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 Fourier Transform (FFT)-based methods are well-suited for respective analysis. While FFT algorithms inherently assume signal periodicity, rotating systems often exhibit true periodic behavior (e.g., shaft rotation frequencies). Using angle-sampled data rather than time-sampled data allows direct analysis of oscillations relative to rotational cycles, which is particularly useful for tracking unbalance or periodic external excitation in rotating assemblies. Modelica provides several built-in resources to address these challenges. First of all, inverse models have the potential to derive an ideal control signal in time domain. For periodic disturbances, this ideal control is likely to be approximated well by a periodic, i.e. Fourier-transformable signal. Modelica is an appropriate model environment to store and retrieve tabled FFT data depending on operating conditions such as rotational speed. In a real-time application, synthesizing control signals from precomputed Fourier tables offers a practical alternative to executing potentially complex inverse models online, reducing computational effort and system complexity. The paper demonstrates this approach using the example of mitigating oscillations induced by an internal combustion engine in a hybrid automotive power train.