Design of Optimal Digital Feedback Regulator Based on First and Second Order Information and its Application to Vibration Control

摘要

Vibration control is important in mechatronics, aerospace engineering, civil engineering and other engineering fields. Recently, active vibration control rather than passive vibration control is being used, reflecting modern control theory. In this paper, we propose an optimal digital feedback regulator which is based only on the first -and second-order information for a system elminating transient disturbance. The Wiener-Hopf criterion is adopted in this control scheme. Since the controller is constructed as a finite-impulse response filter, the computation require to design the optimal filter is reduced to that of solving the finite discrete -time Wiener -Hopf equation. This equation is solved recursively, increasing the order of the system each time, via the fast algorithm proposed here. Furthermore, the solvability condition of the equation is clarified and the stability of the feedback system is proved. The effectiveness of the proposed method is verified experimentally by application of the control system to grab-swing elimination in a moving crane.