Describing function

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

Consensus of second order multi-agents with actuator saturation and asynchronous time-delays

Abstract: This article presents the consensus of a saturated second order multi-agent system with non-switching dynamics that can be represented by a directed graph. The system is affected by data processing (input delay) and communication time-delays that are assumed to be asynchronous. The agents have saturation nonlinearities, each of them is approximated into separate linear and nonlinear elements. Nonlinear elements are represented by describing functions. Describing functions and stability of linear elements are used to estimate the existence of limit cycles in the system with multiple control laws. Stability analysis of the linear element is performed using Lyapunov-Krasovskii functions and frequency domain analysis. A comparison of pros and cons of both the analyses with respect to time-delay ranges, applicability and computation complexity is presented. Simulation and corresponding hardware implementation results are demonstrated to support theoretical results.

Analysis of oscillations in systems with polynomial-type nonlinearities using describing functions

Abstract: Sufficient conditions for the existence of oscillations are obtained in the case of an autonomous single-loop feedback system when the nonlinear elements belong to a class of polynomials. Both a graphical procedure and an algebraic technique are presented for use with describing function analysis, and a graphical procedure is given for use with multiple input describing functions. Graphing is done in a parameter space of the solution, rather than in the complex plane.

Describing functions in non-linear systems with structured and unstructured uncertainties

Abstract: The describing function (DF) method offers a useful a way to analyse the stability of control systems with separable nonlinearities and recently it has been applied to systems with either parametric or norm-bounded perturbations. Here, DFs are employed in an even more general setting, i.e. both types of uncertainty are allowed to enter the system. Furthermore, the high frequency dynamics neglected by the DF technique are also incorporated into the system description. Exploiting some well known results from the robust control literature, computationally tractable stability criteria are derived. Two numerical examples are provided to illustrate the various aspects of these new tools which are, of course, subject to the usual errors and the restrictions of the DF method.

Multiple-input describing function technique applied to design a single channel ON-OFF controller for a spinning flight vehicle:

Abstract: In this study, the guidance and control problem of a single-channel spinning missile is investigated. The missile utilizes a single ON-OFF actuator to drive a pair of control surfaces (e.g. elevato...

Nonlinear Stability Analysis for Three-Phase Grid-Connected PV Generators

Abstract: Numerous emerging oscillatory stability issues have recently arisen as renewable energy sources (RESs) are integrated into the power system. Some of the existing literature attempts to explain these issues through the corresponding simplification, which usually omits the influence of the nonlinear discontinuous elements in the system. Hence, the obtained results are incomplete. To fill this gap, this article proposes a stability analysis method based on the describing function (DF) method to explore the influence of nonlinear discontinuous elements in the system. Without loss of generality, taking the three-phase grid-connected photovoltaic (PV) generator as the research object, the perturbation and observation (P&O)-based power control, which is a typical nonlinear discontinuous element, was carefully studied. First, the complete mathematical model of the three-phase grid-connected PV generator was established, including the outermost P&O-based power control. Then, according to the DF method, the stability of the PV generator was analyzed, and the related influence factors were studied in detail. It was found that the nonlinear discontinuous P&O-based power control has a substantial influence on the stability of the PV generator and can result in the oscillation. At the same time, the DF method and the conventional method were compared, which shows that the proposed DF method can enhance the accuracy of the stability assessment. Especially regarding critical stability, the oscillation magnitude and frequency can be calculated accurately. All the theoretical analyses were verified by the real-time hardware-in-loop (HIL) tests.