Showing papers on "Describing function published in 1978"
TL;DR: A describing-function method is applied to the study of the existence and behavior of limit cycles observed in power systems and results on the qualitative behavior of parameter changes are presented.
21 citations
TL;DR: In this article, the jump resonance in nonlinear feedback systems subject to a sinusoidal input is studied by use of the describing-function method, and the concept of resonant response surface, sea and land parts are distinguished in the gain-frequency characteristics and the conditions for occurrence of jump resonance of three types, the inclined-peninsula type, the island type and the lake type.
Abstract: The jump resonance in nonlinear feedback systems subject to a sinusoidal input is studied by use of the describing-function method. Introducing the concept of resonant response surface, sea and land parts are distinguished in the gain-frequency characteristics and the conditions for occurrence of jump resonance of three types, the inclined-peninsula type, the island type, and the lake type, are geometrically interpreted. The possibility of an island with some lakes is also indicated.
17 citations
TL;DR: In this paper, a dual-loop model of human controllers in single-axis compensatory tracking tasks is introduced, where sensor inputs to the human controller are assumed to be system error and control force.
Abstract: A dual-loop model of the human controller in single-axis compensatory tracking tasks is introduced. This model possesses an inner-loop closure that involves feeding back that portion of controlled element output rate that is due to control activity. A novel feature of the model is the explicit appearance of the human's internal representation of the manipulator-controlled element dynamics in the inner loop. The sensor inputs to the human controller are assumed to be system error and control force. The former can be sensed via visual, aural, or tactile displays, whereas the latter is assumed to be sensed in kinesthetic fashion. A set of general adaptive characteristics for the model is hypothesized, including a method for selecting simplified internal models of the manipulator-controlled element dynamics. It is demonstrated that the model can produce controller describing functions that closely approximate those measured in four laboratory tracking tasks in which the controlled element dynamics vary considerably in terms of ease of control. An empirically derived expression for the normalized injected error remnant spectrum is introduced.
14 citations
TL;DR: In this paper, a theory of Sal Input Describing Function (SIDF) is presented for the characterisation and analysis of a class of nonlinear dyadic systems, where SIDFs are determined for single input as well as dual input dyadic elements.
Abstract: This paper presents a theory of Sal Input Describing Function (SIDF) for the characterisation and analysis of a class of nonlinear dyadic systems. The SIDFs are determined for single input as well as dual input dyadic elements. The theory is applied to evaluate output response of a closed loop system subjected to sal input functions.
7 citations
01 Nov 1978
TL;DR: In this paper, the authors define methods for applying the describing function technique to realistic models of nonlinear rail cars and demonstrate how it can be applied to nonlinear vehicle dynamics problems, including wheel profile and suspension nonlinearities.
Abstract: The objective of the work reported here was to define methods for applying the describing function technique to realistic models of nonlinear rail cars. The describing function method offers a compromise between the accuracy of nonlinear digital simulation and the computational efficiency of linear methods. This work entailed the development of realistic describing function representations for nonlinearities such as the wheel/rail contact interaction and the development of algorithms for using these describing functions to predict the occurrence and stability of hunting and the forced response of rail vehicles to sinusoidal and statistical track irregularities. This report explains the describing function technique, demonstrates how it can be applied to nonlinear rail vehicle dynamics problems, describes algorithms that can be used for such problems, and presents results for typical nonlinear problems, including wheel profile and suspension nonlinearities.
6 citations
TL;DR: Stability aspects of non-linearities introduced by using a microprocessor digital controller in a feedback loop are investigated, using the describing function analysis, and there is no difference between the two types of equipment as far as stability is concerned.
Abstract: Stability aspects of non-linearities introduced by using a microprocessor digital controller in a feedback loop are investigated, using the describing function analysis. In particular, 8- and 16-bit types of equipment are compared. The conclusion reached is that from the practical standpoint, there is no difference between the two types as far as stability is concerned. A system selection procedure, proposed in a previous paper, is implemented in the selection of microprocessor equipment to satisfy specified design criteria. The procedure is composed of stages involving curve-fitting and minimization. A particular example, illustrating the implementation of the procedure, along with final recommendations, is presented.
4 citations
TL;DR: In this article, a class of harmonic oscillators is described which have the frequency of oscillation determined by one parameter of an RC or RL circuit and the amplitude of oscillations by the other parameter.
Abstract: A class of harmonic oscillators is described which has the frequency of oscillation determined by one parameter of an RC or RL circuit and the amplitude of oscillation by the other parameter. These oscillators are useful in the impedance measurement of physical or biological objects when two attributes of the object are related to two electrical parameters of the equivalent circuit. A pole or zero is derived from the measured object by isolating it from the oscillator. The remainder of the oscillator contains linear elements and a single memoryless nonlinearity. Second-order oscillators containing a hard nonlinearity and third-order oscillators containing a soft nonlinearity are presented. The frequency and amplitude relationships are derived using linear theory and the describing function method. The theoretical results are verified by analog computer simulations. The oscillators are described in general terms by means of flow graphs.
3 citations
01 Jan 1978
TL;DR: A method is presented that can be used to evaluate the sinusoidal-input describing function for a class of single- and double-valued nonlinearities.
Abstract: A method is presented that can be used to evaluate the sinusoidal-input describing function for a class of single- and double-valued nonlinearities. The basic approach is simple and straightforward and may be applied to the determination of multiple-input describing functions. The method is applied to nonlinear devices which naturally produce a discontinuous output waveform on the application of a sinusoidal signal.
2 citations
TL;DR: In this article, a simple method for the determination of sinusoidal and other describing functions for static multivalued nonlinearities in combination with a zero-order hold device (zo.h.).
Abstract: A simple method is given for the determination of sinusoidal and other describing functions for static multivalued nonlinearities in combination with a zero-order hold device (z.o.h.).
2 citations
TL;DR: The Authors examine the nonlinear equations of ship rolling from a control engineering viewpoint by considering the ship as represented by a feedback system and discuss the extension of this technique due to West and others which can account for so-called "frequency distortion of the spectrum" in nonlinear systems.
Abstract: In this paper the Authors examine the nonlinear equations of ship rolling from a control engineering viewpoint by considering the ship as represented by a feedback system. This enables the describing function technique to be brought to bear on the problem. They discuss, in detail, the extension of this technique due to West and others which can account for so-called "frequency distortion of the spectrum" in nonlinear systems and point to evidence which appears to show this happening in practice. Accuracy estimates using describing function analysis are difficult to specify since they are affected by many difference factors, however they are commonly reckoned to be about 10% accurate with wideband excitation.
2 citations
01 Jan 1978
TL;DR: In this paper, a new and practical method is developed for evaluating approximately both dc and fundamental ac components of waveforms in steady-state thyristor circuits, which can be applied to any configuration of linear time-invariant circuits containing several thyristors.
Abstract: A new and practical method is developed for evaluating approximately both dc and fundamental ac components of waveforms in steady-state thyristor circuits. The process is purely algebraic and is not based on simulation techniques, which utilizes a modified form of describing-function method for each thyristor. The method can be applied, at least in principle, to any configuration of linear time-invariant circuits containing several thyristors. Two simple but fundamental examples are included to show the limit and utility of the proposed method.
TL;DR: Certain geometric properties of Hatanka's graphical method are presented and it is shown how jump resonance conditions can be approximately evaluated by a very simple graphical method in which circular arcs and straight lines need to be drawn apart from utilizing the Nyquist response of the linear part of the system.
Abstract: Numerous methods exist for the evalution of jump resonance conditions in nonlinear feedback systems. However almost all of the known methods are graphical in nature and are extremely laborious. This paper presents certain geometric properties of Hatanka's graphical method and shows how jump resonance conditions can be approximately evaluated by a very simple graphical method in which circular arcs and straight lines need to be drawn apart from utilizing the Nyquist response of the linear part of the system. The proposed method can be useful in a quick assessment of jump conditions in the design of nonlinear systems. Two examples are included for illustrating the procedure.
TL;DR: In this article, the Covariance Analysis Describing Function Technique (CADET) was compared with the Volterra Series Synthesis approach for the analysis of nonlinear stochastic systems.
Abstract: The superiority of the Covariance Analysis Describing Function Technique (CADET) in comparison with the Volterra Series Synthesis approach for the analysis of nonlinear stochastic systems is demonstrated in this note. The advantages of CADET are greater accuracy and simplicity.