Accurate Frequency Domain Identification of ODEs with Arbitrary Signals

The control of physical systems, governed by differential equations, frequently requires the identification of dynamical systems. Frequency domain identification has seen much progress over the last decades. Errors due to the usage of arbitrary signals and finite samples, originally understood as leakage errors, were identified as transient effects that can be corrected exactly on discrete systems and asymptotically on sampled continuous system. We present an alternative exploration of frequency domain identifications errors, by regarding them as spurious inputs which arise as artifacts of signal windowing. A correction procedure for these effects is proposed. Two families of windowing functions are considered, one leading to polynomial, the other to non-polynomial error convergence. The approach resembles the modulating function technique, filtering out the effects of initial conditions, while retaining the spectral interpretation of frequency domain methods and the low computational cost of computing FFTs.