Time-periodic phenomena, elsewhere also classified as cyclo-stationary processes, show up in many engineering fields. Think of wind turbines or helicopters with blade-to-blade manufacturing deviations, rotating machinery such as anisotropic shaft-bearing systems, the vibrations and acoustic noise in combustion engines and pumps, satellite systems, the electrical impedance of a living heart for cardio-vascular monitoring, respiratory systems, multirate filter banks in digital communications, or the production of harmonic distortions in power distribution networks to name a few. Those systems have the special property that their dynamical behaviour changes (quasi) periodically over time. The cyclic effects in the above-mentioned applications can be faithfully modeled as linear time-periodic (LTP). This way of LTP modeling can be seen as a step from the well-established identification framework for linear time-invariant (LTI) systems towards the more complex approaches for nonlinear time-variant (NLTV) systems. The presented work aims at extracting in a sound and pragmatic way parametric and nonparametric LTP models, including the quantification of the power spectrum of disturbing error sources such as noise, nonlinear distortions and unmodeled time-variations. Different frequency domain identification schemes, using simple as well as more sophisticated techniques, are developed for time-periodic systems operating in open- and closed-loop.
- Weakly nonlinear time periodic systems