Nonlinear Active Vibration Suppression in Aeroelasticity

Lead Research Organisation: University of Liverpool
Department Name: Centre for Engineering Dynamics


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.

Planned Impact

The potential of this research is a significant improvement in flight safety, which is achievable because the methodology is based on vibration measurements that may be carried out in flight. Thus, in flight tests (for example of military aircraft with different store configurations) the control system will be able to adapt, not only to the different configurations, but also to unpredicted instabilities. It can be used to improve the speed and safety of flight flutter tests. In addition, the controller will adjust itself to a changing dynamic brought about, for example by damage to the airframe or, in an extreme case, to the loss of an engine.
Active feedback control for aircraft vibration suppression is a science in its infancy. There are examples of feed-forward control for vibration cancellation, mostly in rotorcraft, and some examples of active damping in fixed-wing aircraft. There are academic examples of flutter suppression in wind tunnels, but nonlinear active feedback control has never been applied to a production aircraft to the PI and CIs' knowledge. Therefore the soonest impact of this research, in term of implementation in a production aircraft, is likely to be medium-term. However, commercial (and other) pressures are likely to intensify the demand for more adaptive and safer aircraft so that a time-scale of ten years is considered feasible. The direct industrial beneficiaries of the research will be Airbus UK and Stirling Dynamics. Engineering scientists from both organisations will participate in the project by attending progress meetings at six-monthly intervals. The research will be connected to what is achievable industrially (but not necessarily restricted by it) and to industrial requirements. Task 8 will be defined in collaboration with engineering scientists from Airbus UK using the XFR-1 model (CAD/FE/CFD) of a long-range twin engine wide body aircraft, including the insertion of nonlinearity/damage unknown to the Liverpool researchers. The investigators have an established collaboration with Airbus UK and Stirling Dynamics through an initiative known as DiPaRT - Distributed Partnership in R&T. Provision of the XFR-1 model represents a significant level of confidence in the project by Airbus UK.
Research results will be published in international journals including AIAA Journal, AIAA Journal of Aircraft, Mechanical Systems and Signal Processing and Journal of Sound and Vibration. In addition papers will be presented at major international conferences such as the AIAA Structures, Structural Dynamics, and Materials Conference (SDM), International Forum on Aeroelasticity and Structural Dynamics (IFASD) and the International Conference on Noise and Vibration Engineering (ISMA).
The Impact Plan includes a Project Web Site on the University of Liverpool VOCAL system where results and links to published journal papers will be made generally available. The methodologies developed in the project will feed into other complementary studies involving the PI and CIs, and these included several EU funded collaborative programmes. Other impact will arise via the School of Engineering's Virtual Engineering Centre (VEC) which is a £5.4m (NWDA, ERDF, BAESYSTEMS, Airbus) initiative that is aimed at transferring fundamental scientific research (TRL levels 1 - 3) through to industry (TRL levels 4 - 6). At the end of the project a two-day Workshop will be organised for the further dissemination of research results especially to other industries, including automotive, aero-engines and machine tools where there is further potential for application of the research.
Posters and information packs for school sixth-forms will be developed by undergraduate MEng students with projects linked to this research programme. The MEng students will give presentations in local schools in Merseyside.


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Description The research addresses a fundamental problem, that engineering analysis is predominantly based on linear theory, whereas real systems to a greater or lesser degree behave nonlinearly. Linear systems in aeroelasticty (and elasto-mechanics generally) have a well-known form, although the parameters of the governing equations may be uncertain. Nonlinear systems are more difficult because they may take different forms, for example smooth nonlinearities described by an uncertain function, or non-smooth nonlinearities, such as bi-linearity or freeplay between hard stops. Nonlinearities may be hardening or softening with increasing displacement. The achievements of the research may be listed as follows:
1. The receptance method developed previously in collaboration with Prof Yitshak Ram for the case of single input partial eigenvalue assignment, was extended to the case of multiple-input, multiple-output control. This fundamental development was the basis of new procedures for linear (and nonlinear) flutter analysis.
2. Non-smooth nonlinearity was treated using feedback linearisation. Important in feedback linearisation is the stability of the zero dynamics, which in the case of non-smooth nonlinearity are dependent upon inequality conditions, requiring the formulation of new theory (using the Filippov differential inclusion).
3. New feedback linearisation theory was developed based entirely on measured data using receptance-method principles. Significantly, there is no need to know or to evaluate the system matrices and, when the input and output are away from the nonlinearity, the form and parameters of the nonlinearity are not needed.
4. All developments in feedback linearisation were validated experimentally. In particular, flutter suppression was demonstrated using a wind-tunnel aerofoil model with adaptation designed to compensate for uncertain nonlinearity in a piezo-stack actuator.
5. Rather that designating specific dynamic behaviour (e.g. eigenvalue assignment) it is advantageous in flutter suppression to design a controller that simply stabilises the system. This was achieved by the development of robust sliding-mode control for an underactuated aeroelastic system (fewer independent actuators than the number of degrees of freedom) based on the Texas A&M University experimental rig.
6. Systems with softening nonlinearity were found to display complicated dynamic behaviour, with instability, bifurcations and chaos dependent upon initial conditions. Even very simple nonlinear binary-flutter models required intricate and detailed analysis.
Exploitation Route Feedback linearisation is readily applicable to both linear and nonlinear vibration and aeroelastic control problems. The research has opened up new opportunities for uncertainty quantification in the suppression of aeroelastic instability - ongoing work includes the development reliability-based control with the purpose of reducing undue conservatism in robust control by balancing the need for optimal performance against an acceptable small probability of instability.
Sectors Aerospace

Defence and Marine



including Industrial Biotechology


Description The research is presently being used in vibration suppression and damping modelling on industrial hardware with Airbus Defence and Space, Spain. This work forms part of a PhD programme, part-funded by Airbus.
First Year Of Impact 2018
Sector Aerospace, Defence and Marine
Description 'Structural Dynamic Model Verification and Validation (V&V); an enabling methodology for the development of computational models that can be used to make engineering predictions with quantified confidence'
Amount € 46,000 (EUR)
Funding ID SW00231 
Organisation Airbus Group 
Department Airbus Spain
Sector Private
Country Spain
Start 08/2019 
End 12/2022
Description Doctoral Training Grant
Amount £3,960,000 (GBP)
Funding ID EP/L015927/1 
Organisation Engineering and Physical Sciences Research Council (EPSRC) 
Sector Public
Country United Kingdom
Description EPSRC Standard Grant
Amount £567,770 (GBP)
Funding ID EP/N017897/1 
Organisation Engineering and Physical Sciences Research Council (EPSRC) 
Sector Public
Country United Kingdom
Start 04/2016 
End 04/2019
Description Damping identification 
Organisation Polytechnic University of Turin
Country Italy 
Sector Academic/University 
PI Contribution Dr Lisitano was a visiting researcher from Turin. He carried out a programme of experimental validation under Prof Mottershead's supervision.
Collaborator Contribution Damping identification of a car body in white carried out in Turin under Dr Bonisoli's supervision.
Impact Paper published in J Sound and Vibration
Start Year 2014