• Title, Summary, Keyword: Describing Function

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Multiple input describing function analysis of non-classical aileron buzz

  • Zafar, Muhammad I.;Fusi, Francesca;Quaranta, Giuseppe
    • Advances in aircraft and spacecraft science
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    • v.4 no.2
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    • pp.203-218
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    • 2017
  • This paper focuses on the computational study of nonlinear effects of unsteady aerodynamics for non-classical aileron buzz. It aims at a comprehensive investigation of the aileron buzz phenomenon under varying flow parameters using the describing function technique with multiple inputs. The limit cycle oscillatory behavior of an asymmetrical airfoil is studied initially using a CFD-based numerical model and direct time marching. Sharp increases in limit cycle amplitude for varying Mach numbers and angles of attack are investigated. An aerodynamic describing function is developed in order to estimate the variation of limit cycle amplitude and frequency with Mach number and angle of attack directly, without time marching. The describing function results are compared to the amplitudes and frequencies predicted by the CFD calculations for validation purposes. Furthermore, a limited sensitivity analysis is presented to demonstrate the potential of the approach for aeroelastic design.

The Prediction of Self-Excited Oscillation of a Fuzzy Control System Based on the Describing Function - Static Case (묘사함수를 이용한 퍼지 제어 시스템의 자기진동 현상의 예측 - 정적 경우)

  • 김은태;노흥식;김동연;박민용
    • Journal of the Korean Institute of Telematics and Electronics C
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    • v.35C no.3
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    • pp.90-96
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    • 1998
  • The self-excited oscillation is the phenomenon which can be observed in the systems composed of nonlinear elements. The phenomenon is of fundamental importance in nonlinear systems and, as far as the design of a nonlinear system is concerned, it should be considered along with the stability analysis. In this paper, the oscillation of a system controlled by a static nonlinear fuzzy controller is theoretically addressed. First, the describing functionof a static fuzzy controller is derived and then, based on the derived describing function, self-excited oscillation of the system controlled by a static fuzzy controller is predicted. To obtain the describing function of the static fuzzy controller, a simple struture is assumed for the fuzzy controller. Finally, computer simulation is included to show an example where the describing function given in the paper is used to predict the self-excited oscillation of a fuzzy-control system.

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The prediction of self-excited oscillation of a fuzzy control system based on the describing function dynamic case (묘사함수를 이용한 퍼지 제어시스템의 자기진동 현상의 예측-동적 경우)

  • Kim, Eun-Tai;Noh, Heung-Sik;Kwon, Chul;Kim, Dong-Yon;Park, Mig-Non
    • Journal of the Korean Institute of Telematics and Electronics C
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    • v.35C no.5
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    • pp.41-49
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    • 1998
  • This paper deals with the self-excited oscillation of a system that is controlled by a dynamic nonlinear fuzzy controller. The self-excited oscillation can be observed in the systems composed of nonlinear elements and its analysis is as important as that of stability in the design of nonlinear systems. by using the frequency transfer function analysis known as the describing function method in nonlinear control theory, the oscillation is theoretically predicted. First, the describing function of a dynamic fuzzy controller is derived and then, based on the derived describing fuction, self-excited oscillation of the system controlled by a dynamic fuzzy controller is predicted. To obtain the describing function of the dynamic fuzzy controller, a simple structure is assumed for the fuzzy controller.

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Vibration Analysis of Structure with Nonlinear Joint Using Describing Function (기술함수를 이용한 비선형 결합부를 가진 구조물의 진동해석)

  • 박해성;지태한;박영필
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.18 no.2
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    • pp.372-379
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    • 1994
  • In this study, the describing function is adopted to represent nonlinearity in the system equations. The compliance can be obtained by solving nonlinear simultaneous algebraic quations for multi-degrees-of-freedom system with multinonlinearities. When the technique is applied, the nonlinearity of the system can be identified from the compliance which is obtained from the sinusoidal excitation of the system. By employing the describing function in the Building Block Analysis, we can extensively develop the BBA into investigation of the continuous systems with nonlinearities. The evaluated compliance can quantitatively show the effects of nonlinearity such as the transfer of the natural frequency, the variance of the compliance at the natural frequency, and the jump phenomena which occur during sweeping of the excitation frequency.

A Vibration Control of a Flexible Beam using a Nonlinear Compensator with Complex Dual-Input Describing Function (복소쌍입력 기술함수를 갖는 비선형 보상기를 이용한 유연한 빔의 진동제어)

  • 권세현
    • Journal of the Korean Society of Marine Engineering
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    • v.23 no.2
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    • pp.227-235
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    • 1999
  • In this paper a vibration control fo a one-link flexible beam is considered. At first a state-space model for a flexible beam is derived by using the assumed-modes approach. Based on this model the transfer function between the applied torque and the tip deflection fo the beam is presented because it is convenient to apply our method. In general there exist some control difference due to flexibility of the beam so we adop a forward-passive controller to reduce these phenomena. And a complex dual-input describing function compensator is used to control the tip deflection. The stabiltiy and the performance of the closed-loop system are analyzed. Finally the validity of the derived model and the effectiveness of proposed controller are confirmed throuth simula-tions and experiments.

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Periodic Disturbance Cancellation by using Dual-Input Describing Function (DIDF) Method (DIDF 방법을 이용한 주기성 외란의 제거)

  • Choe, Yeon-Wook;Lee, Hyung-Ki
    • The Transactions of The Korean Institute of Electrical Engineers
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    • v.59 no.1
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    • pp.168-175
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    • 2010
  • The issue of rejecting periodic disturbances arises in various applications dealing with rotating machinery. A new method using DIDF (Dual-Input Describing Function) is presented for the rejection of periodic disturbances with uncertain frequency. This can be added to an existing feedback control system without altering the closed-loop system stability. The objective is to design a nonlinear compensator to secure specified oscillation amplitude and frequency which are the same as disturbances. We suggest two procedures to determine coefficients for DIDF's synthesis. The structure of the proposed DIDF is so simple that we can easily synthesize. A number of computer simulations were carried out to demonstrate the salient feature of the proposed DIDF compared to the conventional ones(that is, adaptive algorithms).

Stochastic Analysis of Self-sustained Oscillation Loop for a Resonant Accelerometer

  • Hyun, Chul;Lee, Jang-Gyu;Kang, Tae-Sam;Sung, Sang-Kyung
    • 제어로봇시스템학회:학술대회논문집
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    • pp.574-578
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    • 2004
  • In this paper, a nonlinear feedback system is analyzed for a surface micromachined resonant accelerometer. For this, a brief illustration of the plant dynamics is given. In the analysis, the periodic signal in the nonlinear feedback loop is obtained by the limit cycle point, which is best approximated via the describing function method. Considering the characteristic feature of plant dynamics, a simple phase shifted relay with finite slope is designed for the nonlinearity implementation. With a describing function for random plus sinusoidal input, we analyzed the effect of a white Gaussian noise on oscillation frequency. Finally, simulation and experimental result is given.

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A Study of Periodic Solutions of Typical Relay Servo System (릴레이 제어기구 조기해법에 관한 연구)

  • 나계근
    • Journal of the Korean Institute of Telematics and Electronics
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    • v.8 no.3
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    • pp.1-14
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    • 1971
  • A relay servo, one of the nonlinear sytsems, is inherently compact compared to a linear system for an equivalent control problem. The power element or actuator is not adjusted proportionally in accordance with an error signals but rather is switched abruptly between several discrete conditions. Usually switched conditions are off, full, forward or full reverse. The relay system is a particularly simple and compact one, but probably more effort has been expended on its analysis and design than on all other systems together. Early studies in the art were made by Goldfarb, austin, Oppelt and Kochenburger on the describing function method, which can be used as an approximate check on the stability of the system. The describing function method is based on the assumption that any periodic wave could be approximated as a fundamental one in wide ranges of practical applications. A relay servo system usually operates on a limit cycle condition as the loop gain increases. The stability analysis compensation or any improvement effort based on the describing function method sometimes may present considerable discrepancies on physically realized practical systems. An approach to exact periodic solutions of a relay servo system is much important for the analysis, design and system improvement. This paper dells with periodic solutions of a relay servo system on the basis of describing function and generalized chopper wave form which is composed of infinite number of harmonic series. Various ways of graphical representation were attempted to get periodic solutions, some of which have shown its validity in rapid approach to exact solutions and also in judgement of system behavior.

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Limit Cycle Amplitude Prediction Using Results of Flame Describing Function Modeling (화염묘사함수 모델링 결과를 이용한 한계 진폭 예측)

  • Kim, Jihwan;Kim, Jinah;Kim, Daesik
    • Journal of the Korean Society of Propulsion Engineers
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    • v.20 no.6
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    • pp.46-53
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    • 2016
  • It is required to predict a limit cycle amplitude controlled by system's nonlinear behavior as well as an eigen-frequency and initial growth rate of instabilities under the linear motions, in order to fully understand combustion instabilities in a lean premixed gas turbine combustor. Special focus of the current work is placed on the limit cycle amplitude prediction using flame describing function(FDF) where the ratio of a heat release fluctuation to a given flow perturbation is expressed as a function of frequency and amplitude. In this study, the CFD modeling work based on RANS is carried out to obtain FDF, which makes that the nonlinear thermo-acoustic model is successfully developed for predicting the limit cycle amplitude of the combustion instability.

FDF-based analysis of nonlinear combustion instability in the lean premixed combustor (FDF를 이용한 메탄 희박 예혼합 연소기의 비선형 열음향학적 불안정성 해석)

  • Oh, Seungtaek;Shin, Yungjun;Kim, Yongmo
    • 한국연소학회:학술대회논문집
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    • pp.115-116
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    • 2015
  • In the present approach, the flame-acoustics interaction is represented by FDF (Flame Describing Function) which is a important source term in the Helmholtz' equation. In this study, the combustion instability is analyzed by the forced mode strategy with the measured FDF. Numerical results indicate that the present approach reasonably well predicts the essential features of the combustion instability characteristics in the lean premixed combustor under the gas-turbine like environment.

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