An introduction to algebraic discrete-time linear parametric identification with a concrete application

Fliess, Michel; Fuchshumer, Stefan; Schöberl, Markus; Schlacher, Kurt; Sira‐Ramírez, Hebertt

doi:10.3166/jesa.42.211-232

Cited by 8 publications

(5 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…It is thus not possible to use such techniques, since they are, and must include, regularization developments, such as wave number filtering [8], modal truncation [19], regularization techniques [10] which require the adjustment of regularization parameters. To estimate derivatives, some approaches present a natural regularizing aspect using an integral formulation for boundary characterization [20][21] [22][23], using polynomial approximation for damage detection [24], via operational calculus allowing algebraic derivative [23][25] [26] or based on a least square approximation [27] [28]. This kind of differentiation by integration methods allows an accurate and robust estimation of the derivative.…”

Section: Introductionmentioning

confidence: 99%

Indirect boundary force measurements in beam-like structures using a derivative estimator

Chesné

2014

Journal of Sound and Vibration

View full text Add to dashboard Cite

International audienceThis paper proposes a new method for the identification of boundary forces (shear force or bending moment) in a beam, based on displacement measurements. The problem is considered in terms of the determination of the boundary spatial derivatives of transverse displacements. By assuming the displacement fields to be approximated by Taylor expansions in a domain close to the boundaries, the spatial derivatives can be estimated using specific point-wise derivative estimators. This approach makes it possible to extract the derivatives using a weighted spatial integration of the displacement field. Following the theoretical description, numerical simulations made with exact and noisy data are used to determine the relationship between the size of the integration domain and the wavelength of the vibrations. The simulations also highlight the self-regularization of the technique. Experimental measurements demonstrate the feasibility and accuracy of the proposed method

show abstract

Section: Introductionmentioning

confidence: 99%

Indirect boundary force measurements in beam-like structures using a derivative estimator

Chesné

2014

Journal of Sound and Vibration

View full text Add to dashboard Cite

show abstract

“…Then, the WMR can be represented as a switching system. Afterwards, considering that the position and the orientation of the robot, (x, y, θ), and the input torques are measured, an identification scheme for the tire/road contact condition is built using algebraic numerical differentiation, which is a convenient method to estimate the time derivatives of some noisy measurements [1], [9], [10], [14], [17]. In practice, some of the parameters in the WMR model may vary because of exogenous and unknown effects, such as loading or unloading of the mobile robot, irregularity of the road surface, coefficients of the tire materials etc.…”

Section: Introductionmentioning

confidence: 99%

Tire/Road Contact Condition Identification Using Algebraic Numerical Differentiation

Barbot

Floquet

2009

IFAC Proceedings Volumes

View full text Add to dashboard Cite

In this paper, a realistic simulation model for Wheeled Mobile Robot (WMR) is given by a dynamical system that switches between three models corresponding to three different tire/road contact conditions: ideal condition, skidding condition and slipping condition. Then, an algebraic based numerical identification for the discrete state (tire/road contact condition) of this switching system is proposed. Finally, specific estimators for the uncertain parameters encountered in the identification scheme are given.

show abstract

“…Proposition 4.1 System (10) is quadratically equivalent to (11), modulo an output injection if and only if there exists (Φ [2] ,β [2] ,α [1] (y),τ [0] and Φ [2] n , β [2] n , α…”

Section: Observability Normal Formmentioning

confidence: 99%

“…Since the last decade the concept of normal form in control theory was introduced by W. Kang and A. Krener in [21] and [22], (see also [11] for an algebraic point of view). On this basis the appearance of bifurcations under lost of controllability was studied [2,15,17,20,23,39].…”

Section: Introductionmentioning

confidence: 99%

Discrete-time Normal Form for Left Invertibility Problem

Djemaï

Barbot

Belmouhoub

2009

European Journal of Control

View full text Add to dashboard Cite

This paper deals with the design of quadratic and higher order normal forms for the left invertibility problem. The linearly observable case and one-dimensional linearly unobservable case are investigated. The interest of such a study in the design of a delayed discrete-time observer is examined. The example of the Burgers map with unknown input is treated and a delayed discrete-time observer is designed. Finally, some simulated results are commented.

show abstract

An introduction to algebraic discrete-time linear parametric identification with a concrete application

Cited by 8 publications

References 8 publications

Indirect boundary force measurements in beam-like structures using a derivative estimator

Indirect boundary force measurements in beam-like structures using a derivative estimator

Tire/Road Contact Condition Identification Using Algebraic Numerical Differentiation

Discrete-time Normal Form for Left Invertibility Problem

Contact Info

Product

Resources

About