Computation of non-linear transfer functions when constant terms are present

Billings, S.A.; Zhang, H.

doi:10.1006/mssp.1995.0041

Cited by 6 publications

(5 citation statements)

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“…When system ( 1) is stable at a nonzero equilibrium, the output response about the equilibrium can be represented by the corresponding Volterra series as [26]…”

Section: Nonlinear Systems With Non-zero Equilibriamentioning

confidence: 99%

“…Some researchers have considered the nonlinear model standardization for the analysis of specific nonlinear systems [22][23][24][25][26]. For example, the work in [25] and [26] studied the frequency domain analysis of nonlinear systems having nonzero direct current (DC) components. A recursive algorithm was used to determine a Volterra series representation associated with each equilibrium affected by the DC component.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…In the derivation of the new nonlinear model standardization approach, the NARX/NDE models with a DC terms [24][25][26] are considered to take a large class of nonlinear systems into account. The DC term in the model representation is not necessarily to be nonzero, which is a key difference compared to the studies in [25,26]. The new approach is then applied in three case studies which are concerned with the analysis of gravity effects on the detection of cracks in beams, the design of an Auxetic foam structure, and the compensation of nonlinear distortions in engineering systems, respectively.…”

Section: Introductionmentioning

confidence: 99%

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Nonlinear model standardization for the analysis and design of nonlinear systems with multiple equilibria

2021

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In engineering practice, a nonlinear system stable about several equilibria is often studied by linearizing the system over a small range of operation around each of these equilibria, and allowing the study of the system using linear system methods. Theoretically, for operations beyond a small range but still within the stable regime of an equilibrium, the system behaves nonlinearly, and can be described and investigated using the Volterra series approach. However, there is still no available approach that can systematically transform the model of a nonlinear system into a form that can be studied over the whole stable regime about an equilibrium so as to facilitate the system study using the Volterra series approach. This transformation is, in the present study, referred to as nonlinear model standardization, which is the extension of the well-known concept of linearization to the nonlinear case. In this paper, a novel approach to nonlinear model standardization is proposed for nonlinear systems that can be described by a Nonlinear AutoRegressive model with eXogeneous input (NARX) or a nonlinear differential equation (NDE) model. The proposed approach is then used in three case studies covering the applications in nonlinear system analysis, nonlinear system design, and nonlinearity compensation, respectively, demonstrating the significance of the proposed nonlinear model standardization in a wide range of engineering practices.

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“…When system ( 1) is stable at a nonzero equilibrium, the output response about the equilibrium can be represented by the corresponding Volterra series as [26]…”

Section: Nonlinear Systems With Non-zero Equilibriamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Nonlinear model standardization for the analysis and design of nonlinear systems with multiple equilibria

2021

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“…Note the inclusion of the 0th order term y(0). This term is often assumed to be zero in order to simplify the analysis, however, for a system that has non-zero steady state for zero input this assumption is not justified and must be included [37]. The n-th order GFRF, H n (jω 1 , .…”

Section: Frequency-domain Analysismentioning

confidence: 99%

Control-focused, nonlinear and time-varying modelling of dielectric elastomer actuators with frequency response analysis

Jacobs

Wilson

Assaf

et al. 2015

Smart Mater. Struct.

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ReuseUnless indicated otherwise, fulltext items are protected by copyright with all rights reserved. The copyright exception in section 29 of the Copyright, Designs and Patents Act 1988 allows the making of a single copy solely for the purpose of non-commercial research or private study within the limits of fair dealing. The publisher or other rights-holder may allow further reproduction and re-use of this version -refer to the White Rose Research Online record for this item. Where records identify the publisher as the copyright holder, users can verify any specific terms of use on the publisher's website. TakedownIf you consider content in White Rose Research Online to be in breach of UK law, please notify us by emailing eprints@whiterose.ac.uk including the URL of the record and the reason for the withdrawal request. Control September 2014Abstract. Current models of dielectric elastomer actuators (DEAs) are mostly constrained to first principal descriptions that are not well suited to the application of control design due to their computational complexity. In this work we describe an integrated framework for the identification of control focused, data driven and time-varying DEA models that allow advanced analysis of nonlinear system dynamics in the frequency-domain. Experimentally generated input-output data (voltagedisplacement) was used to identify control-focused, nonlinear and time-varying dynamic models of a set of film-type DEAs. The model description used was the nonlinear autoregressive with exogenous input (NARX) structure. Frequency response analysis of the DEA dynamics was performed using generalised frequency response functions (GFRFs), providing insight and a comparison into the time-varying dynamics across a set of DEA actuators. The results demonstrated that models identified within the presented framework provide a compact and accurate description of the system dynamics. The frequency response analysis revealed variation in the time-varying dynamic behaviour of DEAs fabricated to the same specifications. These results suggest that the modelling and analysis framework presented here is a potentially useful tool for future work in guiding DEA actuator design and fabrication for application domains such as soft robotics.

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A frequency-domain approach to improve ANNs generalization quality via proper initialization

et al. 2018

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Computation of non-linear transfer functions when constant terms are present

Cited by 6 publications

References 0 publications

Nonlinear model standardization for the analysis and design of nonlinear systems with multiple equilibria

Nonlinear model standardization for the analysis and design of nonlinear systems with multiple equilibria

Control-focused, nonlinear and time-varying modelling of dielectric elastomer actuators with frequency response analysis

A frequency-domain approach to improve ANNs generalization quality via proper initialization

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