Periodic disturbance rejection to the Nyquist frequency and beyond

In this paper, we address periodic disturbance rejection for sampled-data control systems, where the frequency of the disturbance can be beyond the Nyquist frequency of the limited measured plant output sampling rate. The disturbance effect on steady-state response of the fictitious fast-rate plant output including intersample information is obtained using discrete-time Fourier series. A sufficient condition for disturbance rejection together with a sufficient and necessary condition for perfect disturbance elimination are provided by employing the steady-state response. A simple but effective controller design procedure combining H∞ loop shaping, Youla–Kucera parameterization, and gradient methods is provided to achieve the two conditions. The proposed approach is applied on vibration control beyond the Nyquist frequency in a commercial hard disk drive. The effectiveness of the proposed approach is verified by our simulation results showing disturbance rejection of 62% and perfect disturbance elimination, as well as by our experimental results showing disturbance rejection of 54%.