Extension of Local Polynomial Method for Periodic Excitations

Abstract

This paper extends the Local Polynomial Method (LPM) for linear and time invariant systems excited by periodic signals. LPM is a robust and fast method for finding a non-parametric Frequency Response Function (FRF) estimate. A good FRF estimate is important in designing a good controller. Since both the system FRF and the transient behave smooth as a function of the frequency, LPM assumes that these functions can be approximated locally by a low degree polynomial. However, if the FRF varies strongly as a function of the frequency this assumption results in bias errors due to under-modeling. That is why this paper presents a transient LPM. This transient LPM suppresses the transients as well as the original LPM but does not introduce bias errors due to under-modeling. The variance of the FRF estimate via the transient LPM will be slightly larger than the variance of the FRF estimate via LPM. However, when these non-parametric FRF estimates are used to find a parametric estimate, this variance difference will not affect the result. Thus, the reduced bias of the FRF estimate via the transient LPM will lead to a better parametric FRF estimate. A disadvantage is that the transient LPM cannot estimate the level of the nonlinear distortions..