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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.

PID control has been largely applied in the industry process control because of its robustness and easy realization, But it is very difficult to tune the three parameters of PID controller, which often leads to oscillation and overshoot of the controlled object. Due to no repetition and random of chaos dynamics, a method to search for PID controller parameters based on chaos variable is proposed according to the performance index of control system. and then by which practicality pendulum is controlled. Experiment results show that the method is efficient to realize self-tuning parameters of PID controller, provides an effective way for optimization design of PID controller.