A pole-zero based criterion for optimal placement of collocated sensor-actuator pair. (16th June 2021) - Piron, Dimitri; Pathak, Shashank; Deraemaeker, Arnaud; Collette, Christophe
Highlights: Pole-zero distance based criterion for optimal point sensor/actuator placement. The transmission zero is approximated to reduce the computational time. The proposed criterion leads to better damping compared to existing criteria. Abstract: A new and computationally efficient criterion is developed concerning the optimal placement of a collocated sensor-actuator pair for active control of structural vibrations with a low authority controller. The basic idea behind the proposed criterion is based on the maximization of the pole-zero distance in open-loop which has a direct link with the maximum achievable damping ratio once in closed-loop. Unlike poles, the determination of transmission zeros is computationally tedious because it depends upon the placement of the sensor-actuator pair. Therefore, a new approximation to reliably estimate the transmission zeros is also introduced which remarkably enhances the computational efficiency of the proposed optimization criterion. The effectiveness of the proposed criterion is demonstrated on a cantilever beam and a simply supported plate and is also compared with two other widely used criteria: the Gramian controllability and the spatial H 2 norm. It is shown that the proposed criterion is pertinent and ensures higher damping values for the cantilever beam compared to the other two criteria. Nonetheless, the criterion requires adaptations to improve its reliability for structure with large modal density such as a simply supported plate.