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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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Proceedings ArticleDOI
10 Oct 2001
TL;DR: In this article, a combined nonlinearity consisting of resolution (quantifier) and mechanical backlash has been assumed to operate on a linear plant subject to input discretization under a sampling and zero-order hold device.
Abstract: The main objective in the project of a last year Master Engineering course on discrete control where students develop projects based on discrete control at a Spanish university has been to emphasize that there are several points of view when focusing on discretization and the associate mathematical developments depending on the particular analysis technique and problem at hand. In particular, a combined nonlinearity consisting of resolution (quantifier) and mechanical backlash has been assumed to operate on a linear plant subject to input discretization under a sampling and zero-order hold device. It has been proved through the project that because of sampling the system possess nonlinear inertia with the frequency of the first harmonics of nonlinear steady-state sustained oscillations being dependent on the sampling period and the critical locus being depending on frequency.
Proceedings ArticleDOI
16 Mar 2003
TL;DR: In feedback applications the interaction of the motor dynamics with the nonlinearity of the controller may result in self-sustained oscillations in speed of the closed-loop system.
Abstract: Speed control of AC induction motors by power electronic controllers is considered. The basic method of speed control is obtained by application of variable frequencies to the motor. Certain parameters are subject to modification by the user in the field. A model of the resulting operation is shown to contain a specific nonlinearity. In feedback applications the interaction of the motor dynamics with the nonlinearity of the controller may result in self-sustained oscillations in speed of the closed-loop system. The frequency and amplitude of such oscillations are determined by use of a describing function for the nonlinearity combined with a simplified linear model for the motor dynamics.
Journal ArticleDOI
TL;DR: A new sufficient condition on the global pointwise stability of the systems with multiple Coulomb friction sources is derived by extending the existing result with a single Coulombriction source when the stiction level is larger than the Coulomb lubrication level.
Journal ArticleDOI
TL;DR: The method for the generation of a special kind of switching-type double-valued characteristic using a microprocessor is described, used to stabilize and improve the system performance of a linear control system.
Abstract: A laboratory exercise on a compensation technique using flexible digital tools is presented. The method for the generation of a special kind of switching-type double-valued characteristic using a microprocessor is described. This characteristic is used to stabilize and improve the system performance of a linear control system. A mathematical analysis leads to conclusions about the determination of the nonlinear element characteristics to improve the system response. An approach based on the describing function (DF) method leads to a compensation technique in the complex plane. The circuit, the theoretical analysis, and experimental results for the compensation of a double integrator plant are presented. >
DOI
01 Jan 2022
TL;DR: In this paper, a truncated Taylor series expansion is used to smooth the LuGre friction model so that the harmonic balance method can be used, and the bifurcation diagram of the limit cycle of the system is obtained.
Abstract: Although the time-domain aeroelastic analysis of the fin-actuator system is accurate, it is very time-consuming. Some work in the past used the describing function method to calculate the dynamic stiffness of the actuator, and then obtained the aeroelastic stability of the system in the frequency domain. This greatly shortened the time, but there was a loss in accuracy. In order to improve the accuracy and speed up the calculation to a certain extent, this paper uses high order harmonics to describe the response of the system. The frictional hysteresis loop is difficult to obtain a closed-form solution in the frequency domain. In this paper, a truncated Taylor series expansion is used to smooth the LuGre friction model so that the harmonic balance method can be used. The pseudo-arclength continuation method is used to solve the problem, and the bifurcation diagram of the limit cycle of the system is obtained. The results show that the method used in this paper has achieved a balance between time and accuracy in calculating the aeroelastic stability of the fin-actuator system.

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