Multi-objective optimal design on vibration suppression of building structures with Active Mass Damper based on state difference feedback

The vibration suppression of building structures with Active Mass Damper and delayed PD feedback is studied by regarding the multiple control performance goals. The stable region is obtained firstly by using the method of stability switch. A multi-objective optimization problem is formulated for the control design and is solved with the two-step simple cell mapping method. The Pareto set and Pareto front are obtained. It is shown the Active Mass Damper with delayed PD feedback can improve the stability of building structure significantly, and a proper small time delay is beneficial to the control performance. This finding is confirmed by Numerical simulations and experimental studies. Moreover, it is shown the control performance is sensitive to the time delay, when the time delay deviates from the optimal value, it will deteriorate the control performance, even lead to unstable vibration.