Disturbance observer-based multirate control for rejecting periodic disturbances to the Nyquist frequency and beyond

Intersample behavior cannot be ignored when a sampled-data control system is subject to periodic disturbances beyond the Nyquist frequency. In this paper, a disturbance observer-based multirate control scheme is proposed to deal with such a periodic disturbance problem. First, using discrete-time Fourier series, the effect of the periodic disturbance on steady-state response of the plant output including intersample information is derived. Next, based on the steady-state output response, a sufficient condition is provided for minimization of the disturbance effect on the output. It turns out that solving the sufficient condition is a problem of quadratic optimization with several equality constraints. The proposed approach is applied on vibration control of mechanical resonant modes beyond the Nyquist frequency in a commercial hard disk drive. Perfect disturbance elimination and disturbance deduction of 72% in fast-rate discrete-time response are observed in the simulation and experiment, respectively.