"Robust vibration control of nonlinear systems by the receptance method”
Nonlinear systems have been encountered in almost all engineering sectors. Some examples of nonlinear behaviour are in flexible wings with large vibration amplitudes due to aerodynamic loads, helicopter blades, control surfaces with friction/backlash nonlinearities, turbine blades, cable-stayed bridges , machine and drilling tools with stick-slip motion. Although in some applications nonlinear behaviour is destructive and it may cause effects such as instability and flutter, in other applications, nonlinear behaviour is so crucial that without nonlinearities, the system may malfunction. One interesting example of nonlinearity is the saturation of the active mechanism in cochlea, which allows us to have an increased dynamic range of hearing. Other examples of the positive influence of nonlinearities are in musical instruments, such as the stick-slip phenomenon as the sound generation mechanism in violins, and the sound generated by musical gongs.
Active vibration control techniques are becoming increasingly important across a wide range of engineering sectors. Whilst there is a large amount of literature on active vibration control of linear systems, there is a lack of theoretical, particularly experimental work for active vibration control of nonlinear systems. The existing linear control techniques are not sufficient to control the many of the challenging dynamic behaviour of nonlinear systems such as bifurcation, combined resonances, limit cycles, inherent instability and harmonic distortion.
Nonlinear control techniques such as feedback linearization and gain scheduling are mainly applicable to systems with slowly varying operating points. Model predictive control, robust control and adaptive control are model-based techniques, which require the availability of a nonlinear model and hence rely on system identification techniques. A novel technique in active control, the so-called receptance method,has been developed which is entirely based on measured vibration test data, rather than models of the system, and this method has been implemented on various laboratory structures as well as on a W30 Agusta-Westland helicopter in a ground vibration test. Recently, the D&V group has extended this technique to control nonlinear systems, such as a Duffing oscillator.
The aim of this project is to develop robustcontrol techniques based on the measured receptances to control vibrations of nonlinear systems and assign the eigenvalues. The equations for the eigenvalue sensitivities will also be developed, which are dependent on the excitation level. Minimisation of the sensitivities at different excitation levels together with the eigenvalue assignment will be considered for robust control. The developed control algorithms will then be implemented on a laboratory scale structure with geometric nonlinearity to demonstarte the working of the algorithms. Experiments will be carried out to obtain open-loop and closed-loop responses and the dynamic behaviour and stability after control will be analysed.
We will hire a PhD student who will focus on the development of control algorithms that incorporate nonlinearities in the models of dynamic systems and controllers. It is expected that the PhD student will collaborate with other PhD students within the ENTEG.
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