Motion planning for a damped euler-bernoulli beam

Meurer, Thomas; Schröck, Johannes; Kugi, Andreas

doi:10.1109/cdc.2010.5717186

Cited by 10 publications

(9 citation statements)

References 17 publications

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“…Analog zu den Ausfü hrungen in Meurer et al (2010) fü r das Beispiel eines Euler-Bernoulli-Balkens und in Meurer (2011) fü r ein DiffusionReaktionssystem mit mehrdimensionalem ö rtlichen Definitionsgebiet stü tzt sich die Konvergenzanalyse fü r wðtÞ und u k ðtÞ und k ¼ 1; . .…”

Section: Konvergenzanalyseunclassified

“…Da (14b) ä quivalent zu u k ðtÞ ¼ P l2N c u l q l t j k ðtÞ ist, kann die gleichmä ßige Konvergenz direkt ü ber die ermittelten Schranken fü r c u l , der Gevrey-Bedingung fü r j k ðtÞ und dem Konvergenzsatz von Cauchy-Hadamard nachgewiesen werden. Wie in Meurer et al (2010); Meurer (2011) gezeigt wurde, kann eine ä hnliche Argumentationskette dazu genutzt werden, die Konvergenz von 0 D w n ðq t Þ j k ðtÞ fü r alle n 2 N nachzuweisen. Die Konvergenz der parametrierten Fourier-Reihe (16a) kann zudem abgeleitet werden, falls P n2N P r a n j¼1 j P Np k¼1 ð 0 D w n ðq t Þ j k Þ hb k ; c nj i H =l n j 2 G¥.…”

Section: Konvergenzanalyseunclassified

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Trajektorienplanung für eine piezo-aktuierte elastische Kirchhoff-Platte

Meurer

Schröck

Kugi

2012

Elektrotech. Inftech.

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Die Trajektorienplanungsaufgabe fü r verteilt-parametrische Systeme wird anhand des Beispiels einer einseitig eingespannten orthotropen Kirchhoff-Platte mit ö rtlich verteilten Patch-Aktoren analysiert. Hierzu wird auf Basis der spektralen Darstellung der Bewegungsgleichung ein systematischer Ansatz zur flachheitsbasierten Parametrierung des Auslenkungsprofils und der Stellgrö ßen vorgestellt. Dies ermö glicht einen intuitiven Zugang zur Trajektorienplanung und zur Realisierung hochdynamischer Ü bergä nge zwischen stationä ren Auslenkungsprofilen. Die Verwendung gewichteter Residuenverfahren ermö glicht zudem eine effiziente Computer-gestü tzte Umsetzung des Entwurfsverfahrens. Simulationsergebnisse bestä tigen die Anwendbarkeit der entwickelten Methodik und illustrieren das erzielbare Folgeverhalten. Schlü sselwö rter: verteilt-parametrisches System; Trajektorienplanung; Kirchhoff-Platte; differenzielle Flachheit; Steuerungsentwurf; gewichtete Residuenverfahren; adaptive Flü gelstruktur Motion planning for a piezo-actuated elastic Kirchhoff plate.The motion planning problem is considered for a cantilevered orthotropic Kirchhoff plate with spatially varying coefficients and distributed piezoelectric patch actuators. For this, the spectral representation of the corresponding equations of motion is utilized to systematically construct a flatness-based parametrization of state and inputs. These enable a very intuitive motion planning to realize prescribed high-speed rest-to-rest motions. Moreover, the incorporation of weighted residuals approaches yields a very efficient computational implementation. Simulation results confirm the applicability of the design approach and the achievable tracking performance.

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Section: Konvergenzanalyseunclassified

Trajektorienplanung für eine piezo-aktuierte elastische Kirchhoff-Platte

Meurer

Schröck

Kugi

2012

Elektrotech. Inftech.

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“…As a result z(t) constitutes a flat or basic output of (24)- (25) or (20), respectively. The determined parametrization can be utilized for the design of a feedforward tracking controller by prescribing a smooth desired trajectory t → z d (t) for the flat output z(t).…”

Section: Flatness-based Parametrizationmentioning

confidence: 99%

“…For the case of a viscously damped cantilevered Euler-Bernoulli beam convergence of the parametrizations (33)-(35) is investigated in [25]. However, these results are based on continuously differentiable parameter functions µ(x 1 ), Λ(x 1 ) ∈ C 4 (0, L) and γ i (x 1 ) ∈ C 1 (0, L).…”

Section: Simulation and Numerical Convergencementioning

confidence: 99%

Control of a flexible beam actuated by macro-fiber composite patches: I. Modeling and feedforward trajectory control

Schröck¹,

Meurer²,

Kugi³

2010

Smart Mater. Struct.

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This paper considers a systematic approach for motion planning and feedforward control design for a flexible cantilever actuated by piezoelectric macro-fiber composite (MFC) patches. For accurate feedforward tracking control, special attention has to be paid to the inherent nonlinear hysteresis and creep behavior of these actuators. In order to account for these effects an appropriate compensator is applied which allows to perform the tracking controller design on the basis of a linear infinitedimensional model. A detailed analysis of the nonlinear actuator behavior as well as the compensator design and the overall experimental validation is presented in the companion paper [1]. The governing equations of motion of the hysteresis and creep compensated cantilever are determined by means of the extended Hamilton's principle. This allows to consider the influence of the bonded patch actuators on the mechanical properties of the underlying beam structure in a straightforward manner and results in a model with spatially varying system parameters. For the solution of the motion planning and feedforward control problem a flatness-based methodology is proposed. In a first step, the infinite-dimensional system of the MFC-actuated flexible cantilever is approximated by a finite-dimensional model, where all system variables, i.e. the states, input, and output, can be parametrized in terms of a so-called flat output. In a second step, it is shown by numerical simulations that these parametrizations converge with increasing system order of the finite-dimensional model such that the feedforward control input can be directly calculated in order to realize prescribed output trajectories.

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“…A flatness-based feedforward tracking controller for a cantilevered flexible beam is designed in [6] based on the modal analysis of the distributed parameter system. In [7] a flatnessbased feedforward controller for a Euler-Bernoulli beam with viscous damping is developed using a systematic spectral approach based on the Riesz spectral properties of the system operator. This method is extended to a cantilevered flexible plate-like structure actuated by a finite number of surfacemounted piezoelectric patches to realize prescribed highly dynamic trajectories in [8].…”

Section: Introductionmentioning

confidence: 99%

Vibration control of a flexible single-link robot: A backstepping controller for distributed parameter systems

Muller

Liu

2014

IECON 2014 - 40th Annual Conference of the IEEE Industrial Electronics Society

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In this paper, a two-degree-of-freedom-control concept for a flexible single-link robot is considered offering trajectory tracking as well as vibration damping. The robota flexible link with tip mass attached to a moving cart -is modeled as distributed parameter system including structural damping. The proposed forward controller is designed based on the exact modal approximation of the system dynamics. Based on the infinite dimensional error dynamics formulated in strict feedback form, a backstepping controller is designed that guarantees passivity. Input Shaping is used for planning the desired trajectories. Measurement results at a laboratory experiment show the feasibility of this approach.

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Motion planning for a damped euler-bernoulli beam

Cited by 10 publications

References 17 publications

Trajektorienplanung für eine piezo-aktuierte elastische Kirchhoff-Platte

Trajektorienplanung für eine piezo-aktuierte elastische Kirchhoff-Platte

Control of a flexible beam actuated by macro-fiber composite patches: I. Modeling and feedforward trajectory control

Vibration control of a flexible single-link robot: A backstepping controller for distributed parameter systems

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