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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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Book ChapterDOI
01 Jan 1990
TL;DR: In this article, the problem of finding, within a specific class of nicely nonlinear models, the one that best fits with significant aspects of the (external) behavior of a given plant, relative to a particular control problem defined on it, is addressed.
Abstract: Roughly, a model is said to be nicely nonlinear if it is readily linearizable by output feedback. This paper is primarily concerned with “control-oriented nicely nonlinear modelling”; namely, with the problem of finding, within a specific class of nicely nonlinear models, the one that best fits with significant aspects of the (external) behavior of a given plant, relative to a particular control problem defined on it. The approach proposed here is based on the least square fitting, over a given frequency range, of the plant “nominal” describing function. As an application, a simulation study concerning a binary distillation column is presented. Possible extensions and some current investigations are briefly discussed in the concluding remarks.
Proceedings ArticleDOI
27 Dec 2003
TL;DR: In this article, the global dynamic behavior of nonlinear dynamic arrays is investigated through a spectral approach, based on the joint application of the describing function and the harmonic balance technique, and the authors show that the global dynamics of such arrays can be effectively investigated through the combination of describing functions and harmonic balance techniques.
Abstract: Nonlinear dynamic arrays are described by large systems of locally coupled nonlinear differential equations and might exhibit a complex dynamic behavior, including several attractors and bifurcation processes. We show that the global dynamic behavior of such arrays can be effectively investigated through a spectral approach, based on the joint application of the describing function and of the harmonic balance technique
01 Jan 1993
TL;DR: A discretization-oriented describing function is derived for nonlinear devices combining backlash and quantization ( resolution) while being subject to discretized through a sampler and zero-order hold.
Abstract: In this paper, a discretization-oriented describing function is derived for nonlinear devices combining backlash and quantization ( resolution) while being subject to discretization through a sampler and zero-order hold. Such a describing function is frequency-dependent so that the overall nonlinearity, which includes both resolution and backlash, is interpreted as one posessing nonlinear inertia. That inertia is generated by the sampling process since it does not appear if the system is continuous. The presence of limit cycles is investigated through simulated examples.
Proceedings ArticleDOI
04 Jun 2014
TL;DR: In this paper, a describing function analysis establishes stability assuming an accurate measure of the partial derivative in neural-adaptive control schemes using the method of describing functions.
Abstract: A method proposed for halting weight drift in neural-adaptive control schemes is analyzed using the method of describing functions. The method utilizes a self-evaluating, introspective method with a Cerebellar Model Arithmetic Computer. The average error within the domain of local basis functions is measured, and then used to estimate the effect of weight updates on reducing the error i.e. estimating a partial derivative. The adaptation algorithm halts the weight updates when it is determined that weight updates are no longer beneficial in reducing the average error. In this paper, a describing function analysis establishes stability assuming an accurate measure of the partial derivative.
Proceedings ArticleDOI
25 May 2021
TL;DR: In this article, a proportional-and-hysteretic-damping controller has been proposed for a single-joint test-robot that can achieve a constant damping ratio.
Abstract: Recent experiments have shown that human joints can maintain a constant damping ratio across a wide range of external loads. This behavior can be explained by the use of a “complex stiffness” frequency-domain model approximating the impedance of the human joint. However, for a robot to replicate this naturally beneficial human behavior would require a time-domain model of this nonlinear joint impedance. This paper demonstrates that there exists a nonlinear time-domain model (originally from the structural mechanics community) that has a frequency-domain “describing function” that matches the complex stiffness model observed in humans. We provide an extension of this nonlinear time-domain model that removes the need to implement hard-switching control input. In addition, we demonstrate that this proportional-and-hysteretic-damping controller has inertia-invariant overshoot and therefore offers an advantage over the more common proportional-derivative control approach. Implementing the proposed proportional-and-hysteretic-damping control in a single-joint test-robot, we demonstrate for the first time that the desired frequency domain behavior can be reproduced in practice.

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