Describing function

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

Nonlinear Flame Describing Function Analysis of Galloping Limit Cycles Featuring Chaotic States in Premixed Combustors

Abstract: Nonlinear prediction of combustion instabilities in premixed systems is undertaken on a generic configuration featuring an adjustable feeding manifold length, a multipoint injector composed of a perforated plate and a flame confinement tube. By changing the feeding manifold or flame tube lengths, the system exhibits different types of combustion regimes for the same flow operating conditions. Velocity, pressure and heat release rate measurements are used to examine oscillations during unstable operation. For many operating conditions, a limit cycle is reached at an essentially fixed oscillation frequency and quasi-constant amplitude. In another set of cases, the system features other types of oscillations characterized by multiple frequencies, amplitude modulation and irregular bursts which can be designated by “galloping” limit cycles or GLC. These situations are explored in this article. Imaging during GLCs indicates that the flame is globally oscillating but that the cycle is irregular. Prediction of these special oscillation states is tackled within the Flame Describing Function (FDF) framework. It is shown that it is possible to predict with a reasonable degree of agreement the ranges where a quasi-constant amplitude limit cycle will be established and ranges where the oscillation will be less regular and take the form of a galloping limit cycle. It is found that the FDF analysis also provides indications on the bounding levels of the oscillation envelope in the latter case.Copyright © 2012 by ASME

A w-domain approach to the design of sampled relay control systems

Abstract: This paper illustrates how the use of z–transform describing functions mapped into the w–domain provides a readily understood acceptable approach to the design of digital compensators for sampled relay control systems. The shortcomings of using the sinusoidal input describing function are also highlighted

Beyond the Waterbed Effect: Development of Fractional Order CRONE Control with Non-Linear Reset

Abstract: In this paper a novel reset control synthesis method is proposed: CRONE reset control, combining a robust fractional CRONE controller with non-linear reset control to overcome waterbed effect. In CRONE control, robustness is achieved by creation of constant phase behaviour around bandwidth with the use of fractional operators, also allowing more freedom in shaping the open-loop frequency response. However, being a linear controller it suffers from the inevitable trade-off between robustness and performance as a result of the waterbed effect. Here reset control is introduced in the CRONE design to overcome the fundamental limitations. In the new controller design, reset phase advantage is approximated using describing function analysis and used to achieve better open-loop shape. Sufficient quadratic stability conditions are shown for the designed CRONE reset controllers and the control design is validated on a Lorentz-actuated nanometre precision stage. It is shown that for similar phase margin, better performance in terms of reference-tracking and noise attenuation can be achieved.

A real-time approach for dead-time plant transfer function modeling based on relay autotuning

Abstract: In this article, a modified relay feedback experiment for the generation of sustained oscillations in a class of dead-time plants and their mathematical modeling is presented in a real-time fashion. For the ease of calculation, an equivalent gain of the relay is considered using well-known describing function method and further utilized in the derivation of a set of simple analytical expressions for the estimation of plant model parameters. Simulation studies are considered to show the validation of the proposed models with the model obtained from Matlab System Identification Toolbox (SIT) and literature through integral absolute error index. Yokogawa distributed control system is considered as an experimental platform to conduct the relay autotuning test for the identification of a real-time liquid level control system in-terms of dead-time transfer function models. Finally, the accuracy of proposed models is demonstrated through frequency response plots as well as relay response plots in comparison with models obtained from Ziegler–Nichols tests and Matlab SIT.

Identification of Weakly Nonlinear Systems Using Describing Function Inversion

Abstract: In this paper describing functions inversion is used and the restoring force of a nonlinear element in a MDOF system is characterized. The describing functions can be obtained using linearized frequency response functions (FRFs). The response of the system to harmonic excitation forces at distinct frequencies close to the resonant frequency results in linearized FRFs. The nonlinear system can be approximated at each excitation frequency by an equivalent linear system. This approximation leads to calculation of the first-order describing functions. By having the experimental describing functions calculated and the system's responses corresponding to the nonlinear element (measured or interpolated), nonlinear parameter identification can be performed. Two numerical and experimental case studies are provided to show the applicability of this method.