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Describing function

About: Describing function is a research topic. Over the lifetime, 1742 publications have been published within this topic receiving 26702 citations.


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TL;DR: A new method to identify various linear and nonlinear parameters in PMLM, using a hysteretic relay feedback, derived from the harmonic balance condition, to enable direct computation of model parameters with a minimum number of relay experiments is proposed.
Journal ArticleDOI
TL;DR: The Elliptic Describing Function (EDF) as mentioned in this paper is a new describing function which allows the waveshape of a limit cycle to be determined after the amplitude and frequency have been found.
Abstract: A new describing function called the Elliptic Describing Function (EDF) is defined which allows the waveshape of a limit cycle to be determined after the amplitude and frequency have been found. The application of the EDF is nonrigorous mathematically but is justified by examples. The technique is based on the fitting of the nonlinear characteristic-whatever its shape so long as it is single-valued, odd-symmetrical, and frequency-independent-by an odd cubic polynomial. Considerable evidence exists which justifies this seemingly drastic approximation. Three examples are given illustrating the errors involved. Comparisons are made with the ordinary DF and new RMS DF for two examples and with a total of six DF's for a third. The results are encouraging.
M. A. Johnson1
01 May 1974
TL;DR: In this article, a nonlinear stationary homogeneous digital filter DIRSIT (derivative information recovery by a selective integration technique) is investigated and the spectrum of a quasi-linear discrete describing function (DDF) is obtained by a digital measuring scheme.
Abstract: A nonlinear stationary homogeneous digital filter DIRSIT (derivative information recovery by a selective integration technique) is investigated. The spectrum of a quasi-linear discrete describing function (DDF) to DIRSIT is obtained by a digital measuring scheme. A finite impulse response (FIR) approximation to the quasi-linearization is then obtained. Finally, DIRSIT is compared with its quasi-linear approximation and with a standard digital differentiating technique. Results indicate the effects of DIRSIT on a wide variety of practical signals.
Journal ArticleDOI
TL;DR: In this paper , the authors explore the dependence of limit cycle frequency and magnitude on the dual-rate sampling rates of a particular class of multi-rate haptics controllers and utilize the nonlinear control theory tool of describing function analysis along with numerical simulations to establish the same.
Abstract: The onset of instability during virtual or remote haptic interaction is most often associated with the existence of limit cycles that are perceptible to a human operator’s touch and even hearing. Time discretization due to sampling, position quantization due to ubiquitous use of optical encoders, and the device Coulomb friction are the main factors that contribute to the occurrence of limit cycles in haptic systems. The frequency and magnitude of such limit cycles are important as they limit the control gains that characterize the dynamics of the rendered environments. In earlier works, the effect of discrete sampling and position quantization on the behavior of limit cycles exhibited in uniform-rate haptics controllers has been studied but a similar analysis for multi-rate haptics controllers has not been reported yet. Towards this end, the present work explores how sampling of the position data at two distinct rates - dual-rate sampling - for implementation of stiff virtual walls affect the limit cycle behavior in a particular class of multi-rate haptics controllers. Specifically, we intend to evaluate the dependence of limit cycle frequency and magnitude on the dual-rate sampling rates. We utilize the non-linear control theory tool of describing function analysis along with numerical simulations to establish the same.
Journal ArticleDOI
TL;DR: In this article , a mathematical analysis of four-level (three-phase) phase-shifted carrier modulation class-D amplifiers with analog feedback is proposed, and the nonlinear difference equations are extracted and solved using the perturbation theorem.
Abstract: A mathematical analysis of four-level (three-phase) phase-shifted carrier modulation class-D amplifiers with analog feedback is proposed. The nonlinear difference equations are extracted and solved using the perturbation theorem. In this way, a closed-form function describes the low-frequency part of the output for an arbitrary input signal. The results are generalized for an arbitrary number of levels by analogy, well matched with the previous model of two-, three-, and the proposed four-level ones. The analytical results confirm that, apart from switching frequency, the multilevel class-D amplifiers converge to linear amplifiers as the number of output levels increases. An analytical equation expresses the harmonic distortion of practically interesting five-level amplifiers with bridge-tied load. The model is verified by system-level simulations and circuit-level implementation. In this way, a prototype fully differential five-level circuit is implemented on the printed circuit board to confirm the model.

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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202312
202230
202142
202057
201953
201847