# Dynamics and control of flexible membrane wings

**Project Leader: **Richard Sandberg**Staff: **Simon Illingworth**Student: **Massimiliano Nardini**Primary Contact: **Richard Sandberg (richard.sandberg@unimelb.edu.au)**Keywords: **applied control theory; computational fluid dynamics; fluid dynamics; fluid structure interactions**Disciplines: **Mechanical Engineering**Domains: **Optimisation of resources and infrastructure

Micro Air Vehicles (MAV) are a class of unmanned aerial vehicles characterised by reduced dimensions (a few centimeters). They should be able to perform strict manoeuvres that are impracticable for larger air vehicles and they can be used for aerial reconnaissance of environments that are inaccessible to ground vehicles or are hazardous for human beings. MAVs are expected to find huge applications in the near future, both in civil and military field. One of the main problems in the design of MAVs concerns their manoeuvrability and sensitivity to disturbance. In fact, for small aerial vehicles such as birds and UAVs, the flight dynamic time scales and the aerodynamic time scales are comparable. On the one hand this is an advantage, allowing agile manoeuvres to be performed without inertia terms attenuating them, but it also raises problems, as these vehicles are highly sensitive to disturbances, such as gusts. This project will focus on the__ __fluid-structure interaction of the MAV’s flexible flapping wing using reduced order modelling and feedback control techniques to understand the coupling between the flow and the flexible wing.

**Reduced-order model and control of flexible wings**

Unsteady aerodynamic models can be traced back to the classical models of Wagner and Theodorsen. Previous work on unsteady aerodynamic models have looked at the unsteady lift generated by pitching and plunging manoeuvres, also treating the problem within a modern control framework. By doing so accurate low-order models can be developed, and modern robust control can be readily applied. The aim of this work is to invetsigate the unsteady forces generated by the flexible degrees of freedom of a flexible wing. Clearly a flexible wing, when modelled as a continuum, has an infinite number of degrees of freedom. To make the problem tractable, we can decompose the wing’s flexible motion into its Fourier components, truncating the infinite sum to take into account only the leading Fourier modes. This makes the problem tractable by reducing the wing’s degrees of freedom to a finite, manageable number. This is a prudent step for two reasons:

- it is expected that the largest unsteady forces will be generated by the first few Fourier modes, with the contribution decreasing for increasing mode number;
- part of the motivation for the work is in the valuable information it will provide about how best to actuate a flexible wing, and actuation in a small number of Fourier modes will be more readily realised in practice.

One of the main goals is to understand how to achieve additional manoeuvrability with a flexible surface, and how disturbances can be better dealt with (in response to gust disturbances, for example). The reduced-order model will be used to design feedback control laws. Based on the consideration made about the manoeuvrability and sensitivity to disturbance of MAVs due to their reduced size, the control laws will be aimed at addressing the following two questions:

- How should one actuate the surface in order to improve agility during manoeuvres?
- How should one actuate the surface in order to minimize the effect of gust disturbances?