下，旋转机械的动力学都可以表示为一个线性二阶系统-至少对于小的振荡是这样。系统的特性由三个方阵决定(将位移的第零、一、二阶导数相乘)。对于静态结构，这三个矩阵分别称为刚度矩阵、阻尼矩阵和质量矩阵。可以相信静态结构具有某些特性，这使得它们的分析和控制比机器的控制要容易得多。重要的区别包括：(A)由于旋转引起的陀螺/科里奥利效应，旋转机械的阻尼阵可能具有非常大的斜对称分量；以及(B)在电磁和机械耦合动力学分析中，质量和阻尼阵包含随时间周期性变化的分量。最近10年出现的分析二阶系统的方法将应用于旋转机械系统。该项目的第一部分涉及所谓的模式控制，即运动方程的适当表示，然后进行模型简化，以便显著简化主动控制在旋转机械中的应用。这是将传统的模式控制推广到具有大陀螺/科里奥利效应的系统。对机器工程师的好处是，他们可以为机器行为的不同方面实现不同的控制器，这些控制器根本不会相互干扰。项目的第二部分帮助工程师在设计控制器的同时进行物理系统的设计。尤其是磁轴承，在放大器的设计中需要考虑三个不同的因素：最大电压、最大电流和最大功率。现有的正式控制器设计方法只适用于限制电流的大小，但很明显，应该平衡地考虑所有这三个因素，二阶系统的动力学的一个表示似乎表明了如何可能做到这一点。项目的第三部分适用于电机/发电机集成到机器中的机器。这类机器的例子包括真空泵、压缩机、轴流风扇、船舶推进吊舱、井下泵、汽车燃油泵、动力转向液压泵等。磁场会导致机械和电气动力学之间的相互作用，从而使机器在某些操作条件下不稳定。一条既定的分析路线会产生一个随时间周期性变化的线性系统。由于所生产系统的特殊特征，分析这些周期系统(以确定其稳定性)的标准方法严重失败。将产生新的方法。该项目的基础是诺丁汉大学，但它的成功取决于来自其他大学的两位杰出合作者的参与：西班牙瓦斯科大学的Ion Zaballa教授和加拿大卡尔加里大学的Peter Lancaster教授。

This project addresses theoretical aspects of the control of vibrations in rotating machines but its ultimate motivations are entirely practical. Two of its three main strands deal with active control methods for machines. There is a widespread concensus that further significant progress in efficiency, power-density and cost-reduction of rotating machines is available through active control. These two strands are different but complementary and each has clear value. The third main strand of this project relates to the analysis of machines in which an electrical motor/generator forms an integrated part. The three strands are connected by a single underlying mathematical framework.In any given operating condition, the dynamics of a rotating machine can be represented as a linear second-order system - at least for small oscillations. The characteristics of the system are determined by three square matrices (multiplying the zeroth, first and second derivatives of displacement). For a static structure, these are named the stiffness , damping and mass matrices respectively. Static structures can be relied-upon to have certain properties which make their analysis and control less difficult than the control of machines. The important differences include: (a) the damping matrix for a rotating machine can have very large skew-symmetric components due to gyroscopic/Coriolis effects caused by the rotation; and, (b) in the analysis of coupled electromagnetic and mechanical dynamics, the mass and damping matrices contain components which vary periodically with time. Methods for analysing second-order systems which have emerged within the last 10 years are to be applied to rotating machine systems.The first part of the project deals with so-called modal control, an appropriate representation of the equations of motion followed by a model reduction in order to simplify significantly the application of active control to rotating machines. This presents an extension of conventional modal control to systems with large gyroscopic/Coriolis effects. The benefit to machines engineers is that they can implement distinct controllers for different aspects of the machine behaviour and these controllers will not interfere with each other at all.The second part of the project helps engineers to do the design of the physical system at the same time that they are doing the design of the controller. For magnetic bearings in particular, three distinct considerations apply in the design of the amplifiers: maximum voltage, current and power. Existing formal controller-design methods cater only for limiting the magnitudes of current but it is obvious that a balanced account should be taken of all three and one representation of the dynamics of second-order systems appears to indicate how this can probably be done.The third part of the project applies to machines where an electrical motor/generator is integrated into the machine. Examples of such machines include vacuum-pumps, compressors, axial-flow fans, ship-propulsion pods, downhole pumps, automotive fuel-pumps, hydraulic pumps for power-steering, etc. The magnetic field causes an interaction between the mechanical and electrical dynamics which can make the machine unstable in certain operating conditions. One established analysis route produces a linear system which varies periodically with time. Because of particular features of the systems produced, standard methods for analysing these periodic systems (to determine their stability) fail badly. New methods will be produced.The project is based at the University of Nottingham but its success depends upon the participation of two distinguished collaborators from other universities: Prof. Ion Zaballa at Universidad del Pais Vasco in Spain and Prof. Peter Lancaster at University of Calgary, Canada.