Identification of nonlinear dynamic models of electrostatically actuated MEMS

Casenave, Céline; Montseny, Emmanuel; Camon, Henri

doi:10.1016/j.conengprac.2010.04.002

Cited by 5 publications

(2 citation statements)

References 23 publications

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“…Note that, as the linear operator

ϕ_{x_{m}, A_{m}}^{ϵ}

depends on the noise, some of the classical estimators (as the least squares one mentioned previously) can be biased . Some bias reduction methods can be used to mitigate this problem.Remark This identification method can easily be extended, up to simple technical adaptation, to the case where function g is different from one trajectory to the other, that is

g \circ x : = {((), g^{i} \circ x^{i})}_{i = 1 : I}

. In such cases, the cancellation of the function g is only possible for j = i ; thus, only the sets

{normalΩ}_{x, ϵ}^{i, i}

will be used, which implies that the difference operator D x , ϵ will be given by

{((), D_{x, ϵ}^{i, i})}_{i = 1 : I}

.…”

Section: Description Of the Identification Methodsmentioning

confidence: 99%

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System identification by operatorial cancellation of nonlinear terms and application to a class of Volterra models

Casenave¹,

Montseny

2016

Intl J Robust & Nonlinear

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Summary In this paper, a method is proposed for the identification of some SISO nonlinear models with two ill‐known components of different nature: a linear (possibly dynamic) part and a static nonlinear one. This method is well adapted when no a priori information is available about the nonlinear component to be identified. It is based on a difference operator, which enables to cancel the nonlinear term when applied to the model. Only the ill‐known linear part remains in the transformed model; it can therefore be identified independently of the nonlinear term. Based on the identified linear component, we have access to a pseudograph of the nonlinear term, whose shape can give precious information for the parameterization of the unknown nonlinear part and its identification. The identification model under consideration is defined in an abstract framework, with very weak hypotheses, so that the proposed approach has a large scope. To highlight the method, a class of dynamic Volterra models including some hybrid models such as dynamic inclusions is considered for application. Copyright © 2016 John Wiley & Sons, Ltd.

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“…Note that, as the linear operator

ϕ_{x_{m}, A_{m}}^{ϵ}

g \circ x : = {((), g^{i} \circ x^{i})}_{i = 1 : I}

. In such cases, the cancellation of the function g is only possible for j = i ; thus, only the sets

{normalΩ}_{x, ϵ}^{i, i}

will be used, which implies that the difference operator D x , ϵ will be given by

{((), D_{x, ϵ}^{i, i})}_{i = 1 : I}

.…”

Section: Description Of the Identification Methodsmentioning

confidence: 99%

“…Note that, as the linear operator " x m ;A m depends on the noise, some of the classical estimators (as the least squares one mentioned previously) can be biased [1]. Some bias reduction methods [35][36][37] can be used to mitigate this problem.…”

Section: Remark 32mentioning

confidence: 99%

System identification by operatorial cancellation of nonlinear terms and application to a class of Volterra models

Casenave¹,

Montseny

2016

Intl J Robust & Nonlinear

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Adaptive control and signal processing literature survey (No. 21)

2010

Adaptive Control & Signal

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In order to keep readers up-to-date, the journal will contain a list of recently published journal articles relevant to the fields of adaptive control and signal processing six times a year. This list is compiled from a wide range of journals. Please note that even though the list has been broadly categorized these classifications are by no means strict, and are there to assist the reader. Please also note that inclusion in the list is not an endorsement of a paper's quality. If you have any suggestions or comments, please e-mail Erfu Yang at erfu.yang@eee.strath.ac.uk. 1. ADAPTIVE SYSTEMS Adetola V, Guay M. Performance improvement in adaptive control of linearly parameterized nonlinear systems. IEEE Transactions on Automatic Control 2010; 55(9):2182-2186. Bartoszewicz A, Nowacka-Leverton A. ITAE optimal sliding modes for third-order systems with input signal and state constraints. IEEE Transactions on Automatic Control 2010; 55(8):1928-1932. Bresch-Pietri D, Krstic M. Delay-adaptive predictor feedback for systems with unknown long actuator delay. IEEE Transactions on Automatic Control 2010; 55(9):2106-2112. Chen W, Jiao L, Li R, Li J. Adaptive backstepping fuzzy control for nonlinearly parameterized systems with periodic disturbances. IEEE Transactions on Fuzzy Systems 2010; 18(4):674-685. Cheng C-C, Chien S-H, Shih F-C. Design of robust adaptive variable structure tracking controllers with application to rigid robot manipulators. Immersion and invariance adaptive control of nonlinearly parameterized nonlinear systems. IEEE Transactions on Automatic Control 2010; 55(9):2209-2214. Miller D, Mansouri N. Model reference adaptive control using simultaneous probing, estimation, and control. IEEE Transactions on Automatic Control 2010; 55(9):2014-2029. Mizumoto I, Ohdaira S, Iwai Z. Output feedback strict passivity of discrete-time nonlinear systems and adaptive control system design with a PFC. Automatica 2010; 46(9):1503-1509. Moreno-Valenzuela J, Santibáñez V, Orozco-Manrııquez E, González-Hernández L. Theory and experiments of global adaptive output feedback tracking control of manipulators. IET Control Theory and Applications 2010; 4(9):1639-1654. Plestan F, Shtessel Y, Brégeault V, Poznyak A. New methodologies for adaptive sliding mode control. International Journal of Control 2010; 83(9):1907-1919.Reinhartz-Berger I, Soffer P, Sturm A. Extending the adaptability of reference models.

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