Controller and sensor placement for a 3D irregular building based on Hankel norm

Abstract

Placing controllers and sensors properly is important in structural health monitoring and control. Many optimization methods require much computation efforts. This paper used Hankel norms to develop the placement rules, because they involve the input and output gains and thus could be shaped by the locations. In modal form, their computations are relatively simple. The location and mode influences on norms were arranged in rows and columns, respectively, to form a matrix, and was normalized by the column (mode) root mean square. The optimization goal is to choose locations with higher index values and lower correlations to ensure higher controllability and observability, and with less effort to be compensated for by gains. Hankel norm is compatible with the LQR control objectives in that they are both 2-norm, so the methodology is appropriate to be applied to the base isolation benchmark building for structural control, which is an eight-story irregular building with ninety-two candidate locations for controllers and thirty-six locations for sensors. Following the method, ten controller locations and eighteen sensor locations were determined. Earthquake time history analysis using LQG technique validated the effectiveness of thus determined subset of locations by comparing with other subset of locations.