Showing papers on "Describing function published in 1984"
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06 Jun 1984TL;DR: In this paper, the authors report on recent progress in developing nonlinear control system design techniques based on sinusoidal-input describing function (SIDF) methods and illustrate a fundamental difference between SIDF and RIDF models of nonlinear systems.
Abstract: In this paper, we report on recent progress in developing nonlinear control system design techniques based on sinusoidal-input describing function (SIDF) methods. Primarily, this involves illustrating a fundamental difference between SIDF and random-input describing function (RIDF) models of nonlinear systems, developing the nonlinear controller design method more fully, and demonstrating it by applying it to a significant nonlinear control design problem in robotics. Based on these results, the use of this nonlinear controller design method should be substantially better understood.
32 citations
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TL;DR: In this paper, the authors formulate and establish a rigorous stability analysis for limit cycles for a large class of nonlinear feedback systems using the classical sinusoidal-input describing function and the theory of integral manifolds.
Abstract: We formulate and establish a rigorous stability analysis for limit cycles for a large class of nonlinear feedback systems. Our approach uses the classical sinusoidal-input describing function and the theory of integral manifolds. The present results constitute an improvement of earlier results by the present authors. We demonstrate the usefulness of the present results by means of a specific example.
13 citations
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TL;DR: This paper illustrates how the use of z–transform describing functions mapped into the w–domain provides a readily understood acceptable approach to the design of digital compensators for sampled relay control systems.
Abstract: This paper illustrates how the use of z–transform describing functions mapped into the w–domain provides a readily understood acceptable approach to the design of digital compensators for sampled relay control systems. The shortcomings of using the sinusoidal input describing function are also highlighted
8 citations
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TL;DR: In this paper, the describing function concept is applied to the power waves incident on, and reflected by, a nonlinear element, which allows us to define the nonlinear reflection coefficient (NLRC) on the power wave basis.
Abstract: At microwaves, it is necessary to define rigorously the large signal reflection coefficient of a nonlinear device. In this paper, the describing function concept is applied to the power waves incident on, and reflected by, a nonlinear element. This method allows us to define the nonlinear reflection coefficient (NLRC) on the power wave basis. This NRLC is then compared with that defined on the current or voltage basis. Numerical calculations applied to nonlinear elements illustrate the theoretical results.
5 citations
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TL;DR: In this article, the frequency domain stability conditions for non-linear two-port amplifiers were derived for a turned transistor amplifier with saturated class-C type transfer characteristic, and the theoretical considerations and the experimental results were in close agreement.
Abstract: Based on the two-port describing function characterization, frequency domain stability conditions are derived for non-linear two-port amplifiers. the conditions are applied to the case of a turned transistor amplifier with saturated class-C type transfer characteristic. the theoretical considerations and the experimental results are in close agreement.
3 citations
01 Sep 1984
TL;DR: This chapter describes the method used to obtain visual-cortical describing functions, results for different subjects under different cognitive processing demands, and discusses of what these results indicate.
Abstract: The thrust of the present work is to explore the utility of using a sum of sinusoids (seven or more) to obtain an evoked response and, furthermore, to see if the response is sensitive to changes in cognitive processing. Within the field of automatic control system technology, a mathematical input/output relationship for a sinusoidally stimulated nonlinear system is defined as describing function. Applying this technology, sum of sines inputs to yield describing functions for the visual-cortical response have been designed. What follows is a description of the method used to obtain visual-cortical describing functions. A number of measurement system redesigns were necessary to achieve the desired frequency resolution. Results that guided and came out of the redesigns are presented. Preliminary results of stimulus parameter effects (average intensity and depth of modulation) are also shown.
2 citations
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01 Dec 1984TL;DR: Preliminary results are presented for the case when the reference input is a polynomial function and a multi-dimensional observable vector is available for feedback, based on augmenting the system by additional state variables and then feeding back delayed observable vectors as well as the augmented state variables.
Abstract: Difficulties one faces in designing a satisfactory controller for systems involving stiff nonlinearities are well known. Stictions, Coulomb frictions and backlashes are but a few such examples. Unfortunately, there are few mechanical systems without such nonlinearities. The problem becomes even more complex if some of the state variables are not directly measurable, a situation which occurs not infrequently in practical systems. Unlike in linear systems where the missing state variables may be reconstructed [1], no corresponding methods are available for nonlinear systems. In fact, no general methods are currently available for analyzing and synthesizing controllers for nonlinear systems. At present, the describing function method is perhaps the best tool available for investigating stiff nonlinear systems [2]. A stable system is designed by adjusting the system gain or inserting a simple lead-lag compensation network. The parameter values are determined by graphically examining the Nyquist curve and the describing function. The process becomes very difficult, if not impossible, to apply when the order of the system is high and only the measurable variables are to be used in the feedback. When the reference input is a constant and only the output is available for feedback, the delayed feedback controller was given in [3]. In this paper, preliminary results are presented for the case when the reference input is a polynomial function and a multi-dimensional observable vector is available for feedback. It is based on augmenting the system by additional state variables and then feeding back delayed observable vectors as well as the augmented state variables.
2 citations
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2 citations
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TL;DR: In this article, the steady-state temperature responses of 1-2 pass heat exchangers subject to sinusoidal flow rate changes of large amplitude were derived for various values of amplitude, and the experimental input-output relations of the fundamental components were determined from the recorded data using a Fourier analysis technique on a digital computer.
Abstract: A computational method is presented for obtaining the steady-state temperature responses of 1-2 pass heat exchangers subject to sinusoidal flow rate changes of large amplitude. The frequency- and amplitude- dependent describing functions between the input sinusoidal flow rate changes and the fundamental component of the steady-state response of the outlet temperature of tube-side or shell-side fluid are also derived. Numerical examples are given and it is shown that this method can reduce the computation time remarkably. Experiments are carried out: the steady-state responses to input sinusoidal flow rate changes are recorded for various values of amplitude. The experimental input-output relations of the fundamental components are determined from the recorded data using a Fourier analysis technique on a digital computer, and the experimental data are shown to be in good agreement with the theoretical results obtained by the present describing functions.
2 citations
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01 Dec 1984TL;DR: In this paper, the stability of limit cycles in feedback systems with hysteresis nonlinearities was investigated and it was shown that the describing function method can be given a rigorous mathematical basis to explain the presence of distortions in solutions of the class of feedback systems considered in this paper.
Abstract: In this paper, we concern ourselves with the stability of limit cycles in feedback systems which have hysteresis nonlinearities. Although the quasistatic analysis of limit cycles (Loeb criterion) predicts, in most cases correctly, the stability properties of limit cycles, it is well known that analyses which are based on the method of describing functions may lead to erroneous conclusions. In this paper, we show to what extent the describing function method can be given a rigorous mathematical basis. We show that for a specific example, the main result of this paper predicts correctly the stability of a limit cycle while the Loeb criterion yields an incorrect result. Also, we show that our analysis explains to a certain extent the presence of distortions in solutions of the class of feedback systems considered herein. In arriving at the main result of this paper, use is made of several known facts for functional differential equations and of a result on integral manifolds.
2 citations
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01 Jan 1984TL;DR: In this article, the stability of oscillations in a wide class of nonlinear control systems with their linear part given by the transfer function G(s) = p(s)/q(s), where p and q are polynomials over the real numbers.
Abstract: We analyze the stability of oscillations in a wide class of nonlinear control systems which have their linear part given by the transfer function G(s) = p(s)/q(s), where p and q are polynomials over the real numbers. The analysis employs the classical single-input sinusoidal describing function, elementary control theory, and the theory of integral manifolds. We demonstrate, by means of specific examples, how the present results can be used to obtain detailed information concerning the behavior of the solutions.
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TL;DR: The software uses a new theoretical method for the exact evaluation of limit cycles in a discrete system with any nonlinear element and a describing function based procedure is also included for obtaining initial estimates of possible limit cycle parameters.
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TL;DR: In this article, the authors present the analysis of limit cycle oscillations observed in a magnetic suspension system which utilizes an optical transducer and verify these conditions using the stability criterion of Gelb and Van der Velde.
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TL;DR: In this paper, the authors formulate and establish a rigorous stability analysis for limit cycles for a large class of nonlinear feedback systems using the classical sinusoidal-input describing function and the theory of integral manifolds.
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01 Dec 1984
TL;DR: In this paper, a nonlinear model for the frequency-domain analysis of RC-active circuits based on amplifiers with highly asymmetrical slew rates is presented, with the describing function for a sinusoidal-plus-bias signal (SBDF), with the defining integrals calculated by Steklov's approximation.
Abstract: A nonlinear model for the frequency-domain analysis of RC-active circuits based on amplifiers with highly asymmetrical slew rates is shown. The model uses the describing function for a sinusoidal-plus-bias signal (SBDF), with the defining integrals calculated by Steklov's approximation. Hence, explicit expressions for the circuit frequency response and for the amplifier output bias are obtained. Analytical expressions are derived for the main parameters describing the regenerative phenomena, and a necessary and sufficient condition for phenomena-free circuits is obtained.