Describing function

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

Nonlinear Resonant Jump in Rudder Positioning Electrohydraulic Systems

Abstract: The rudder positioning electrohydraulic system, as many other complex systems, is a nonlinear system. In nonlinear systems, a nonlinear resonant jump can occur. The paper deals with the analysis of the rudder positioning electrohydraulic system regarding the nonlinear resonant jump caused by saturation of the electrohydraulic proportional valve. The meaning of the term "resonant jump" is explained in the introduction. Then, the basics needs for occurrence of nonlinear resonant jump phenomenon are given. The rudder positioning electrohydraulic system is also described. Two methods of analyzing system with respect to resonant jumps are described: the analytical method and the simulation method. When performing the analytical analysis based on the describing function approach, the analysis of the variations of important parameters, including saturation, is performed. Then, the confirmation of the results of analytical analysis is illustrated by the simulation method. Also, the simulation procedures, like creating an excitation signal and accelerating the simulation by using vectors in Simulink/Matlab simulation software package, are explained in detail.

A Comparison between the Fourier and Ritz Describing Functions for the Damped Driven Duffing Equation

Abstract: Fourier and Ritz describing functions are obtained for the damped, driven Duffing equation. These results are compared to the pseudo-describing function, which is defined as the ratio of the first harmonic output amplitude obtained with a real filter to the input amplitude. The results indicate that the Ritz describing function is a better approximation to the pseudo-describing function. Since a number of important nonlinear systems can be represented or approximated by the Duffing equation, it seems that the Ritz describing function has significance as another tool in nonlinear system analysis.

Design of Nonlinear Frequency Controller for Isolated Thermal Power System with Generation Rate Constraint

Abstract: A nonlinear control scheme for thermal power system frequency control is described. Nonlinear controller is developed through describing function stability analysis of the system Controller ensures stability of the system for any input. Simulation results are given showing the smooth operation of described control scheme. Paper describes in detail the stability analysis and controller design.

Nonlinear Compensation of Solar Array Simulators with Dual Power Regulation

Abstract: During the tests of the spacecraft electrical systems there is a need for simulators of individual parts of the spacecrafts, in particular, solar array simulators (SAS). One of the topologies of medium and high power SAS simulators has dual control of consumed power and contains series or parallel connected linear and switching regulators. This topology allows to provide wide bandwidth and high efficiency, but the range of the resistance change of periodically switched SAS load is limited to the value of the stabilized attribute. Nonlinear compensator (NC) allows to reduce the average feedback voltage of the switching regulator in case of periodic load switching, which, in turn, allows to increase the average value of the stabilized attribute. The describing function method provides a mathematical description of the NC electrical circuit, which allows to select parameters of NC that eliminate the excitation of self-oscillation based on the SAS load switching frequency range and to study the switching regulator stability.

Frequency-domain simulation of power electronics circuits by using describing functions in a modified nodal approach

Abstract: A new approach for AC analysis of switching-mode power converters is presented. It is based on the use of two concepts: the bifrequency transfer function, which relates the input and output spectrums of the power electronics circuit, and the describing function. In order to calculate the input-to-output or control-to-output frequency response, small sinusoidal perturbations in either the line voltage or the control variable are considered. The fundamental component of the output variable at the perturbation's frequency is determined by using the zeroth order term of the Fourier transform of the impulse response, allowing then for the deduction of the line and control describing functions. No additional approximations (as neglecting higher order terms, etc) are required. The method is applied for the simulation of a switched-capacitor-based DC-to-DC converter.