Estimation of nonparametric harmonic transfer functions for linear periodically time-varying systems using periodic excitations

In this paper a nonparametric estimation procedure is proposed in order to identify continuous (discrete)-time, linear periodically time-varying (LPTV) systems. Further, multisine excitations are applied onto a LPTV system such that the system transient effects will vanish completely when the system is operating in steady state. The key idea is to decompose a LPTV system into an (in)finite series of transfer functions, the so-called harmonic transfer functions (HTF). From an identification point of view, the parallel structure, which consists of a weighted sum of the HTF´s, is truncated to a desirable order. A high quality estimate of the nonparametric HTF´s with its uncertainty embedded in an errors-in-variables framework is then obtained from only one experiment; making use of methods, the so-called local polynomial method (LPM), that are recently developed for multivariable linear time invariant systems. The effectiveness of the LPM will be first pointed up through simulations before a real system will be identified. The methodology is then eventually demonstrated on a real-life periodically time-varying electronic system.