Bound for the magnitude characteristics of nonlinear output frequency response functions

Bound for the magnitude characteristics of nonlinear output frequency response functions by S. A. . Billings Download PDF EPUB FB2

Billings SA, Lang ZQ () A bound of the magnitude characteristics of nonlinear output frequency response functions. Int J Control, Part 1, 65(2)– and Part 2, Author: Xingjian Jing, Ziqiang Lang. Magnitude bounds of nonlinear frequency response functions, including the GFRFs and output spectrum, have been studied in [32] [33][34] with a parametric characteristic point of.

Magnitude bounds of nonlinear frequency response functions, including the GFRFs and output spectrum, have been studied in [32][33] [34] with a parametric characteristic point of.

In Part 1 of this paper the concept of a bound for the output frequency response magnitude characteristics of nonlinear systems was proposed, and general calculation and analysis procedures were.

When some components within the systems have nonlinear characteristics, the whole system will behave nonlinearly. The concept of Nonlinear Output Frequency Response Functions (NOFRFs) was proposed by the authors recently and provides a simple way to investigate nonlinear systems in the frequency domain.

The present study is concerned. Output Frequency Characteristics of Nonlinear Systems into the super-harmonic and inter-modulation phenomena in output frequency response of.

Nonlinear effects may significantly modify the shape of the resonance curves of harmonic of all, the resonance frequency is shifted from its "natural" value according to the formula = +, where is the oscillation amplitude and is a constant defined by the anharmonic coefficients.

Second, the shape of the resonance curve is distorted (foldover effect). Billings SA, Lang ZQ () A bound of the magnitude characteristics of nonlinear output frequency response functions.

Int J Control, Part 1, 65(2)– and Part 2, 65(3)– Google Scholar. Jing XJ, Lang ZQ (a) On the generalized frequency response functions of Volterra systems. Trans ASME J Dyn Syst Meas Control (6) Google Scholar Jing XJ, Lang ZQ, Billings SA, Tomlinson GR () The parametric characteristic of Author: Xingjian Jing, Ziqiang Lang.

GA is applied to solve an optimisation problem associated with generalised frequency response functions of nonlinear systems. The result is then used, together with other techniques developed by the authors, to evaluate a bound on the system output frequency response. The new bound is shown to be more accurate and less conservative compared.

Conclusions. The OFRF based representation for output frequency responses of nonlinear systems (Lang, Billings, Yue, & Li, ) has demonstrated significant advantages in both the system analysis and design.

However, the OFRF only shows a polynomial relationship between the system’s output spectrum and nonlinear characteristic parameters; it cannot explicitly Cited by: 2. A bound for the magnitude characteristics of nonlinear output frequency response functions: Part 2. Practical computation of the bound for systems described by the nonlinear autoregressive model with exogenous input.

Int J Control,– Google ScholarCited by: 1. The concept of Nonlinear Output Frequency Response Functions (Lang & Billings, ) – NOFRFs – is a new extension of the FRF to the nonlinear case. One of its most attractive feature is its one-dimensional nature, which has many advantages, as has been demonstrated by a wide range of studies Lang and Peng (), Peng et al.

().Cited by: 7. An important phenomenon for nonlinear systems in the frequency domain is that there are always very complicated output frequencies, appearing as super-harmonics, sub-harmonics, inter-modulation and so on. This usually makes it rather difficult to analyze and design the output frequency response for nonlinear systems, compared with linear by: The Nonlinear Output Frequency Response Functions (NOFRFs) are a concept which provides a new extension of the well-known concept of the Frequency Response Function (FRF) of linear systems to the nonlinear case.

The present study introduces a NOFRFs based approach for the analysis of nonlinear systems in the frequency domain. It is well known that a nonlinear Cited by: 7.

Magnitude bounds of frequency response functions of nonlinear systems can also be studied with a parametric characteristic approach, which result in novel parametric convergence criteria for any given parametric nonlinear model whose input-output relationship allows a convergent Volterra series expansion.

Output Frequency Response Function (NOFRF) [15], Output Frequency Response Function (OFRF) [16], and Higher Order Sinusoidal Input Describing Functions (HOSIDF) [17] have been proposed. The OFRF reveals an analytical relationship between the output frequency response of nonlinear systems and the parameters which define the system nonlinearities and.

Given the range of the input frequency, an explicit expression for the output frequency range has been derived by Lang and Billings (). Based on the above results for output frequency responses of nonlinear systems, a new concept known as Nonlinear Output Frequency Response Functions (NOFRF) was recently introduced in (Lang and Billings, ).Cited by: 3.

Frequency Domain Analysis and Design of Nonlinear Systems based on Volterra Series Expansion The Generalized Frequency Response Functions and Output Spectrum of Nonlinear Systems.

Xingjian Jing, Ziqiang Lang. Pages Output Frequency Characteristics of Nonlinear Systems. Xingjian Jing, Ziqiang Lang. Pages The characteristics of oeneralised frequency response functions (GFRFs) of nonlinear systems in hiaher dimensional space are investþated using a combination of graphical and symbolic decomposition techniques.

It is shown how a systematic analysis can be achieved for a wide class of nonlinear systems in the frequency domain usina the proposed. The above simulation studies sufficiently demonstrate the significance of the proposed output frequency response function of nonlinear systems in the representation of the system output spectrum and the effectiveness of the method, which numerically determines this function as described in Proposition 4 or Corollary directly from the system output by: A unified theory of time-domain and frequency-domain four-wave mixing processes, which is based on the nonlinear response function R(t 3, t2, t), is developed.

The response function is expressed in terms of the four-point.3. Nonlinear Output Frequency Response Functions Nonlinear Output Frequency Response Functions under General Inputs The definition of NOFRFs is based on the Volterra series theory of nonlinear systems.

The Volterra series extends .