Numerical Solution to the Inverse Sinusoidal Input Describing Function

Fatemeh Zamanian, Matthew A. Franchek, Behrouz Ebrahimi, Karolos M. Grigoriadis

Research output: Contribution to journalArticlepeer-review


A computational solution to the inverse sinusoidal input describing function (SIDF) for a broad class of static nonlinearities is presented. The proposed numerical solution uses the SIDF gain and phase distortions to identify the nonlinearity. This solution, unlike existing methods in the literature, does not require a priori knowledge of the nonlinearity structure in the estimation process and is applicable to both single- and double-valued nonlinearities. The output from the algorithm is a nonparametric model of the nonlinearity from which a parametric model can be recovered by least-square estimation (LSE) method. Three examples are presented to validate the proposed algorithm.

Original languageEnglish (US)
Article number051008
JournalJournal of Dynamic Systems, Measurement and Control, Transactions of the ASME
Issue number5
StatePublished - May 1 2017


  • asymmetric nonlinearities
  • gain and phase distortions
  • hysteresis nonlinearities
  • inverse sinusoidal input describing function
  • memoryless nonlinearities
  • static (explicit) nonlinearities

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Information Systems
  • Instrumentation
  • Mechanical Engineering
  • Computer Science Applications


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