Stable active vibration control of building structure subjected to bidirectional earthquake

Proportional-derivative (PD) is highly favored algorithms in terms of industrial applications. Although, there are infrequent broadcasted theory results of PD controller in connection to structural vibration control applications. In this paper, we analyze the stability of the active vibration control system for both the linear model and nonlinear model of building structures under bidirectional seismic excitation taking into consideration lateral-torsional vibrations. We state comprehensive sufficient conditions for choosing the PD gains. The stability theories are verified through numerical simulations and a two-storey building prototype. The extracted results validates our theory analysis.