Nonlinear Active Vibration Suppression in Aeroelasticity

自然界中所有的系统都是非线性的，因此，应用非线性分析方法可以改善系统的建模和性能。在一定的操作范围内，将它们视为线性是很方便的，而且通常是非常有用的。在线性近似范围之外，应用微扰方法是有用的，微扰方法主要应用于轻度非线性问题，但最近发展起来用于强非线性问题。频域方法适用于包括飞机颤振和LCO在内的周期性非线性振动。新的方法将被开发，使非线性气动弹性系统的动力将分配在其非线性固有频率和阻尼值。该研究将基于两种技术：(1)通过反馈线性化过程中和固有非线性；(2)抑制颤振进入lco。这将涉及新理论的形成及其在实验中的实施。该方法基于线性代数的一个结果，谢尔曼-莫里森公式，由PI和他的同事发展成为线性主动振动抑制的新技术。这种方法被称为接受方法，与传统的矩阵建模相比有许多优点，并且完全基于振动试验的数据，即不需要M、C、K矩阵，也不需要通常由各种专有代码获得的气动弹性影响系数确定的气动弹性阻尼和刚度矩阵。特别重要的是，开环系统的解析（数学）模型的缺失延伸到任何可能存在的结构或流场非线性。利用飞行试验结果，接收方法有可能用于控制飞机的非线性振动。利用接收矩阵在希尔伯特变换下不变的特性，提出了一种新的频域反馈线性化方法。然后可以应用传统的线性控制技术。特征值分配在lco的情况下特别相关，lco是中性稳定的，因此很容易在频域中分配。将开发包括分配稳定lco的技术，这样，如果扰动导致振幅增加，系统是耗散的，如果振幅减少，系统从气流中吸收能量，直到恢复到扰动前的原始振幅和频率。在相当大的速度范围内保证稳定的LCO行为将允许飞机飞行包线的扩展。控制器非线性将使用描述函数（DF）来表示，包括最近开发的高阶DF，它允许传统的零阶DF无法提供的非线性效应。该研究将包括一个使用低速风洞的实验项目，以及跨声速范围内CFD代码的开发和应用。后者将包括对XFR-1（一种远程双引擎宽体飞机）的研究，由空客英国公司的工程科学家插入非线性/结构损伤，利物浦研究人员不知道。

All systems in nature are inherently nonlinear - therefore the modelling and performance of systems can be improved by applying nonlinear analysis methods. It is convenient, and often very useful, to treat them as linear within a certain range of operation. Outside the range of linear approximation it can be useful to apply perturbation methods, which have mostly been applied to problems of mild nonlinearity but have been developed more recently for problems where the nonlinearity is strong. Frequency domain approaches are applicable whenever the nonlinear vibration is periodic, which includes flutter and LCO in aircraft. New methods will be developed so that the dynamic of a nonlinear aeroelastic system will be assigned in terms of its nonlinear natural frequencies and damping values. The research will be based on two techniques: (1) neutralising the inherrent nonlinearity by a process of feedback linearisation and (2) suppressing flutter into LCOs. This will involve the formulation of new theory and its implementation in experiments.The method is based on a result from the linear algebra, the Sherman-Morrison formula, developed into a new technique for linear active vibration suppression by the PI and his colleagues. This approach, known as the receptance method, has many advantages over conventional matrix modelling and is based entirely on data from vibration tests, i.e. there is no need for the M, C, K matrices or for the aeroelastic damping and stiffness matrices often determined from aeroelastic influence coefficients obtained from various proprietary codes. It is particulary significant that the absence of an an analytical (mathematical) model of the open-loop system extends to any structural or flowfield nonlinearity that might be present. Potentially, the receptance method can be used to control the nonlinear vibration of aircraft by using in-flight test results.A new frequency-domain method for feedback linearisation is proposed by making use of a property of the receptance matrix, i.e. that it is invariant under the Hilbert transform. Conventional linear control techniques may then be applied. Eigenvalue assignment is especially relevant in the case of LCOs, which are neutrally stable and therefore are readily assignable in the frequency domain. Techniques will be developed that include the assignment of stable LCOs, so that the system is dissipative if perturbation leads to an increase in amplitude and absorbs energy from the airflow if the amplitude is reduced, until returning to the original amplitude and frequency before the disturbance. Guaranteed stable LCO behaviour over a considerable velocity range will allow the extension of an aircraft flight envelope.The controller nonlinearity will be represented using describing functions (DFs), including recently developed higher-order DFs that admit nonlinear effects not available from the conventional zero-th order DF.The research will include an experimental programme using the low-speed wind tunnel as well as the development and application of CFD code in the transonic range. The latter will include a study of the XFR-1 (a long-range twin engine wide body aircraft) with nonlinearity/structural damage inserted by engineering scientists from Airbus UK, unknown to the Liverpool researchers.