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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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01 Dec 2012
TL;DR: In this paper, a flame model with a simple saturation nonlinearity is coupled to simple duct acoustics, and the success of the FDF in predicting limit cycles is studied over a range of flame positions and acoustic damping parameters.
Abstract: In any thermoacoustic analysis, it is important not only to predict linear frequencies and growth rates, but also the amplitude and frequencies of any limit cycles. The Flame Describing Function (FDF) approach is a quasi-linear analysis which allows the prediction of both the linear and nonlinear behaviour of a thermoacoustic system. This means that one can predict linear growth rates and frequencies, and also the amplitudes and frequencies of any limit cycles. The FDF achieves this by assuming that the acoustics are linear and that the flame, which is the only nonlinear element in the thermoacoustic system, can be adequately described by considering only its response at the frequency at which it is forced. Therefore any harmonics generated by the flame’s nonlinear response are not considered. This implies that these nonlinear harmonics are small or that they are sufficiently filtered out by the linear dynamics of the system (the low-pass filter assumption). In this paper, a flame model with a simple saturation nonlinearity is coupled to simple duct acoustics, and the success of the FDF in predicting limit cycles is studied over a range of flame positions and acoustic damping parameters. Although these two parameters affect only the linear acoustics and not the nonlinear flame dynamics, they determine the validity of the low-pass filter assumption made in applying the flame describing function approach. Their importance is highlighted by studying the level of success of an FDF-based analysis as they are varied. This is achieved by comparing the FDF’s prediction of limit-cycle amplitudes to the amplitudes seen in time domain simulations.

3 citations

Proceedings ArticleDOI
08 Jun 2005
TL;DR: The stability analysis of a system with single input single output (SISO) fuzzy controller using describing functions to represent known nonlinearity in the system and linear systems stability analysis method and comparison to check the stability of the system with fuzzy controller.
Abstract: The stability analysis of a system with single input single output (SISO) fuzzy controller is described. The given example uses describing functions to represent known nonlinearity in the system and linear systems stability analysis method and comparison to check the stability of the system with fuzzy controller

3 citations

Proceedings ArticleDOI
TL;DR: This paper proposes a strategy for the analysis and design of a nonlinear robust control system with variable parameters, founded on introduction of system compensation with two degrees of freedom, and demonstrates significant improvement in the system performance in terms of insensitivity to variations of the system parameters.
Abstract: This paper proposes a strategy for the analysis and design of a nonlinear robust control system with variable parameters. A digital robust controller is implemented in the system. The approach for the controller design is founded on introduction of system compensation with two degrees of freedom. As a result, the targeted robustness of the system is achieved. The system’s stability and robust assessment is based on the interaction between its nonlinear and linear sections. D-partitioning, timeresponse and describing function analyses are implemented before and after the robust compensation. These analyses demonstrate significant improvement of the system performance in terms of insensitivity to variations of the system parameters. The digital robust controller is build of microcontrollers, based on the difference equations of its sections.

3 citations

Journal ArticleDOI
TL;DR: In this article, the authors formulate and prove a theorem which gives a rigorous theoretical justification for the use of describing functions to predict the existence of limit cycles in a multiple nonlinear feedback system.
Abstract: We formulate and prove a theorem which gives a rigorous theoretical justification for the use of describing functions to predict the existence of limit cycles in a multiple nonlinear feedback system and to predict the stability properties of these limit cycles. Our approach uses the classical sinusoidal-input describing function and the theory of integral manifolds. We demonstrate the applicability of our result by means of two specific examples.

3 citations

Journal ArticleDOI
TL;DR: In this article, a combination of analytical and computational approaches is used to represent the input-output responses of biomolecular signalling systems, which can add more insight into the local behaviour of these systems than standard linearization.
Abstract: Mathematical methods provide useful framework for the analysis and design of complex systems. In newer contexts such as biology, however, there is a need to both adapt existing methods as well as to develop new ones. Using a combination of analytical and computational approaches, we adapt and develop the method of describing functions to represent the input-output responses of biomolecular signalling systems. We approximate representative systems exhibiting various saturating and hysteretic dynamics in a way that is better than the standard linearization. Further, we develop analytical upper bounds for the computational error estimates. Finally, we use these error estimates to augment the limit cycle analysis with a simple and quick way to bound the predicted oscillation amplitude. These results provide system approximations that can add more insight into the local behaviour of these systems than standard linearization, compute responses to other periodic inputs, and to analyze limit cycles.

3 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202312
202230
202142
202057
201953
201847