Determination of optimal sensor-actuator position for active vibration damping in collocated SISO systems using a pole-zero distance criterion for fast convergence of the search algorithm

The position of the transducers in active control architectures is critical to ensure the performance and has consequently been studied during the last few decades. However, the placement criteria often require the use of extensive search algorithms that demand numerous iterations, leading to prohibitive computational time for large and/or complex structures. To overcome this limitation, this paper investigates the use of the pole-zero (PZ) distance placement criterion as the starting point for a simple gradient algorithm. This open-loop criterion is based on the direct link between the PZ distance and the maximum reachable damping: the obtained position locates in the vicinity of a high damping area which ensures the convergence of the search algorithm, for fewer iterations. A numerical simulation is performed to assess the performance of the proposed approach and compared to a genetic algorithm optimization. A significant reduction of the processing time is observed while the solution shows an improved robustness to transducers misplacement.