Active Vibration Control of Parametrically Excited Systems

研究了参数激励系统的振动主动控制问题。问题是开发控制策略，以抑制或增强工程系统中的参数共振。主动控制具有控制大振幅振动和非常有效地修改系统动力学的潜力。它特别适用于PES，因为PES的动力学是周期性的。动态方程中周期性时变参数的出现会导致复杂的响应，包括固有的不稳定性，或求和型或差分型的组合共振。因此，了解PES的动力学及其控制是本研究的主要目的。将用于PES的控制策略是基于申请人为线性时不变系统开发的接受方法。该方法不需要系统矩阵的知识，不需要模型约简技术，不需要观测器对未测量状态进行估计，具有显著的优点。该方法完全基于实测振动数据；因此，控制器的设计中考虑了执行器、传感器和滤波器的动力学特性。其他基于Floquet理论的控制策略也将被开发出来。以斜拉桥为代表的斜拉桥为例，对主动控制技术在斜拉桥上的实际应用进行了验证。许多工程结构都受到参数激励，这是由一些外部荷载与结构相互作用产生的。在土木工程中，日本南部的Aratsu桥就是一个例子，参数共振是锚固处裂缝的起源。当结构频率与参数激励频率的特定比值重合时，就会发生参数共振。例如，在挪威的Skarnsundet大桥上，垂直甲板的频率正好是基本电缆频率的两倍。振动控制可以通过使用极点放置技术将结构频率从特定比率移开来实现。在航空航天领域，由于机翼与气动载荷的相互作用，参数共振会引起飞机机翼的颤振。最近，一架公务机原型机由于尾翼颤振而发生了致命事故，研究的目的是开发控制这种不稳定性的方法。在海洋工程中，由于隔水管与表面波的相互作用，会在隔水管系统中发生参数共振。这些立管的不良动态行为可以通过张力控制来避免。如果不考虑参数激励，这些隔水管的波激振动会导致失稳甚至灾难性失效，从而造成严重的环境和经济损失，因此采用更灵活的主动控制方法可以使系统更加安全。该研究还将有助于浮动器等能量转换器的设计，因为它可以增强参数共振，从而从波浪能中提取大量的能量。

This project considers active vibration control of parametrically excited systems (PES). The problem is to develop control strategies for the suppression, or enhancement, of parametric resonances in engineering systems. Active control has the potential to control large amplitudes of vibration and modify the dynamics of the system very efficiently. It is particularly suitable for PES since the dynamics of PES are periodic-time dependent. The appearance of the periodic-time-dependent parameter in the dynamic equation results in a complex response including inherent instabilities, or combined resonances of summed or difference type. Understanding the dynamics of PES and its control is thus the main objective of this research. The control strategy that will be used for PES is based on the receptance method developed by the applicant for linear time-invariant systems. The method has significant advantages, since there is no requirement for knowledge of system matrices, no requirement for model reduction techniques and no requirement for observers to estimate the unmeasured states. The method is entirely based on the measured vibration data; therefore the dynamics of the actuators, sensors and filters are all included in the design of the controller. Other control strategies based on the Floquet theory will also be developed. The control techniques will be implemented on a cable-supported structure, representing a cable-stayed bridge, to demonstrate the practical application of the active control on PES.Many engineering structures are subjected to parametric excitation, which is produced by some external loads interacting with the structure. In civil engineering, Aratsu Bridge in Southern Japan is an example where parametric resonance was the origin of the cracks close to the anchorages. Parametric resonance occurs when the structural frequency coincides with a specific ratio of the parametric excitation frequency. For instance in the Skarnsundet Bridge in Norway, a vertical deck frequency was exactly twice the fundamental cable frequency. Vibration control can be achieved by moving the structural frequency away from that specific ratio using pole placement techniques.In aerospace, parametric resonance can cause flutter of airplane wings due to the interaction of the wing with the aerodynamic loads. Recently, a fatal accident occurred involving a prototype of a business jet due to the tail-plane flutter, and the research aims to develop methods by which such instability can be controlled.In marine engineering, parametric resonance can occur in riser systems due to the interaction of the risers with surface waves. The undesirable dynamic behaviour of these risers can be avoided using tension control. If parametric excitation is not included in the design of these risers, the wave induced vibration can result in instability and even catastrophic failure, thereby causing severe environmental and economic damage so that a more flexible method of active control would make the system safer. The research will also be beneficial in the design of the energy converters such as floaters since it can enhance the parametric resonance, which is used to extract significant amount of power from the wave energy.