Necessity of Nonlinear Control for Robust Rejection of Periodic Disturbances

Dr R.C.H. Lee (CUED)

Abstract

Consider a linear plant with a strictly proper rational transfer function and an input which is a known periodic waveform of unknown amplitude and phase. In the case when the periodic waveform has infinitely many non-zero harmonics, it is pointed out that a linear controller cannot robustly stabilize the plant and achieve asymptotic rejection of the disturbance. For a specific linear plant and a triangular wave disturbance, it is shown by construction that the problem is soluble with a nonlinear controller. Robustness is measured using the gap metric robust stability margin.