Describing function

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

Receptor-Based CNN Model with Hysteresis for Pattern Formation

Abstract: In this paper receptor-based Cellular Nonlinear Network model with hysteresis is considered. Dynamics and stability of such model are studied by applying describing function technique. Comparison of the obtained results with the classical ones is made as well. Numerical simulations and discussions about the pattern formation in such model are presented.

Synchronization framework for modeling transition to thermoacoustic instability in laminar combustors

Abstract: We, herein, present a new model based on the framework of synchronization to describe a thermoacoustic system and capture the multiple bifurcations that such a system undergoes. Instead of applying flame describing function to depict the unsteady heat release rate as the flame's response to acoustic perturbation, the new model considers the acoustic field and the unsteady heat release rate as a pair of nonlinearly coupled damped oscillators. By varying the coupling strength, multiple dynamical behaviors, including limit cycle oscillation, quasi-periodic oscillation, strange nonchaos, and chaos can be captured. Furthermore, the model was able to qualitatively replicate the different behaviors of a laminar thermoacoustic system observed in experiments by Kabiraj et al.~[Chaos 22, 023129 (2012)]. By analyzing the temporal variation of the phase difference between heat release rate oscillations and pressure oscillations under different dynamical states, we show that the characteristics of the dynamical states depend on the nature of synchronization between the two signals, which is consistent with previous experimental findings.

A Gaussian-process-based framework for high-dimensional uncertainty quantification analysis in thermoacoustic instability predictions

Abstract: When combining a flame model with acoustic tools to predict thermoacoustic instability, uncertainties embedded in the flame model and acoustic system parameters propagate through the thermoacoustic model, inducing variations in calculation results. Therefore, uncertainty quantification (UQ) analysis is essential for delivering a reliable prediction of thermoacoustic instability. The present paper proposes a general, surrogate-based framework to efficiently perform UQ analysis in thermoacoustic instability predictions that (1) can handle large variational ranges and flexible statistical descriptions of the uncertain parameters, (2) takes into account uncertainties from both acoustic system parameters and high-dimensional flame response models (e.g. the finite impulse response model (FIR), the flame describing function (FDF), etc.), (3) quantifies uncertainties in modal frequency and linear growth rate for linear thermoacoustic analysis, or (4) quantifies uncertainties in limit cycle frequency and amplitude for nonlinear thermoacoustic analysis. The framework is built upon Gaussian process (GP) surrogate models. An active learning strategy from the machine learning community has been adopted to significantly enhance the efficiency of GP model training, thus achieving a significant reduction in computational cost. The effectiveness of the proposed UQ framework is demonstrated by two case studies: one linear case with an uncertain FIR model and acoustic system parameters, and one nonlinear case with an uncertain FDF dataset and acoustic system parameters. Compared with reference Monte Carlo simulations, the case studies reveal UQ analyses that are, respectively, 20 and 15 times faster, but nevertheless highly accurate. The proposed GP-based framework also forms an efficient foundation on which to address other types of studies, in which repetitive thermoacoustic calculations are required, such as parametric investigations, sensitivity analyses, nonlinear bifurcation studies and robust design.

Nonlinear loop shaping for suppressing sensitivity hump in hard disk drive servo systems

Abstract: In hard disk drive (HDD) servo system that uses voice coil motor (VCM) as the actuator, the sensitivity hump is unavoidable according to Bode's integral theorem (BIT). That results in amplification of disturbances with frequencies beyond bandwidth. This paper proposes a nonlinear loop shaping method to suppress sensitivity hump of the conventional servo. The proposed nonlinear algorithm consists of two parts. One is the conventional track-following control law, the other is a nonlinear PD type control law designed based on the conventional one to shape its high frequency response. The simulated describing function shows that sensitivity peak can be suppressed with the proposed algorithm without degrading low frequency disturbance rejection, which could lead to increase the track-following accuracy. The efficacy is verified through vibration test with disk flutter. Although sensitivity is improved, the effect of high frequency measurement noise on the position error signal (PES) which is governed by complementary sensitivity function is not degraded. The robustness is also verified with high frequency plant uncertainties.