Describing function

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

Design and Stability of an On-Orbit Attitude Control System Using Reaction Control Thrusters

Abstract: Principles for the design and stability of a spacecraft on-orbit attitude control system employing on-off Reaction Control System (RCS) thrusters is presented. Both the vehicle dynamics and the control system actuators are inherently nonlinear, hence traditional linear control system design approaches are not directly applicable. This paper has three main aspects: It summarizes key RCS control System design principles from the Space Shuttle and Space Station programs, it demonstrates a new approach to develop a linear model of a phase plane control system using describing functions, and applies each of these to the initial development of the NASA's next generation of upper stage vehicles. Topics addressed include thruster hardware specifications, phase plane design and stability, jet selection approaches, filter design metrics, and automaneuver logic.

H/sub /spl infin// Optimal Control of a Simple Nonlinear System Analyzed using Simplicial Algorithms

Abstract: This paper covers a new method for designing an H/sub /spl infin// optimal controller for a nonlinear system, then conducting a stability analysis using simplicial algorithms. Simple gains are used as the H/sub /spl infin// weighting functions. The system analyzed is an unstable first order plant, driven by a Bang-Bang actuator. A describing function model of the actuator was used in this analysis.

Robust stability of nonlinear hydraulic servo systems using closest Hopf bifurcation techniques

Abstract: A critical evaluation of current methods for analyzing hydraulic servo systems indicates a need for alternative methods that are better able to quantify robust stability, especially with respect to the existence of nonlinear oscillations. This paper addresses that need by examining a new analysis method that is capable of predicting stability robustness for nonlinear systems with high-dimensional parameter spaces. The method is based on the computation of "closest" Hopf bifurcations which correspond to the birth of limit cycle oscillations. A formal procedure that makes use of closest Hopf bifurcations for analyzing the robust stability of nonlinear systems is presented and applied. Practical implementation issues are addressed, with emphasis on interpretation of results to yield a meaningful quantitative measure of stability robustness. The new analysis method is validated via comparisons with previously published describing function results and new simulation results.

Oscillations in a two-dimensional non-linear system†

Abstract: The conditions necessary to obtain stable oscillations in a two-dimensional non-linear symmetrical system are found using the describing function technique, and the results are applied to two examples.

Describing Function Analysis and Experimental Investigation of a High Power Utility Friendly AC-DC Converter System

Abstract: In this paper, a utility friendly synchronous link three level diode clamped ac-dc converter having rectification and regeneration capability is presented. The three-level ac-dc converter draws sinusoidal ac current with low harmonics from the supply and keeps the DC-link voltage constant. Hysteresis current controller is used for current control because of its simplicity, easy implementation and good performance. The paper presents an analysis for limit cycle control of switching logic for the three-level synchronous link converter. The ideal hysteresis current control method leads to infinite frequency and that results in chattering phenomenon. In medium and high voltage converter applications, the switching elements, such as IGBT and GTO, have finite switching frequency. To bring the switching frequency into the limit of practical devices, hysteresis logic with a suitable band width (h) is required. The hysteresis logic being non-linear, describing function (DF) analysis is applied with non-linearity replaced by its DF. Thus, by using DF analysis, the maximum possible switching frequency for a given hysteresis band can be predicted. The closed-loop control scheme with hysteresis current control is implemented for the three-phase three-level synchronous link converter (SLC). Simulation and laboratory prototype test results demonstrate the validity of the proposed hysteresis current control method. The converter is found to be stable for a large range of hysteresis band.