A geometric-based methodology that was recently proposed provides a systematic controller design approach for controlling remote vibration at multiple points using only a restricted number of sensors and actuators. Valuable physical insight into the existence of control solutions for vibration attenuation at multiple locations is retained with this approach in contrast to alternatives, such as    $\mathcal {H}_{2}$    and    $\mathcal {H}_{\infty }$    methods. A drawback of the existing geometric design approach is that the controller implementation for the broadband case incorporates an inverted local control path transfer function. When the sensor and actuator are noncollocated or when there is significant latency or phase lag in the system, the local control path model will have nonminimum phase characteristics. Therefore, the resulting controller for this situation will itself be unstable due to the inclusion of an inverted nonminimum phase transfer function. In this brief paper, a systematic procedure is presented, which extends the previous work and which yields both a stable and stabilizing controller without requiring a minimum phase control path assumption. Furthermore, robustness against control spillover at out-of-band frequencies is incorporated within this modified design procedure without deteriorating controller performance within the design bandwidth. The detailed control design procedure is illustrated using a simulated beam vibration problem. Finally, the design approach is experimentally validated using a test rig that replicates the problem of vibration transmission in rotary propulsion systems.
['Ur Rehman Eusufzai Ubaid', 'Stephen Daley', 'Simon Pope', 'Ilias Zazas']
Design of Stable and Broadband Remote Vibration Controllers for Systems With Local Nonminimum Phase Dynamics