Design of optimal digital controller considering frequency-shaped cost function

This paper presents the optimal digital feedback controller for eliminating stationary disturbance, the design of which is based on the system's impulse response data and the spectral density function of the disturbance signal. This control scheme adopts the Wiener-Hopf criterion which minimizes the frequency-shaped cost function. Since the free parameter of the controller is constructed as a FIR filter, the computation for designing the optimal filter is reduced to 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. Furthermore, the stability of the feedback system is guaranteed. The effectiveness of the proposed method is verified both simulations and experiments by application to the oscillation control of a load hanging from a traveling crane.