Extension of Local Polynomial Method for Periodic Excitations

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3 Citations (Scopus)


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.
Original languageEnglish
Title of host publicationProceedings of the 16th IFAC Symposium on System Identification, Brussels, Belgium, July 11-13, 2012
Number of pages5
ISBN (Print)978-3-902823-06-9
Publication statusPublished - 11 Jul 2012
Event16th IFAC Symposium on System Identification (Sysid 2012) - SQUARE Brussels Meeting Center, Brussels, Belgium
Duration: 11 Jul 201213 Jul 2012

Publication series

NameIFAC Proceedings Volumes
ISSN (Print)1474-6670


Conference16th IFAC Symposium on System Identification (Sysid 2012)
Abbreviated titleSysid 2012
OtherThe scope of the symposium covers all major aspects of system identification, experimental modelling, signal processing and adaptive control, ranging from theoretical, methodological and scientific developments to a large variety of application areas. To enhance the applications and industrial perspective of the symposium, participation by authors from industry is particularly encouraged. It is the intention of the organizers to promote SYSID 2012 as a meeting place where scientists and engineers from several research communities can meet to discuss issues related to these areas.
Internet address


  • system identification
  • periodic
  • transfer function
  • non-parametric identification
  • leakage


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