Stability analysis of active vibration control of building structures using PD/PID control

Proportional-derivative (PD) and proportional-integral-derivative (PID) controllers are the most popular algorithms in industrial applications. However, there are few published theory results of PD/PID controllers on the structural vibration control applications. In this paper, we analyze the stability of the active vibration control system for both the linear and nonlinear structures. We give explicit sufficient conditions for choosing the PID gains. The theory conclusions are verified via numerical simulations and a two-story building prototype. These results give validation of our theory analysis.