Frequency Domain Analysis of Nonlinear Systems Driven by Multiharmonic Signals

Solomou, M.; Rees, D.; Chiras, Neophytos

doi:10.1109/tim.2003.822477

Cited by 21 publications

(8 citation statements)

References 12 publications

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“…Substituting these results into Equations (18)(19), the output spectrum is clearly a power series with respect to the parameter c. When there are more nonlinear terms, it is obvious that the computation process above can directly result in a straightforward multivariate power series with respect to these nonlinear parameters. To check the alternating phenomenon of the output spectrum, consider the following values for each linear parameter: m=240, k0=16000, B=296, Fd=100, and 8.165  …”

Section: Alternating Phenomenon In the Output Spectrum And Its Influencementioning

confidence: 99%

“…The output spectrum at frequency  is given in (18)(19). From Lemma 3 in Appendix D, it can be derived for this case that…”

Section: Alternating Conditionsmentioning

confidence: 99%

“…Frequency domain methods for nonlinear analysis have been investigated for many years. There are several different approaches to the analysis and design for nonlinear systems, such as describing functions [5,13], harmonic balance [18], and frequency domain methods developed from the absolute stability theory [10], for example the well-known Popov circle theorem [12,21] etc. Investigation of nonlinear systems in the frequency domain can also be done based on the Volterra series expansion theory [11,15,16,19,20].…”

Section: Introductionmentioning

confidence: 99%

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Vibration Control by Exploiting Nonlinear Influence in the Frequency Domain

Jing

2012

Advances on Analysis and Control of Vibrations - Theory and Applications

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Section: Alternating Phenomenon In the Output Spectrum And Its Influencementioning

confidence: 99%

“…The output spectrum at frequency  is given in (18)(19). From Lemma 3 in Appendix D, it can be derived for this case that…”

Section: Alternating Conditionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Vibration Control by Exploiting Nonlinear Influence in the Frequency Domain

Jing

2012

Advances on Analysis and Control of Vibrations - Theory and Applications

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“…This conflicts with the sinusoidal excitation condition required [Slotine, & Weiping Li, 1991, Atherton, 1975, Nuij, Bosgra, & Steinbuch, 2006, Nuij, 2007. This harmonic input signal u(t) causes several non-linear phenomena in the output signal y(t) [Bussgan, Ehran, & Graham, 1974, Wiener, & Spina, 1980, Billings, & Tsang, 1989, Solomou, Evans, Rees, & Chiras, 2002, Yue, Billings, & Lang, 2005 …”

Section: Hosidf Of a Non-linear Plant In A Controlled Systemmentioning

confidence: 99%

Measuring the higher order sinusoidal input describing functions of a non-linear plant operating in feedback

Nuij

Steinbuch

Bosgra

2008

Control Engineering Practice

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In this paper two measuring techniques are presented for measuring the Higher Order Sinusoidal Input Describing Functions (HOSIDF) of a non-linear plant operating in feedback. The HOSIDF relate the magnitude and phase of the harmonics of the periodic response of a non-linear system to the magnitude and phase of the sinusoidal excitation. In a controlled system the harmonics generated by the non-linear system will be fed back to the input changing the sinusoidal excitation into a harmonic excitation. The first method applies linear techniques to compensate the bias caused by the harmonic components in the excitation signal. The second method uses a modified repetitive control scheme to suppress the harmonic components in the excitation signal. The effectiveness of both methods is tested in simulations of a mass subjected to Coulomb friction, Stribeck-effect and hysteresis in the pre-sliding regime. The friction forces are modeled with the modified Leuven friction model. The results are compared with the HOSIDF simulated under open loop condition. Both methods prove able to produce reliable results.

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“…Frequency domain methods for nonlinear systems have also been investigated for many years. There have already been several different approaches to the analysis and design for nonlinear systems, such as describing functions (Graham andMcRuer 1961, Nuij et al 2006), harmonic balance (Solomou et al 2002), and frequency domain methods developed from the absolute stability theory (Leonov et al 1996), for example the wellknown Popov circle theorem, and so on. systems, the generalized frequency response function (GFRF) was defined in George (1959), which is similar to the transfer function of linear systems.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear influence in the frequency domain: Alternating series

Jing

Lang

Billings

2011

Systems & Control Letters

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Abstract:The nonlinear influence on system output spectrum is studied for a class of nonlinear systems which have Volterra series expansion. It is shown that system output spectrum can be expressed into an alternating series with respect to some model nonlinear parameters under certain conditions. This alternating series has some interesting properties by which system output spectrum can be suppressed easily. The sufficient (and necessary) conditions in which the output spectrum can be transformed into an alternating series are studied. These results reveal a novel characteristic of the nonlinear influence on a system in the frequency domain, and provide a novel insight into the analysis and design of a class of nonlinear systems. Examples are given to illustrate the results.

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Frequency Domain Analysis of Nonlinear Systems Driven by Multiharmonic Signals

Cited by 21 publications

References 12 publications

Vibration Control by Exploiting Nonlinear Influence in the Frequency Domain

Vibration Control by Exploiting Nonlinear Influence in the Frequency Domain

Measuring the higher order sinusoidal input describing functions of a non-linear plant operating in feedback

Nonlinear influence in the frequency domain: Alternating series

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