Performance-based optimization of LQR for active mass damper using symbiotic organisms search

Abstract

The linear-quadratic regulator (LQR) has been applied to structural vibration control for decades; however, selection of the weighting matrices of an LQR mostly depends on trial and error. In this study, a novel metaheuristic optimization method named as symbiotic organisms search (SOS) algorithm is applied to tuning LQR weighting matrices for active mass damper (AMD) control systems. A 10-story shear building with an active mass damper installed at the top is adopted as a benchmark for numerical simulation in order to realize the optimization performance considering three objective functions for mitigation of structural acceleration. Two common optimization methods including genetic algorithm (GA), and particle swarm optimization (PSO) are also applied to this benchmark for comparison purposes. Numerical simulation results indicate that SOS is superior to GA and PSO on searching the minimized solution of the three objective functions. Meanwhile, minimizing the square root of the sum of the squares of peak modal acceleration achieves the best control performance of structural acceleration among the three objective functions. In addition, force saturation is proposed and applied in the optimization process such that the control force level is close to the force capacity of AMD under specified earthquake intensity. Furthermore, the control performance of the optimized LQR is compared with that of the LQR designed by applying three common weighting selection methods when the 10-story building is subjected to various earthquake excitations. Simulation results demonstrate that the optimized LQR significantly outperforms the three LQRs on structural acceleration responses as expected and reduces story drift slightly better than the three LQRs. Finally, the performance-based optimized LQR is experimentally validated by conducting shake table testing in the laboratory. The experimental results and structural control performance are discussed and summarized thoroughly.