Grey forecasting model for active vibration control systems

Based on the grey theory, a GM(1,1) forecasting model and an optimal GM(1,1) forecasting model are developed and assessed for use in active vibration control systems for earthquake response mitigation. After deriving equations for forecasting the control state vector, design procedures for an optimal active control method are proposed. Features of the resulting vibration control and the influence on it of time-delay based on different sampling intervals of seismic ground motion are analysed. The numerical results show that the forecasting models based on the grey theory are reliable and practical in structural vibration control fields. Compared with the grey forecasting model, the optimal forecasting model is more efficient in reducing the influences of time-delay and disturbance errors.