We consider gradient-based adaptive feed-forward cancellation of measured sinusoidal disturbances with applications to propulsion systems for electric trains. Here the design of the adaptive feed-forward controller corresponds to tracking a complex number. We show that a Cartesian or a polar complex number parameterization unexpectedly leads to quite different adaptation properties. For the polar form, all valid operating points are covered by a fixed controller structure. This is not the case for the Cartesian form algorithm, but this approach is more robust to the choice of initial conditions. The corresponding two algorithms are analyzed and successfully evaluated using power lab experiments.
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