Topic
Describing function
About: Describing function is a research topic. Over the lifetime, 1742 publications have been published within this topic receiving 26702 citations.
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TL;DR: In this article, an indirect numerical approach is described which shows that, for a system of nonlinear differential equations, the eigenvalues of the quasi-linear system simply indicate all limit cycles and, additionally, yield stability regions for the linearized case.
Abstract: In the calculation of periodic oscillations of nonlinear systems –so-called limit cycles – approximative and systematic engineeringmethods of linear system analysis are known The techniques, working inthe frequency domain, perform a quasi-linearization of the nonlinear system,replacing nonlinearities by amplitude-dependent describing functionsFrequently, the resulting equations for the amplitude and frequency ofpresumed limit cycles are solved directly by a graphical procedure in aNyquist plane or by solving the nonlinear equations or a parameteroptimization problem In this paper, an indirect numerical approach isdescribed which shows that, for a system of nonlinear differentialequations, the eigenvalues of the quasi-linear system simply indicateall limit cycles and, additionally, yield stability regions for thelinearized case The method is applicable to systems with multiplenonlinearities which may be static or dynamic It is demonstrated foran example of aircraft nose gear shimmy dynamics in the presence ofdifferent nonlinearities and the results are compared with those fromsimulation
30 citations
TL;DR: In this paper, a fractional interpolation based smoothing scheme is proposed to eliminate the limit cycle, and maintain a reasonable tracking precision bound for a DC servo motor with unmodeled stator and sensor dynamics.
30 citations
TL;DR: In this paper, a non-linear circuit with integrated Mach-Zehnder interferometers on LiNbO 3 was analyzed by the describing function technique, and the conditions for stable oscillations and oscillator synchronization were well confirmed by experiments.
30 citations
TL;DR: It is shown that the convergence rate in a system controlled by a SOSM controller depends on the angle between the high- frequencies of the Nyquist plot of the plant and the low-amplitude asymptote of the negative reciprocal of the describing function of the controller, which is named the phase deficit.
30 citations
22 Apr 1996
TL;DR: The closed-loop system of a mass with nonlinear friction is found to be amenable to control without limit cycles and by decoupling the joints of the robot the authors find similar results within a good accuracy range.
Abstract: This paper investigates the control of robots with nonlinear friction and dynamic backlash in the joints. The study is based on the describing function (DF) of nonlinear systems. The controllers studied are the first order model and the second order model variable structure controllers (FOM-VSC and SOM-VSC). The authors start by studying nonlinear plants consisting of a mass subjected to Coulomb plus viscous friction or two masses subjected to dynamic backlash. The worst case for the limit cycle generation is found to be the closed-loop system having two masses with backlash. On the other hand, the closed-loop system of a mass with nonlinear friction is found to be amenable to control without limit cycles. By decoupling the joints of the robot the authors find similar results within a good accuracy range.
30 citations