Quasi-Periodic Feedforward Control Based on Inverse Model Tabled FFT

Abstract

Mitigating periodic oscillations (e.g. in rotating systems)is a common control engineering problem. Fast FourierTransform (FFT)-based methods are well-suited forrespective analysis. While FFT algorithms inherently assumesignal periodicity, rotating systems often exhibit trueperiodic behavior (e.g., shaft rotation frequencies). Usingangle-sampled data rather than time-sampled data allowsdirect analysis of oscillations relative to rotationalcycles, which is particularly useful for tracking unbalanceor periodic external excitation in rotating assemblies.Modelica provides several built-in resources to addressthese challenges. First of all, inverse models have thepotential to derive an ideal control signal in time domain.For periodic disturbances, this ideal control is likely tobe approximated well by a periodic, i.e.Fourier-transformable signal. Modelica is an appropriatemodel environment to store and retrieve tabled FFT datadepending on operating conditions such as rotational speed.In a real-time application, synthesizing control signalsfrom precomputed Fourier tables offers a practicalalternative to executing potentially complex inverse modelsonline, reducing computational effort and systemcomplexity. The paper demonstrates this approach using theexample of mitigating oscillations induced by an internalcombustion engine in a hybrid automotive power train.