| Summary: | The majority of active vibration control problems are tackled by mounting sensors and actuators at the location where vibration attenuation is desired. But for some special vibration attenuation problems, the constraint due to space and weight prohibit positioning of sensors and actuators at these points. This necessitates development of control design methods that overcomes these stringent limitations. One such method makes use of remotely located sensor actuator pair to counteract the problematic excitation. A novel control design methodology based on a geometric approach for remotely located sensor actuator pair had previously been developed to address this issue. It was experimentally tested to attenuate vibration for a harmonic or tonal excitation. It gives better physical insight as compared to alternative control design techniques. The final compensator implementation for controlling vibration due to broadband excitation involves model inversion of the local control path dynamics. So, the controller itself is unstable if the local control path is non-minimum phase. Although collocated sensor and control actuator pair can be employed here, it is difficult to avoid non-minimum phase transfer function due to non-ideal practical conditions. A stable controller design using a similar geometric approach is developed in this work such that even if the local control path transfer function is non-minimum phase, the controller will be stable. A solution is provided by means of a modified design procedure which is necessary but not sufficient for the final controller to be stable and stabilising. The sufficiency conditions for stability of controller are presented in terms of the new design freedom parameter. Furthermore, robustness to unmodelled high frequency dynamics is taken into account as part of the modified design procedure. The controller implementation using the modified approach enjoys the advantage of robustness to control spillover at unmodelled high frequencies without deteriorating the performance in the disturbance frequency bandwidth. The applicability of this method to address spatially global reduction requirements is also investigated. A sequential loop closing control design for multiple local feedback loops is also shown using this design for each individual control loops.
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