By Xingjian Jing, Ziqiang Lang
This ebook is a scientific precis of a few new advances within the region of nonlinear research and layout within the frequency area, concentrating on the appliance orientated conception and strategies in line with the GFRF proposal, that's normally performed via the writer long ago eight years. the most effects are formulated uniformly with a parametric attribute procedure, which supplies a handy and novel perception into nonlinear impact on procedure output reaction when it comes to attribute parameters and therefore facilitate nonlinear research and layout within the frequency area. The booklet begins with a short creation to the heritage of nonlinear research within the frequency area, via recursive algorithms for computation of GFRFs for various parametric types, and nonlinear output frequency homes. Thereafter the parametric attribute research technique is brought, which ends up in the recent realizing and formula of the GFRFs, and nonlinear attribute output spectrum (nCOS) and the nCOS dependent research and layout technique. according to the parametric attribute method, nonlinear effect within the frequency area should be investigated with a singular perception, i.e., alternating sequence, that's by way of a few software ends up in vibration keep watch over. importance bounds of frequency reaction features of nonlinear platforms can be studied with a parametric attribute technique, which lead to novel parametric convergence standards for any given parametric nonlinear version whose input-output dating permits a convergent Volterra sequence enlargement. This publication objectives these readers who're operating within the parts with regards to nonlinear research and layout, nonlinear sign processing, nonlinear process identity, nonlinear vibration keep watch over, and so forth. It rather serves as a superb reference in the event you are learning frequency area tools for nonlinear systems.
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Additional resources for Frequency Domain Analysis and Design of Nonlinear Systems based on Volterra Series Expansion: A Parametric Characteristic Approach
X H n ðjω1 , Á Á Á, jωn Þ all the permutations of f1; 2; . . 4), asymmetric GFRFs suffice. 3 The GFRFs for a Single Input Double Output Nonlinear System In many practical cases, nonlinear system models are usually described by a nonlinear state equation with a general nonlinear output function of system states. Sometimes, the output function of interest can also be a nonlinear objective function to optimize. Therefore, the computation of the GFRFs for nonlinear systems in this form would be more relevant in practice.
4 Nonlinear Effect in Each Frequency Generation Period Fig. 1 (Jing et al.
There are also three categories of nonlinearities in terms of input u(t) and output x(t) (similar to those from input u(t) to output x(t)), and there is one linear output y(t). Note that there are no nonlinearities in terms of y(t), and all the nonlinearities come from input u(t) and output x(t). For this reason, the GFRFs from u(t) to y(t) are dependent on the GFRFs from u(t) to x(t). 28b) have no relationship with y(t) but x(t). 28a,b). Similar results can be obtained for the following SIDO NDE system M1 X m K X X cp, mÀp ðk1 ; Á Á Á; km Þ m¼1 p¼0 k1 , km ¼0 M2 X m K X X m¼1 p¼0 k1 , km ¼0 p m Y dki xðtÞ Y d ki uðtÞ ¼0 dtki i¼pþ1 dtki i¼1 p m Y d ki xðtÞ Y d ki uðtÞ e ¼ yðtÞ c p, mÀp ðk1 ; Á Á Á; km Þ dtki i¼pþ1 dtki i¼1 ð2:34aÞ ð2:34bÞ where x(t), y(t), u(t) 2 ℝ.
Frequency Domain Analysis and Design of Nonlinear Systems based on Volterra Series Expansion: A Parametric Characteristic Approach by Xingjian Jing, Ziqiang Lang