Describing function

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

Automatic Tuning of Two-Degree-of-Freedom Control for D.C. Servo Motor Systems

Abstract: In this paper, we present the first application of the relay feedback approach to the automatic tuning of a two-degree-of-freedom (2-DOF) controller to achieve robust motion control for d.c. servo motor systems. The only specifications required from the user are simple and classical parameters for the desired closed-loop transfer function and an appropriate sensitivity function determining the robustness of the closed-loop system. Heuristics are provided for the selection of key parameters of these functions. Two variations of the conventional relay feedback methods were proposed and investigated. Both of these variations introduce an appropriate phase angle in the negative inverse describing function of the relay to excite a sustained limit cycle oscillation. Simulation and experimental results from a voltage controllable d.c. motor system illustrate the effectiveness of the proposed methods.

Computer-aided Nonlinear Control System Design: Using Describing Function Models

Abstract: A systematic computer-aided approach provides a versatile setting for the control engineer to overcome the complications of controller design for highly nonlinear systems. Computer-aided Nonlinear Control System Design provides such an approach based on the use of describing functions. The text deals with a large class of nonlinear systems without restrictions on the system order, the number of inputs and/or outputs or the number, type or arrangement of nonlinear terms. The strongly software-oriented methods detailed facilitate fulfillment of tight performance requirements and help the designer to think in purely nonlinear terms, avoiding the expedient of linearization which can impose substantial and unrealistic model limitations and drive up the cost of the final product. Design procedures are presented in a step-by-step algorithmic format each step being a functional unit with outputs that drive the other steps. This procedure may be easily implemented on a digital computer with example problems from mechatronic and aerospace design being used to demonstrate the techniques discussed. The authors commercial MATLAB-based environment, available separately from insert URL here, can be used to create simulations showing the results of using the computer-aided control system design ideas characterized in the text. Academic researchers and graduate students studying nonlinear control systems and control engineers dealing with nonlinear plant, particularly mechatronic or aerospace systems will find Computer-aided Nonlinear Control System Design to be of great practical assistance adding to their toolbox of techniques for dealing with system nonlinearities. A basic knowledge of calculus, nonlinear analysis and software engineering will enable the reader to get the best from this book.

Theory of nonlinear control

Abstract: In the introduction the author discusses the nonlinearity in Nature as exemplified by a simple pendulum, inverse square laws of gravitation and electromagnetism, electronics, and planetary motion.Nonlinear feedback control systems have been analyzed in symposia sponsored by Polytechnic Institute of Brooklyn, American Society of Mechanical Engineers, and Institute of Radio Engineers. Even nonlinear system synthesis has been attempted. Part II discusses the three stages in the study of physical systems: (1) Development of linear system analysis and idealization of actual systems as linear; (2) Recognition of nonlinear systems and analysis of such systems as they actually are; and (3) Introduction of the new concept of nonlinear control and improvement of the performance of linear and nonlinear systems. Under (3) it is recognized that besides linear compensation of systems with nonlinearities the logical alternative might be the nonlinear feedback control of physical systems for either stability or optimum response. Part I I I starts with a review of linearizing techniques developed by Kochenburger, Johnson, Klotter, and others, known as the describing function method. Other quasi-linearization, equivalent linearization, and piecewise linearization techniques by Chen, Booton, Bass, and Stern are discussed. Part IV deals with the phase-space, the switching surface, and related concepts. The method of simultaneous phase-plane equations in a multi-degree-of-freedom system is especially adaptable to nonlinear feedback control system analysis. The phase-space approach has been used by Kalman, Hopkin, and others for the design of nonlinear servomechanisms. Part V covers new analytic techniques and new transforms.Papers by Pipes, Madwed, L. J. Lewis, Gillies, Stout, E. Weber, and others are reviewed. Taylor-Cauchy transforms for nonlinear systems are presented. Part VI discusses theory of nonlinear systems, including recent developments in stability theory and criteria, optimum nonlinear control systems, sampled-data systems, and nonlinear systems with random igputs.These recent developments give substantial support to the author's statement: “The newest aspect of feedback control is the development of the theory of nonlinear control.”

Accurate Small-Signal Modeling of Resonant Converter Based on Perturbation on the State Plane

Abstract: Resonant converters operate the switching frequency close to the resonant frequency to achieve soft switching. However, this also posts a great challenge on the small-signal modeling. Based on the fundamental approximation, E. Yang develops the first small-signal equivalent circuit model. Recently, the authors propose a simpler model based on the average concept on a rotating state plane. The assumptions of the two models are shown to be equivalent. This implies the two approaches are applicable only when there is an effective bandpass filter. However, the resonant tank in more popular resonant converters such as LLC converter does not behave like a good band-pass filter. Therefore, this paper aims at providing a more accurate small-signal modeling. It is based on perturbation on the state plane and describing function method. Using the series resonant converter (SRC) as an example, the model shows a perfect match to a simulation result. Based on the fact that the system poles can be captured by the natural response, a simplified, yet accurate, second-order model for an SRC is provided. All the small-signal dynamic are well-explained using the proposed model. The proposed modeling and simplification methods show a promising extension to model the LLC converter.

Memristor Circuits for Simulating Neuron Spiking and Burst Phenomena.

Abstract: Since the introduction of memristors, it has been widely recognized that they can be successfully employed as synapses in neuromorphic circuits. This paper focuses on showing that memristor circuits can be also used for mimicking some features of the dynamics exhibited by neurons in response to an external stimulus. The proposed approach relies on exploiting multistability of memristor circuits, i.e., the coexistence of infinitely many attractors, and employing a suitable pulse-programmed input for switching among the different attractors. Specifically, it is first shown that a circuit composed of a resistor, an inductor, a capacitor and an ideal charge-controlled memristor displays infinitely many stable equilibrium points and limit cycles, each one pertaining to a planar invariant manifold. Moreover, each limit cycle is approximated via a first-order periodic approximation analytically obtained via the Describing Function (DF) method, a well-known technique in the Harmonic Balance (HB) context. Then, it is shown that the memristor charge is capable to mimic some simplified models of the neuron response when an external independent pulse-programmed current source is introduced in the circuit. The memristor charge behavior is generated via the concatenation of convergent and oscillatory behaviors which are obtained by switching between equilibrium points and limit cycles via a properly designed pulse timing of the current source. The design procedure takes also into account some relationships between the pulse features and the circuit parameters which are derived exploiting the analytic approximation of the limit cycles obtained via the DF method.