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

Periodic disturbances existing beyond the Nyquist frequency will cause intersample oscillations and degrade the control performance. In this paper, we propose a disturbance observer-based multirate control scheme for rejecting such periodic disturbances. When the disturbance is a single sinusoid, the solution for system output including the intersample information is derived in the steady state. Based on the steady-state output response, a sufficient condition is given for rejecting periodic disturbance beyond the Nyquist frequency. As a matter of fact, solving the sufficient condition is a problem of quadratic programming with some constraints. To remove the constraints, a periodic time-varying filter is also suggested to enhance the disturbance rejection performance. A numerical example is presented to demonstrate the effectiveness of the proposed method.