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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
01 Jul 1997
TL;DR: The theorem is given asserting that the considered non-linear system is optimal in the sense of H∞ norm criterion if corresponding harmonically linearized system is ideal in the same sense.
Abstract: The problem of H ∞ optimal control for the plant consisting from two-mass and non-linear spring is considered in the paper. Till now two mass problem (benchmark problem) was considered for linear cases only. The novelty our work is generalisation of this problem (using the describing function method) for non-linear cases. The H ∞ control theory is firstly adapted to cope with non-linear plants. To this end the theorem is given asserting that the considered non-linear system is optimal in the sense of H ∞ norm criterion if corresponding harmonically linearized system is optimal in the same sense. This fact enables one, by utylization of describing function method, to bring the non-linear two-mass dynamical model to the linear approximation form and thereby to apply H ∞ — type procedures.

3 citations

Proceedings Article
01 Mar 2005
TL;DR: The main purpose of this paper is to analyze the robust stability for a fuzzy vehicle steering control system and a systematic procedure is proposed to solve this problem.
Abstract: The main purpose of this paper is to analyze the robust stability for a fuzzy vehicle steering control system. In general, fuzzy control system is a nonlinear control system. Therefore, the fuzzy controller may be linearized by the use of describing function first. After then, parameter plane method is then applied to determine the conditions of robust stability when the system has perturbed or adjustable parameters. A systematic procedure is proposed to solve this problem. The effects of plant parameters and control factors are both considered here. Furthermore, the problem of relative stability by using gain-phase margin tester is also addressed. The limit cycles provided by a static fuzzy controller can be easily suppressed if the control factors are chosen properly. Simulation results show the efficiency of our approach.

3 citations

Proceedings ArticleDOI
Xue Feng Han1, Ming Ge1, Yang Bai1, Hongguang Jia1, Wen-qi Ge1 
12 Sep 2011
TL;DR: In this article, the effect of backlash nonlinear on the resonance frequency of an electric actuator transmission system was studied, and the theoretical analysis and simulation results showed that the theoretical results are basically consistent with simulation results when it is zero backlash.
Abstract: In order to study the effect of backlash nonlinear on resonance frequency of electric actuator transmission system, in the premise of meeting the stability, it establishes balanced equation of dynamics system with backlash, and does some theory research and dynamic analysis of backlash nonlinearity and system natural frequency and resonance frequency. First, according to describing function to theoretically model the backlash nonlinear, the relation between describing function and the amount of backlash and input amplitude is analyzed; then, the dynamic equilibrium equation of transmission system with backlash is established, the effect of backlash on system natural frequency and resonance frequency; Finally, it makes dynamic simulation analysis for the transmission system based on virtual prototype technology, and the theoretical values and simulation values are compared. Theoretical analysis and simulation results show that the theoretical analysis is basically consistent with simulation results when it is zero backlash, and the error of theoretical analysis and simulation results is within 10%. Therefore, it can be concluded that considering the transmission system theoretical analysis of backlash nonlinearity is feasible, and it is much closer to the actual system with instructive significance.

3 citations

01 Jan 2011
TL;DR: The extended describing function method is used, which implements both frequency-domain and time-domain analysis of the series resonant converter, and it is observed that the theoretical steady-state values agrees with the simulated results obtained using SABER Sketch.
Abstract: Ayachit, Agasthya. M.S.Egr, Department of Electrical Engineering, Wright State University, 2011. Small-Signal Modeling of Resonant Converters. Resonant DC-DC converters play an important role in applications that operate at high-frequencies (HF). Their advantages over those of pulse-width modulated (PWM) DC-DC converters have led to the invention of several topologies over the traditional forms of these converters. Series resonant converter is the subject of study in this thesis. By variation in the switching frequency of the transistor switches, the optimum operating points can be achieved. Hence, the steady-state frequency-domain analysis of the series resonant converter is performed. The operational and characteristic differences between the series resonant and parallel resonant and series-parallel resonant configurations are highlighted. In order to understand the converter response for fluctuations in their input or control parameters, modeling of these converters becomes essential. Many modeling techniques perform analysis only in frequency-domain. In this thesis, the extended describing function method is used, which implements both frequency-domain and time-domain analysis. Based on the first harmonic approximation, the steady-state variables are derived. Perturbing the steady-state model about their operating point, a large-signal model is developed. Linearization is performed on the large-signal model extracting the small-signal converter state variables. The small-signal converter state variables are expressed in the form of the transfer matrix. Finally, a design example is provided in order to evaluate the steady-state parameters. The converter is simulated using SABER Sketch circuit simulation software and the steady-state parameters are plotted to validate the steady-state parameters. It is observed that the theoretical steady-state values agrees with the simulated results obtained using SABER Sketch.

3 citations

Journal ArticleDOI
TL;DR: In this article, the internal nonlinear mechanism of a class of current-mode active elements used in sinusoidal oscillators is analyzed and it is shown how it must operate to guarantee the stability of the oscillation amplitude.
Abstract: In this work the internal nonlinear mechanism of a class of current-mode active elements used in sinusoidal oscillators is analysed. By means of the describing function formalism it is shown how it must operate to guarantee the stability of the oscillation amplitude. An illustrative example is given.

3 citations


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