scispace - formally typeset
Search or ask a question
Topic

Describing function

About: Describing function is a research topic. Over the lifetime, 1742 publications have been published within this topic receiving 26702 citations.


Papers
More filters
Book ChapterDOI
01 Jan 2000
TL;DR: This chapter shows the utility of employing the van der Pol and Poincare models as theoretical constructs for characterizing the dynamic behavior observed in physiological oscillators, such as cardiac and circadian pacemakers.
Abstract: This chapter shows the utility of employing the van der Pol and Poincare models as theoretical constructs for characterizing the dynamic behavior observed in physiological oscillators, such as cardiac and circadian pacemakers. One feature that distinguishes a nonlinear oscillator from a linear oscillatory system is that the former can exhibit the phenomenon of entrainment or phase‐locking. In the nonlinear case, the phase‐plane plot shows a closed‐loop figure, but the structure of the plot is much more irregular than the ellipse. The chapter illustrates a specific application of the describing function method. Although the Hodgkin‐Huxley equation set is able to reproduce many features of neuronal dynamics, it constitutes an unwieldy model, containing several state variables and a large number of empirical constants. The changes in dynamics exhibited by the Poincare oscillator or any nonlinear system that occurs abruptly as a system parameter is decreased or increased are commonly referred to as bifurcations .

5 citations

Proceedings ArticleDOI
01 Aug 1974
TL;DR: In this paper, the existence and characteristics of self-sustained oscillations in the dynamic behavior of the LST system due to the presence of nonlinear gimbal friction in the control moment gyroscopes (CMGs).
Abstract: The purpose of the investigation reported upon is to study the existence and characteristics of self-sustained oscillations in the dynamic behavior of the Large Space Telescope (LST) system due to the presence of nonlinear gimbal friction in the control moment gyroscopes (CMGs). A continuous-data single-axis model of the LST is considered. A solid friction model is used to represent CMG gimbal friction. A rigorous mathematical model is derived for use in a continuous describing function analysis. Conditions for self-sustained oscillations are then determined.

4 citations

Journal ArticleDOI
TL;DR: In this paper, the design procedure for a nonlinear reactor control system is described, and the final control scheme (a velocity servo with stepping motors) has been throughly tested on the analog computer with noisy inputs, and theoretically studied with a describing function method extended to the case of systems with multiple nonlinearities connected by linear sections.
Abstract: The design procedure for a nonlinear reactor control system is described. The control system contains two nonlinearities, separated by a linear section: a dead-band, normally used to reduce the noise excitation of the control system, and a gear backlash, which in this case is particularly important, due to the fact that the control elements are cylinders with limited effective angular range. The type of electrical motors was also defined (Slo-Syn motors, which can operate as synchronous or stepping motors). The work has been developed using analog and analytical methods in parallel, and the final control scheme (a velocity servo with stepping motors) has been throughly tested on the analog computer with noisy inputs, and theoretically studied with a describing function method extended to the case of systems with multiple nonlinearities connected by linear sections.

4 citations

01 Jan 2005
TL;DR: A study of this problem, which relates the maximum achievable object stiffness to the elements of the control loop, examines how the sampling rate, quantization, computational delay, and amplifier dynamics interact with the inertia, natural viscous, and Coulomb damping of the haptic device.
Abstract: Rendering stiff virtual objects remains a core chal- lenge in the field of haptics. A study of this problem is presented, which relates the maximum achievable object stiffness to the elements of the control loop. In particular, we examine how the sampling rate, quantization, computational delay, and amplifier dynamics interact with the inertia, natural viscous, and Coulomb damping of the haptic device. Nonlinear effects create distinct stability regions and many common devices operate stably, yet in violation of passivity criteria. An energy based approach provides theoretical insights, supported by simulations, experimental data, and a describing function analysis. The presented results subsume previously known stability conditions.

4 citations

Journal ArticleDOI
TL;DR: In this article, a simplified algorithm using Taylor series expansion about an arbitrary point, a, for the construction of minimal realizations for generalized transfer functions is developed. And the state space realization is given in the form of a linear, time-invariant, discrete-time, singular system.
Abstract: A simplified algorithm is developed using Taylor series expansion about an arbitrary point, a, for the construction of minimal realizations for generalized transfer functions. The state space realization is given in the form of a linear, time-invariant, discrete-time, singular system. Compared to existing methods, the proposed method reduces the computational effort and memory storage requirements. Furthermore, the quadruple [E, A, B, C] resulting from this technique is more general than similar expressions from existing approaches.

4 citations


Network Information
Related Topics (5)
Control theory
299.6K papers, 3.1M citations
90% related
Linear system
59.5K papers, 1.4M citations
88% related
Control system
129K papers, 1.5M citations
86% related
Robustness (computer science)
94.7K papers, 1.6M citations
83% related
Electric power system
133K papers, 1.7M citations
80% related
Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202312
202230
202142
202057
201953
201847