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 study considered Euler-Lagrange systems, with emphasis in underactuated systems, and proposed a two fuzzy inference system, which is based on fuzzy logic theory, in order to generate a periodic output.
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TL;DR: A new numerical method, based on an iterative technique using describing functions, has been developed for calculating and plotting jump resonance curves for single-input single-output and multi-input multi-output feedback systems.
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28 Sep 2020TL;DR: A novel approach for modelling RC is considered, which uses state-dependent impulse inputs and is shown to permit an accurate computation of closed-loop RC behaviour starting from an open-loop model, thus linking both aspects, enhancing system understanding.
Abstract: The ever-increasing industry desire for improved performance makes linear controller design run into its fundamental limitations. A nonlinear controller, such as Reset Control (RC), is needed to overcome these. RC is promising since, unlike other nonlinear methods, it easily integrates into the PID design framework preferred by industry. Thus far, closed-loop behaviour of RC has been analysed in the frequency domain either through Describing Function analysis or by direct closed-loop numerical computation. The former method computes a simplified closed-loop RC response by ignoring all harmonics, an approach which literature has found to inflict significant modelling errors. The latter method gives an accurate solution but does not provide understanding of how open-loop RC design affects closed-loop performance. No methods link these aspects, which impairs RC design and tuning. The main contribution of this work is aimed at providing this link, while achieving an accurate closed-loop RC model. A novel approach for modelling RC is considered, which uses state-dependent impulse inputs. This approach is shown to permit an accurate computation of closed-loop RC behaviour starting from an open-loop model, thus linking both aspects, enhancing system understanding. A frequency-domain description for closed-loop RC is obtained, as needed for the PID design framework, which is solved for analytically by inserting several well-defined assumptions. This solution is verified using a simulated high-precision stage, critically examining sources of modelling errors. The accuracy of the proposed method is further substantiated using controllers designed for various specifications.
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TL;DR: A method of incorporating these stability conditions into the many optimization procedures which use the gradients of stability constraints is shown, and an example of its use in the design of a compensator in a nonlinear control system is also presented.
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