Topic
Describing function
About: Describing function is a research topic. Over the lifetime, 1742 publications have been published within this topic receiving 26702 citations.
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01 Jan 2012
TL;DR: In this article, the authors present a systematic computer-aided approach for the control engineer to overcome the complications of controller design for highly nonlinear systems. But their approach is based on the use of describing functions.
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.
01 Dec 2009
TL;DR: In this paper, a torque disturbance compensator for a digital controlled angle designation loop that uses an analog rate loop with proportional gain as an inner loop in an anti-backlash geared platform is proposed.
Abstract: This paper proposes a torque disturbance compensator for a digital controlled angle designation loop that uses an analog rate loop with proportional gain as an inner loop in anti-backlash geared platform. This is basically designed as alternative scheme based on conventional disturbance observer so as to be adopted in the analog rate loop where measurable state variables are limited. The stabilities for linear closed-loop, and for internal disturbance with nonlinear characteristics are, respectively, evaluated by Nyquist Diagram, and extended Nyquist criterion which uses a relay-type describing function. The design guideline to make the angle designation loop robust is presented step by step. In the end, the improved performances in real plant are demonstrated by experimental results of both frequency and time responses.
TL;DR: In this article, the Covariance Analysis Describing Function Technique (CADET) was compared with the Volterra Series Synthesis approach for the analysis of nonlinear stochastic systems.
Abstract: The superiority of the Covariance Analysis Describing Function Technique (CADET) in comparison with the Volterra Series Synthesis approach for the analysis of nonlinear stochastic systems is demonstrated in this note. The advantages of CADET are greater accuracy and simplicity.
14 Jun 2021
TL;DR: In this paper, a circuit-based method to reduce the order for both series and parallel resonant circuits is proposed. But the model is not extended to the high-order resonant tank of IPT.
Abstract: As a DC-DC converter, an inductive power transfer (IPT) system requires a feedback control to stabilize the output. An accurate and simple small signal model is important for IPT systems to evaluate the control performance. In the past years, the extended describing function (EDF) is powerful to address the modeling issue for resonant converter. However, the high-order resonant tank of IPT would lead to a complicated model if EDF is directly applied. In order to simplify the model, this paper explores a circuit-based method to reduce the order for both series and parallel resonant circuits. An example LCC-C compensated system is used to explain the concept. This general simplification can be extended for any other high-order IPT systems.
Proceedings Article•
22 Jul 2009TL;DR: In this paper, the authors present some results and simulations about the limit cycle prediction in nonlinear systems with relay type nonlinearities using multiple-input describing functions, together with derivations of three-sinusoid inputs for the ideal relay nonlinearity.
Abstract: In this paper we present some results and simulations about the limit cycle prediction in nonlinear systems with relay type nonlinearities using Multiple-input describing functions. The introduction of Describing Functions (DFs) theory is given, together with the derivations of three-sinusoid-input describing functions for the ideal relay nonlinearity. Then the application of this approach for analysis of the limit cycles in second order nonlinear systems with ideal relay type nonlinearity is shown. The applicability of the approach is demonstrated by example.