Describing function

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

Modeling and Digital Control of a Phase-Controlled Series–Parallel Resonant Converter

Abstract: A nonlinear model for a phase-controlled series-parallel resonant converter is developed using the extended describing function method and d-q decomposition. The model is linearized and reduced using the balanced model reduction technique. Based on the reduced model and taking into account the zero-order hold delay and the computation delay in the sampled-data system, a digital controller for the converter is designed. The controller is implemented with a digital signal processor (DSP). The closed-loop converter with the DSP controller is built and tested experimentally. Recorded transient waveforms show that the closed-loop converter is capable of not only responding to the reference input change as required by the design specifications, but also stabilizing the output effectively under disturbances from both the output and the input

Nonlinear mode triggering in a multiple flame combustor

Abstract: A nonlinear analysis of combustion instability is carried out by making use of the Flame Describing Function (FDF) framework. Predictions are compared with data obtained from experiments on a multipoint injection combustor. The burner comprises a premixer manifold of variable length, an injection system and a flame tube. This device features several types of self-sustained oscillation and its dynamics is characterized by nonlinearities like transient frequency shifting, mode switching, mode triggering and hysteresis phenomena which cannot be anticipated from a classical linear stability analysis. It is shown that many of these phenomena can be suitably predicted by including the amplitude dependent response of the flame in a matrix analysis of the system dynamics. More specifically, the present work centers on processes which cannot be anticipated from linear analysis such as mode switching linked to a triggering by the nonlinear flame response.

Generating Self-Excited Oscillations via Two-Relay Controller

Abstract: A tool for the design of a self-excited oscillation of a desired amplitude and frequency in linear plants by means of the variable structure control is proposed. An approximate approach based on the describing function method is given, which requires that the mechanical plant should be a low-pass filter - the hypothesis that usually holds when the oscillations are relatively fast. The proposed approach is demonstrated via the controller design and experiments on the Furuta pendulum.