Describing function

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

Swirling Flame Instability Analysis Based on the Flame Describing Function Methodology

Abstract: Thermoacoustic instabilities are analyzed by making use of a nonlinear representation of flame dynamics based on the describing function. In this framework, the flame response is determined as a function of frequency and amplitude of perturbations impinging on the combustion region. This methodology is applied to confined swirling flames in a laboratory scale setup (2.5 to 4 kW) comprising an upstream manifold, an injection unit equipped with a swirler (swirl number = 0.55) and a cylindrical flame tube. The flame describing function is experimentally determined and is combined with an acoustic transfer matrix representation of the system to provide growth rates and oscillation frequencies as a function of perturbation amplitude. These data can be used to determine regions of instability, frequency shifts with respect to the acoustic eigenfrequencies and they also yield amplitude levels when self-sustained oscillations of the system have reached a limit cycle. This equilibrium is obtained when the amplitude dependent growth rate equals the damping rate in the system. This requires an independent determination of this last quantity which is here based on measurements of the resonance response curve. Results obtained are compared with observations from systematic experiments carried out by varying the test combustor geometry. The demonstration of the FDF framework in a generic configuration indicates that this can be used in more general situations of technological interest.Copyright © 2010 by ASME

Convergence and computation of describing functions using a recursive Volterra series

Abstract: Presented in this paper is a comparison of algorithms for computing an approximation to the sinusoidal input describing function (SIDF) for the nonlinear differential equation ẏ(t)+b1y(t)+b2u2(t)y(t) = K(u(t)+b3u(t)) The importance of this nonlinear differential equation comes from the context of nonlinear feedback controller design Specifically, this equation is either a linear lead or lag controller (depending on the coefficient values) augmented with a nonlinear, polynomial type term Consequently, obtaining a SIDF representation of this nonlinear differential equation or creating a process to obtain SIDFs for other similar differential equations, will facilitate nonlinear controller design using classical loop shaping tools The two SIDF approximations studied include the well-established harmonic balance method and a Volterra series based algorithm In applying the Volterra series, several theoretical issues were addressed including the development of a recursive solution that calculates high order Volterra transfer functions, and the guarantee of convergence to an arbitrary accuracy Throughout the paper, case studies are presented Copyright © 2004 John Wiley & Sons, Ltd

Modeling and digital nonlinear control of active magnetic bearing (abstract)

Abstract: In the first part of the paper we propose a complete nonlinear dynamic model of a magnetic bearing. The bearing is made up to two controlled axes and three passive axes. This model takes into account the changeover of the power between the two coils of each controlled axis in order to control each axis without exciting currents. In this case, the model is not linear anymore. In the second part we compute a linear regulator taking into account the nonlinearity of the model. For that, we use the ‘‘describing function approach’’ (the nonlinearity is approximated by a complex gain which is a function of the magnitude of the input signal). The stability of the control is assumed first by using the frequency response of the linear part of the model and second by using the describing function of the nonlinearity. In the third part, the regulator is implemented on a digital computer with a sampling period of 0.4 ms. The matching between simulation results and experimental trials shows the accuracy of both the mod...

Analysis of steady state behavior of second order sliding mode algorithms

Abstract: An analysis of a second order sliding mode algorithm, which is known as the super-twisting algorithm, is carried out in the frequency domain with the use of the describing function method. It is shown that in the presence of an actuator, the transient process converges to a periodic motion. Parameters of this periodic motion are analyzed. A comparison between the periodic solutions in the systems with higher order sliding mode controllers and the oscillations that occur in classical sliding mode systems with actuators is done.

Simulation of microwave and millimeter-wave oscillators, present capability and future directions 1

Abstract: The current state-of-the art of oscillator simulation techniques is presented. Candidate approaches for the next genertion of oscillator simulation techniques are reviewed. The method is presented which uses an ecient and robust convolution-based procedure to integrate frequency-domain modeling of a distributed linear network in transient simulation. The impulse response of the entire linear distributed network is obtained and the algorithm presented herein ensures that aliasing eects are minimized by introducing a procedure that ensures that the interconnect network response is both time-limited and band-limited. In particular, articial ltering to bandlimit the response is not required. I. Introduction Large signal simulation of microwave oscillators is necessary to provide steady-state characterization of oscillator performance. Such quantities as power and harmonic content information are then readily available. This is particularly important in achieving rst pass successful design of monolithicly integrated oscillators. Circuit simulation of microwave oscillators by the method of harmonic balance is reasonably mature with several commercial products available and used on a regular basis and been adapted to some rather unusual applications, e.g. [44]. However large signal oscillator analysis in the time domain using programs such as SPICE [20] enables the build-up of oscillations to be observed. In spite of being time-consuming and the diculty of determining the time at which steady state is obtained, time-domain simulation techniques have the ability to predict the start-up of oscillation in addition to the frequency of oscillation and non-steady-state behavior. There a many diculties in applying transient analysis techniques to distributed circuits but these are gradually being addressed. The near future will see a rapid development of these techniques and will be used regularly in microwave oscillator simulation. In this paper we review the current state of microwave oscillator simulation using the harmonic balance approach and describing function methods. We then consider the current state of transient microwave oscillator simulation and focus on transient simulation techniques that have potential for microwave oscillator simulation. We present a new method of transient simulation which integrates the distributed nature of microwave circuits into a transient simulator by using convolution of the impulse response of the linear circuit. Particular attention is given to reducing aliasing eects in deriving the impulse response and in handling of high Q linear circuits.