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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TL;DR: This chapter considers discrete-time NCSs with communication constraints and actuator constraints, which have been extensively studied during the 1960s due to their intimate connection with optimal control.
Abstract: In Chaps. 2– 8, we have studied networked control for continuous-time plants. Chapters 9– 12 will present our analysis on networked control for discrete-time plants. In this chapter, we consider discrete-time NCSs with communication constraints and actuator constraints. Systems with actuator constraints were extensively studied during the 1960s due to their intimate connection with optimal control. Concurrently, the design approaches, such as the describing function method, which dealt specifically with nonlinearities such as saturation were developed. Only very limited research into actuator saturation was carried out during the 1970s and 1980s with the emphasis being placed mostly on the development of the linear state space approach and its numerous offshoots.
36 citations
TL;DR: The proposed technique significantly extends the results available in the literature and can be applied to almost all complex networks of oscillators, in particular two-dimensional, space variant and fully connected networks can be dealt with here.
Abstract: The global dynamics of weakly connected oscillatory networks is investigated: as a case study, one-dimensional arrays of third-order oscillators are considered. Through the joint application of the describing function technique and Malkin's Theorem a very accurate analytical expression of the phase deviation equation (i.e. the equation that describes the phase deviation due to the weak coupling) is derived. The total number of limit cycles and their stability properties are estimated via the analytical study of the phase deviation equation. The proposed technique significantly extends the results available in the literature and can be applied to almost all complex networks of oscillators. In particular two-dimensional, space variant and fully connected networks can be dealt with here.
36 citations
17 Oct 1999
TL;DR: The method is based on describing function analysis, and can predict the steady state motion of the system, analyze stability, and be used to determine robustness to system changes.
Abstract: Neural oscillators offer simple and robust solutions to problems such as locomotion and dynamic manipulation. However, the parameters of these systems are notoriously difficult to tune. This paper presents an analysis technique which alleviates the difficulty of tuning. The method is based on describing function analysis, and can predict the steady state motion of the system, analyze stability, and be used to determine robustness to system changes. The method is illustrated using a number of design examples including an implementation of juggling on a real robot.
36 citations
TL;DR: In this article, the authors describe and apply the arc-length method to solve a system of nonlinear equations obtaining as a result the nonlinear frequency response, where the fundamental harmonic component is considered the most relevant and for some cases can be considered an approximation to the effect of all harmonics.
36 citations
TL;DR: This article uses computer-aided design tools to develop a describing function analysis of a pendulum clock as a control system that allows the pendulum to provide the required time keeping and add enough energy to the pendula to overcome the damping caused by friction.
Abstract: This article uses computer-aided design tools to develop a describing function analysis of a pendulum clock. We design the escapement as a control system that allows the pendulum to provide the required time keeping and, at the same time, add enough energy to the pendulum to overcome the damping caused by friction. We use analysis tools in the MATLAB Control System Toolbox to accomplish the design and analysis. A by-product of our analysis is a simple MATLAB/Simulink model and a script that generates describing functions for any arbitrary nonlinear system (including systems with multiple nonlinearities and with frequency-dependent describing functions). We also develop a Simulink model of the clock to verify the results of the analysis. The analysis described here uses some object-oriented programming features of MATLAB.
36 citations