Describing function

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

Computer-aided control engineering environment for nonlinear systems analysis and design

Abstract: We report on recent progress in developing a computer-aided nonlinear control system analysis and design environment based on sinusoidal-input describing function (SIDF) methods. In particular, two major additions have been made to our CAD software for nonlinear controls during 1984: a simulation-based program for generating amplitude-dependent SIDF input/output models for nonlinear plants, and a frequency-domain nonlinear compensator design package. Both of these are described in detail. This software can treat very general nonlinear systems, with no restrictions as to system order, number of nonlinearities, configuration, or nonlinearity type. An overview of the application of this software to the design of controllers for a realistic, nonlinear model of an industrial robot is presented in Taylor (1984). which serves to illustrate the use of these tools. Based on the software presented here, the use of SIDF-based nonlinear control system analysis and design methods is substantially easier to carry out.

Coexistent multiple-stability of a fractional-order delayed memristive Chua’s system based on describing function

Abstract: In this paper, in order to analyze the coexistent multiple-stability of system, a fractional-order memristive Chua’s circuit with time delay is proposed, which is composed of a passive flux-control...

Modeling of stable and unstable second order systems with time delay

Abstract: Estimation of stable and unstable second order plus time delay (SOPDT) process model parameters is proposed in this paper by using relay with hysteresis and describing function approximation (DFA) technique. The process models concerned in this paper are assumed to have only real poles. Relay with hysteresis reduces the effect of measurement noise on process model parameters. DFA technique is used to derive mathematical expressions to identify the unknown model parameters. Measurement noise which is an important issue in real time systems, may lead to inaccurate estimation of process model parameters. The effectiveness of the proposed method is studied in the noisy environment. For denoising, Fourier series based curve fitting technique is used. The general usefulness of the proposed method is validated with simulation results.

Stability analysis of control systems having two non-linear elements with calculations for saturation and backlash

Abstract: Control systems are considered in which two non-linear relationships are present. No difficulty arises if these are adjacent in the control sequence in the sense that the two may be considered as a single nonlinear element. The more difficult case is when the non-linear relationships are separated, so that the input of the second depends upon the output of the first in a manner which, although linear, involves time. The paper shows how this case may be analysed, and presents a method of determining values of the various system parameters that will inhibit sustained oscillations. To illustrate the procedure, the case is considered of systems in which there are elements having, respectively, torque limitation and backlash, other elements being linear. Calculations are given for two variants of a second-order control system. In the first case stabilization is by feedback from a point in the control sequence after the second non-linear element. In the second, the system is stabilized by feeding back a signal from a point between the two elements. The results are compared with measurements taken from an analogue computer, and are shown to be generally in good agreement, but the presence of sudden changes in amplitude and frequency at particular values of relevant parameter ratios (`jump' phenomena) are not revealed by the calculations using describing functions.

Identification of the de-synchronization, synchronization and forced oscillation phenomenon of a nonlinear system

Abstract: The phenomena of de-synchronization, synchronization, and forced oscillation has been investigation using describing function theory for a two input and two output nonlinear system containing saturation-type nonlinearities and subjected to high-frequency deterministic signal for the purpose of limit cycle quenching. The analytical results have been compared with the results of digital simulation Matlab-Simulink for a typical example varying the nonlinear element.