Harmonic Modeling and Control

Harmonic modeling involves transforming a periodic systemPeriodic system into an equivalent time-invariant model of infinite dimension. The states of this model, also referred to as phasors, are represented by coefficients obtained through a sliding Fourier decomposition process. This chapter aims to present a unified and coherent mathematical framework for harmonic modeling and control. By adopting this framework, the analysis and design processes become significantly simplified, as all the methods established for time-invariant systems can be directly applied. Within this framework, we explore the application of these methods to tackle the task of designing control laws based on harmonic pole placementHarmonicpole placement for Linear Time-Periodic (LTP) systems. Additionally, we delve into the computational aspects associated with these control designs.