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Research Papers

Numerical Solution to the Inverse Sinusoidal Input Describing Function

[+] Author and Article Information
Fatemeh Zamanian

Mechanical Engineering Department,
University of Houston,
Houston, TX 77004
e-mail: s.zamanian@gmail.com

Matthew A. Franchek, Karolos M. Grigoriadis

Professor
Mechanical Engineering Department,
University of Houston,
Houston, TX 77004

Behrouz Ebrahimi

Mechanical Engineering Department,
University of Houston,
Houston, TX 77004

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received June 13, 2016; final manuscript received November 13, 2016; published online March 13, 2017. Assoc. Editor: Davide Spinello.

J. Dyn. Sys., Meas., Control 139(5), 051008 (Mar 13, 2017) (11 pages) Paper No: DS-16-1314; doi: 10.1115/1.4035296 History: Received June 13, 2016; Revised November 13, 2016

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.

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Topics: Algorithms , Signals
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Figures

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Fig. 1

Describing function representation

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Fig. 2

(L) Piecewise continuous nonlinearity and (R) corresponding SIDF

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Fig. 3

Example of an explicit double-valued nonlinearity

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Fig. 4

Illustration of the method of cursors

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Fig. 5

Schematic of the hysteresis nonlinearity

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Fig. 6

Nonparametric output solution for the hysteresis nonlinearity for η1 and Δ1

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Fig. 7

Nonparametric output solution for the hysteresis nonlinearity for η2 and Δ2

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Fig. 8

Nonlinear controller gain from the proposed numerical solution, KP

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Fig. 9

Comparison for estimation of KP gain from two different methods (Ref. [7] and this work)

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Fig. 10

Schematics of the asymmetric hysteresis nonlinearities: (L) with biased output and (R) with asymmetric input amplitude range and biased output

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Fig. 11

Output of the proposed inverse SIDF algorithm for the first asymmetric hysteresis nonlinearity

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Fig. 12

Output of the proposed inverse SIDF algorithm for the second asymmetric hysteresis nonlinearity

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