The internal model principle for periodic disturbances with rapidly time‐varying frequencies

In this paper, we study the limitations of scheduling an internal model to reject disturbances with a time-varying frequency. Hence, any adaptive method that uses scheduling and frequency estimation is also limited in the same manner. The limitations of scheduling are to investigate by posing and solving the problem of rejecting periodic disturbances from a multichannel system when the frequencies of the periodic disturbances are changing rapidly in time by designing an scheduled controller that satisfies the internal model principle. The periodic disturbances are modeled by a sum of sinusoids and the frequencies of the disturbances are used for scheduling the controller. It is shown that a controller that regulates input additive disturbances may not regulate the same disturbances added to the output of the system. This is in contrast to the classical case where the frequency of the disturbances is constant. Copyright © 2011 John Wiley & Sons, Ltd.

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