The dual-input describing function and its use in the analysis of non-linear feedback systems

West, John C; Douce, J.L.; Livesley, R. K.

doi:10.1049/pi-b-1.1956.0191

Cited by 32 publications

(21 citation statements)

References 5 publications

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“…21 Dual-input describing functions relate the appropriate component of the output to one of the input sinusoids. A complete graphical representation requires a family of curves with the amplitude of the test sinusoid and the amplitude and fre-682 LEVISON, BARNETT, JACKSON quency of the second sinusoid as parameters.…”

Section: Appendix B Sinusoidal Describing Function Analysismentioning

confidence: 99%

Nonlinear Analysis of the Baroreceptor Reflex System

1966

Circulation Research

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The regulation of blood pressure by the baroreceptor reflex was examined in anesthetized dogs. The receptor feedback path was broken by surgical intervention, the input (carotid sinus pressure) was controlled by an external servo system, and simultaneous records of input and output (systemic arterial pressure) were obtained. A variety of pressure waveforms were applied to the carotid sinus so that the nonlinear behavior could be explored thoroughly. Most of the input waveforms consisted of relatively small signals about an operating point in the normal blood pressure range. The nonlinear behavior of the reflex was illustrated in a number of ways. Square waves, sinusoids, and short pulses produced asymmetric arterial pressure waveforms. An overshoot in the arterial pressure always followed the rising edge of the input square wave, but was generally absent following the negative-going part of the square wave. Either positive or negative pulses caused a transient drop in arterial pressure. The sinusoidal response was often distorted, with the falling portion of the output waveform steeper than the rising portion. The system behaved as a rectifier, or envelope-detector, as illustrated by 1) the decrease in mean arterial pressure when either the amplitude or the frequency of a sinusoidal input was increased and 2) the appearance in the arterial pressure waveform of a component correlated with the envelope of a modulated carrier. Another nonlinear phenomenon was the decrease in low-frequency sinusoidal gain caused by the addition of a high-frequency sinusoid to the sinus pressure waveform. This behavior indicates that if closed loop behavior in the intact animal is to be predicted from the open loop sinewave response, the effects of the cardiac pressure pulse must be considered. A model was constructed from standard electronic components to simulate the input-output behavior of the baroreceptor reflex. The model was able to simulate the response to high- and low-frequency sinusoids and to reproduce the essential features of the square-wave and pulse responses. On this basis the model was considered adequate for simulating the performance of the baroreceptor reflex in certain open loop and closed loop situations.

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Section: Appendix B Sinusoidal Describing Function Analysismentioning

confidence: 99%

Nonlinear Analysis of the Baroreceptor Reflex System

1966

Circulation Research

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“…A dual input describing function [21] is applied to the analogous feedback system with consideration given to the aerodynamic phase lag and the program can include an initially small torsional motion. Recent computations have indicated from the resulting Nyquist diagrams that bounded regions for divergent oscillations can exist beyond k ~ 0.25 in most practical cases.…”

Section: Discussionmentioning

confidence: 99%

Damping loss in a cascade of fluttering phased aerofoils

Thornton

1968

J. Aust. Math. Soc.

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Summary.A study is made of the aerodynamic damping in a cascade of oscillating aerofoils in subsonic compressible flow with the system mode described by a constant interblade phasing predicted by Lane (9). The integral downwash equation is obtained as an extension of Possio's equation for an isolated aerofoil. Procedures for a practical solution of the equation have allowed the aerodynamic reactions and damping derivatives to be evaluated with a digital computer after minimisation of the critical flutter velocity with respect to interblade phase angle. The effect of aerodynamic lag in separation conditions as a function of reduced frequency and chordwise location is compared with results without separation.

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“…Secondly, the input may excite an oscillation in the feedback loop which can be either a rational or irrational multiple of the input frequency. The former situation is known as a subharmonic oscillation [11,12]. Finally, the output c{t) may be chaotic [13], a phenomenon which has received little attention in the control literature but is increasingly attracting the interest of mathematicians.…”

Section: Characteristics Of Nonlinear Behaviourmentioning

confidence: 99%

Analysis and design of nonlinear feedback systems

Atherton

1981

IEE Proc. D Control Theory Appl. UK

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The paper discusses methods, primarily those using frequency-domain techniques, for the analysis and design of nonlinear feedback control systems. The behavioural properties peculiar to nonlinear feedback systems are first discussed. This is followed by a review and discussion of the applicability of absolute stability criteria and describing-function methods for single-variable and multivariable systems. The calculation of limit cycles in relay systems, time-domain methods of analysis and simulation techniques are then considered. Finally, a few applications are considered which highlight both the applicability and limitations of the available analytical techniques for nonlinear systems. IntroductionThe aim of this paper is to give an overview of methods available for the analysis and design of nonlinear systems. As a consequence of the distinct behaviour of nonlinear systems, most methods of analysis are directed at solutions to specific problems, such as system stability or the existence of limit cycles. Unlike the case for linear systems, the approach may be of limited usefulness for answering other questions of concern, such as, for example, the time-response behaviour. Further, in several methods, the assumptions made are based on the expected form of the solution, so that some knowledge of the possible forms of nonlinear behaviour is a requirement for the analyst. Because of the limited applicability and the approximations often involved in methods of nonlinear analysis, it is important for the engineer to be familiar with a variety of techniques, to appreciate their limitations, and to know how to combine their useful attributes. The nonlinear features of a system may originate inherently or intentionally. Inherent nonlinearity is an inseparable characteristic of the laws governing the operation of the system to be controlled. This situation has frequently been handled by considering the linearised performance about one or more system operating points, often resulting in loss of accuracy, unreliable predictions and the need for costly testing. Intentional nonlinearity, on the other hand, is deliberately introduced into the design of the system as the best way to achieve the desired performance. Typical examples of this are the use of on/off time-optimal position controls [1 ] and the application of jet thrusters in the attitude control loops of current communication [2], and some scientific [3], satellites. The increasing use of microprocessor controllers will, without doubt, result in the more frequent use of nonlinear control strategies as, in contrast to analogue controllers, they allow complex nonlinear algorithms to be easily implemented. The requirements placed on process-controller algorithms to achieve both satisfactory control of set-point changes and regulation are rarely compatible, and thus an opportunity for the use of nonlinear techniques clearly exists. Some nonlinear controllers which have recently become available [4,5] have been designed primarily on the basis of mimicking the behaviour ...

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The dual-input describing function and its use in the analysis of non-linear feedback systems

Cited by 32 publications

References 5 publications

Nonlinear Analysis of the Baroreceptor Reflex System

Nonlinear Analysis of the Baroreceptor Reflex System

Damping loss in a cascade of fluttering phased aerofoils

Analysis and design of nonlinear feedback systems

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