Describing function

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

Bias Removal in Higher Order Sinusoidal Input Describing Functions

Abstract: In this paper a novel method is presented for the reduction of bias caused by harmonic excitation in the identification of higher order sinusoidal input describing functions (HOSIDF). HOSIDF are a recently introduced generalization of the theory of the describing function. HOSIDF describe the magnitude and phase relations between the individual harmonic components in the output signal of a non-linear system and the sinusoidal excitation signal. In the presented method, the output signal of a non-linear system subjected to harmonic excitation is numerically split up into a fraction caused by the non-linear response due to the fundamental input signal component and the fraction caused by the quasi-linear response due to the harmonic input signal components. This separation is based on the assumption that the non-linear effects of intermodulation can be neglected, compared to the the effects caused by the generation of harmonics and gain compression/expansion. The method is demonstrated with real measurements on a mechanical system with friction.

Delayed feedback tracking controller for single-input single-output nonlinear systems

Abstract: Difficulties one faces in designing a satisfactory controller for systems involving stiff nonlinearities are well known. Stictions, Coulomb frictions and backlashes are but a few such examples. Unfortunately, there are few mechanical systems without such nonlinearities. The problem becomes even more complex if some of the state variables are not directly measurable, a situation which occurs not infrequently in practical systems. Unlike in linear systems where the missing state variables may be reconstructed [1], no corresponding methods are available for nonlinear systems. In fact, no general methods are currently available for analyzing and synthesizing controllers for nonlinear systems. At present, the describing function method is perhaps the best tool available for investigating stiff nonlinear systems [2]. A stable system is designed by adjusting the system gain or inserting a simple lead-lag compensation network. The parameter values are determined by graphically examining the Nyquist curve and the describing function. The process becomes very difficult, if not impossible, to apply when the order of the system is high and only the measurable variables are to be used in the feedback. When the reference input is a constant and only the output is available for feedback, the delayed feedback controller was given in [3]. In this paper, preliminary results are presented for the case when the reference input is a polynomial function and a multi-dimensional observable vector is available for feedback. It is based on augmenting the system by additional state variables and then feeding back delayed observable vectors as well as the augmented state variables.

Continuation Methods for Nonlinear Flutter

Abstract: Continuation methods are presented that are capable of treating frequency domain flutter equations, including multiple nonlinearities represented by describing functions A small problem demonstrates how a series of continuation processes can find all limit-cycle oscillations within a specified region with a reasonable degree of confidence Curves of the limit-cycle amplitude variation with velocity, indicating regions of stability and instability with colors, give a compact view of the nonlinear behavior throughout the flight regime A continuation technique for reducing limit-cycle amplitudes by adjusting various system parameters is presented These processes are economical enough to be a routine part of aircraft design and certification