Describing function

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

Small-Signal Modeling for Phase-Shift Controlled Resonant Converters

Abstract: The extended describing function (EDF) method is widely used in modeling the resonant converters. This article finds that the model of the phase-shift controlled resonant converter deduced by this method might be inaccurate especially when the duty-cycle is close to 1. The reason behind it is investigated, showing that derivation of the inverter bridge model based on its fundamental harmonic will cause error. A novel model of the inverter bridge by Fourier analysis is proposed. Incorporating the novel model into the EDF-based resonant model, the accuracy of the phase-shift controlled resonant converter is greatly improved. A series–series compensated inductive power transfer system is fabricated in the lab to verify the validity of the proposed model.

Describing function analysis of second-order sliding mode observers

Abstract: The second-order sliding mode observer dynamics are analyzed in the frequency domain. The so-called super-twisting algorithm is utilized for generating the second-order sliding mode in the observer dynamical system. The frequency response of the observer dynamics is obtained and used as a characteristic of the observer. The analysis proposed is based on the describing function method and the concept of the equivalent gains of nonlinear functions of the super-twisting algorithm.

Analysis of Digital PCM-Controlled Boost Converter With Trailing-Edge Modulation Based on z -Domain and Describing-Function Model

Abstract: Digital trailing-edge modulated peak-current-mode (PCM) control scheme is commonly used in power converters, due to the similar excellent characteristics with its peer analog controller and being achieved easily in practice. However, the additional issues, such as time delays, quantization error, and resolution of the digital pulsewidth modulator (DPWM), in the digital controller, not only reduce the stability of the converter but also make the modeling and analysis more complicated. Taking the digital controlled boost converter as an example, this article presents a $z$ -domain model of the whole converter system on the basis of a describing-function method by considering the effects of the abovementioned problems. The influences of time delays from analog-to-digital conversion (ADC) and DPWM and resolution from the DPWM module can be analyzed clearly according to the proposed model. And more importantly, the critical resolution between stable and unstable operations of the converter can be determined by checking the eigenvalues. Furthermore, the stability analysis based on the presented $z$ -domain model is verified by the simulations and experiments.

A Low-Order Modelling of Ducted Flames With Temporally Varying Equivalence Ratio in Realistic Geometries

Abstract: The interaction between unsteady heat release and acoustic pressure oscillations in gas turbines results in self-excited combustion oscillations which can potentially be strong enough to cause significant structural damage to the combustor. Correctly predicting the interaction of these processes, and anticipating the onset of these oscillations can be difficult. In recent years much research effort has focused on the response of premixed flames to velocity and equivalence ratio perturbations. In this paper, we develop a flame model based on the so-called G-Equation, which captures the kinematic evolution of the flame surfaces, under the assumptions of axisymmetry, and ignoring vorticity and compressibility. This builds on previous work by Dowling [1], Schuller et al. [2], Cho & Lieuwen [3], among many others, and extends the model to a realistic geometry, with two intersecting flame surfaces within a non-uniform velocity field. The inputs to the model are the free-stream velocity perturbations, and the associated equivalence ratio perturbations. The model also proposes a time-delay calculation wherein the time delay for the fuel convection varies both spatially and temporally. The flame response from this model was compared with experiments conducted by Balachandran [4, 5], and found to show promising agreement with experimental forced case. To address the primary industrial interest of predicting self-excited limit cycles, the model has then been linked with an acoustic network model to simulate the closed-loop interaction between the combustion and acoustic processes. This has been done both linearly and nonlinearly. The nonlinear analysis is achieved by applying a describing function analysis in the frequency domain to predict the limit cycle, and also through a time domain simulation. In the latter case, the acoustic field is assumed to remain linear, with the nonlinearity in the response of the combustion to flow and equivalence ratio perturbations. A transfer function from unsteady heat release to unsteady pressure is obtained from a linear acoustic network model, and the corresponding Green function is used to provide the input to the flame model as it evolves in the time domain. The predicted unstable frequency and limit cycle are in good agreement with experiment, demonstrating the potential of this approach to predict instabilities, and as a test bench for developing control strategies.Copyright © 2011 by ASME