A numerical method for choice of weighting matrices in active controlled structures

A feedback control system usually implements active and semi-active control of seismically excited structures. The objective of the control system is described by a performance index, including weighting matrix norms. The choice of weighting matrices is usually based on engineering experience. A new procedure for weighting matrix components choice based on the parametric optimization method is developed in this study. It represents a two-step optimization process. In the first step a discrete-time control system is synthesized according to a quadratic performance index. In the second step the weighting coefficients are obtained using the results of the first step. Numerical simulation of a typical structure subjected to earthquakes is carried out in order to demonstrate the effectiveness of the proposed method. It shows that applying the proposed technique provides a choice of the weighting matrices and results in enhanced structural behaviour under different earthquakes.