Describing function

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

Phase synchronization and synchronization frequency of two-coupled van der Pol oscillators with delayed coupling

Abstract: In this paper, phase synchronization and the frequency of two synchronized van der Pol oscillators with delay coupling are studied. The dynamics of such a system are obtained using the describing function method, and the necessary conditions for phase synchronization are also achieved. Finding the vicinity of the synchronization frequency is the major advantage of the describing function method over other traditional methods. The equations obtained based on this method justify the phenomenon of the synchronization of coupled oscillators on a frequency either higher, between, or lower than the highest, in between, or lowest natural frequency of the aggregate oscillators. Several numerical examples simulate the different cases versus the various synchronization frequency delays.

Development of vehicle dynamics model for real-time electronic control unit evaluation system using kinematic and compliance test data

Abstract: A functional suspension model is proposed as a kinematic describing function of the suspension, that represents the relative wheel displacement in polynomial form in terms of the vertical displacement of the wheel center and steering rack displacement. The relative velocity and acceleration of the wheel is represented in terms of first and second derivatives of the kinematic describing function. The system equations of motion for the full vehicle dynamic model are systematically derived by using velocity transformation method of multi-body dynamics. The comparison of test and simulation results demonstrates the validity of the proposed functional suspension modeling method. The model is computationally very efficient to achieve real-time simulation on TMS 320C6711 150 ㎒ DSP board of HILS (hardware-in-the-loop simulation) system for ECU (electronic control unit) evaluation of semi-active suspension.

Design of Self-Limiting Transistor Sine-Wave Oscillators

Abstract: By combining the describing function approach with a large signal transistor model and certain simplifying assumptions, it has been possible to develop a set of universal curves yielding selflimiting operating amplitudes for a large class of transistor sinewave oscillators. The variable parameter in this presentation is the dc voltage drop across the emitter bias resistor in the circuit with oscillations absent. Since this parameter may be easily calculated, the material presented allows the design of oscillators for any allowable operating amplitude. In a companion paper the method is extended to include collector saturation limiting and calculations of the onset of squegging.

Feedback linearization control of magnetorheological fluid damper based systems with model uncertainty

Abstract: This paper is concerned with the effects of magnetorheological (MR) fluid damper model uncertainties on system stability, when local feedback linearization schemes are utilized to stabilize an inherently unstable system with negative damping. The objectives of the research are to characterize such effects, and develop a robust control law for given uncertainty bounds. First, for the purpose of discussion, sine functions are used as examples to represent the possible deviations between the actual MR damper force and the force predicted by the model. The limit cycle behavior is predicted using the describing function method and parameters influencing the limit cycle characteristics are identified. An effort is then made to identify the worst-case model deviation, given the bounds on the possible model uncertainties. Based on these results and the limit cycle analysis, the minimum control gain to eliminate the limit cycle instability can be derived. With such gains, the closed-loop system is robust against all uncertainties within the bounds.