Sensor placement for modal analysis and optimal output feedback control

Abstract

Performance of experimental modal analysis and output feedback control depends on the set of sensor locations due to limited measurement information and measurement noise. The modal analysis is one of system identification methods for structures and output feedback control is one of control systems for structures with easy implementation. Stochastic optimal output feedback control is newly developed for structural control with easy implementation and consideration of noise statistics. We propose systematic methods to select the optimal set of sensor locations based on the estimation error cost function for modal analysis and control performance index for stochastic optimal output feedback control, respectively. The measure of the estimation error cost function is obtained from the preliminary eigenvector information obtained by FEM analysis or preliminary experiments. This method utilizes ``singularity factor(SF)`` concept, which is developed to deal with damped asymmetric systems in state space form for various types of sensors and orthogonality of partial eigenvectors by limited measurement. SF is a measure of full state estimation error based on noisy partial measurement. The control performance measure is obtained from linear quadratic performance integral. The optimal control performance measure is the minimum performance measure for a given measurement condition. Depending on the set of sensor locations, the optimal output feedback control performance varies or even the stable control is impossible because of unobservability. The optimal set of sensor locations for modal analysis and stochastic optimal output feedback control can be obtained by performance calculations of all possible candidates. To overcome this problem, a search method to find a suboptimal set with much reduced computational load is also presented.