Equivalence between adaptive feedforward cancellation and disturbance rejection using the internal model principle

The paper shows that a large class of adaptive algorithms for disturbance cancellation yields control systems that are equivalent to compensators implementing the internal model principle (IMP). The fact has been known to be true for periodic disturbances with fixed frequency. However, the paper shows that the result can be extended to disturbances of time-varying frequency (i.e. frequency-modulated signals), regardless of the rate of variation of the frequency. In particular Several adaptive controllers, are shown to be equivalent to linear lime-varying compensators implementing the IMP. Further, a pseudo-gradient algorithm produces the same responses as a polytopic linear parameter-varying compensator. Copyright (C) 2009 John Wiley & Sons, Ltd.