Abstract:
Vibrations can be described in terms of modes, in which the motion of a structure is described as a linear combination of the modes of that structure. Vibrations can also be described in terms of waves. Waves propagate through a structure and are partially transmitted and partially reflected at discontinuities. Accordingly there exist two vibration control approaches, namely modal and wave vibration control. Modal control is a global, high-authority control, as the control design is based on the global modal properties of the structure; while wave control is a local, low authority control, in that the wave transmission and reflection depend on the local properties of the structure. In terms of active vibration control of a distributed structure, both modal and wave vibration control have their disadvantages. In modal control, modal uncertainties in the model and spillover problems induced by modal truncation exist. In wave control the wave vibrational description requires the wavelength to be much smaller than the size of the structure, which means wave approach is suitable for relatively higher frequencies. In this thesis, a novel control approach, which is named hybrid vibration control, is developed. In the hybrid control, local, low-authority feedback wave control is designed first, which aims to absorb the vibrational energy in a broadband frequency range. The implementation of the wave controller modifies the system. Global high-authority modal control is then designed based on this new, wave controlled, now normally non-self-adjoint system, aiming at adding more damping at the lowest few modes which normally dominate the response of the system. In the hybrid approach, the local wave control is implemented prior to the global truncated modal control design. After the implementation of the wave control, the relatively high frequency modes are generally damped, the responses can then be expressed in terms of the truncated modes with more accuracy. Hybrid control, thus, improves the model accuracy and the robustness of the system. Both simulation and experimental results have been obtained to validate the theory.