Gain-scheduled ${{\mathscr{H}}}_{\infty }$ buckling control of a circular beam-column subject to time-varying axial loads

Schaeffner, M; Platz, Roland

doi:10.1088/1361-665x/aab63a

Cited by 7 publications

(10 citation statements)

References 24 publications

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“…This section introduces the investigated beam-column system used for active buckling control in [14,15]. In the concept for active buckling control, a slender beam-column subjected to a compressive axial load F x is stabilized by two piezoelastic supports at both beam-column ends, as depicted in the schematic sketch in Fig.…”

Section: System Descriptionmentioning

confidence: 99%

“…As in many applications relying on model predictions, the performance of the active buckling control is primarily determined by the quality of the underlying mathematical model used for the model-based controller synthesis, as e.g. in [14,15]. In particular, the model of the beam-column system shown in Figs.…”

Section: Mathematical Model Of the Active Beam-columnmentioning

confidence: 99%

“…The mathematical FE model of the slender beam-column with piezo-elastic supports used for active buckling control in an experimental test setup is derived in detail in [14,15]. The resulting state space beam-column model in the Laplace domain according to [18] (2)…”

Section: Mathematical Model Of the Active Beam-columnmentioning

confidence: 99%

“…In this paper, the parameters of a beam-column system subjected to axial loading and prone to buckling, [14,15], are calibrated using two different approaches for non-deterministic parameter calibration, namely a forward parameter calibration approach [14] and a Bayesian inference parameter calibration approach [10,16]. The calibrated beam-column model is used to design an active buckling control, which is intended to increase the maximum bearable load of the beam-column [14,15]. The accuracy and credibility of the mathematical beam-column model is essential for the successful application of the active buckling control.…”

Section: Introductionmentioning

confidence: 99%

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Forward vs. Bayesian Inference Parameter Calibration: Two Approaches for Non-deterministic Parameter Calibration of a Beam-Column Model

Schaeffner

Gehb

Feldmann

et al. 2021

Lecture Notes in Mechanical Engineering

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Mathematical models are commonly used to predict the dynamic behavior of mechanical structures or to synthesize controllers for active systems. Calibrating the model parameters to experimental data is crucial to achieve reliable and adequate model predictions. However, the experimental dynamic behavior is uncertain due to variations in component properties, assembly and mounting. Therefore, uncertainty in the model parameters can be considered in a non-deterministic calibration. In this paper, we compare two approaches for a non-deterministic parameter calibration, which both consider uncertainty in the parameters of a beam-column model. The goal is to improve the model prediction of the axial load-dependent lateral dynamic behavior. The investigation is based on a beam-column system subjected to compressive axial loads used for active buckling control. A representative sample of 30 nominally identical beam-column systems characterizes the variations in the experimental lateral axial load-dependent dynamic behavior. First, in a forward parameter calibration approach, the parameters of the beam-column model are calibrated separately for all 30 investigated beam-column systems using a least squares optimization. The uncertainty in the parameters is obtained by assuming normal distributions of the separately calibrated parameters. Second, in a Bayesian inference parameter calibration approach, the parameters are calibrated using the complete sample of experimental data. Posterior distributions of the parameters characterize the uncertain dynamic behavior of the beam-column model. For both non-deterministic parameter calibration approaches, the predicted uncertainty ranges of the axial load-dependent lateral dynamic behavior are compared to the uncertain experimental behavior and the most accurate results are identified.

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Section: System Descriptionmentioning

confidence: 99%

Section: Mathematical Model Of the Active Beam-columnmentioning

confidence: 99%

Section: Mathematical Model Of the Active Beam-columnmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Forward vs. Bayesian Inference Parameter Calibration: Two Approaches for Non-deterministic Parameter Calibration of a Beam-Column Model

Schaeffner

Gehb

Feldmann

et al. 2021

Lecture Notes in Mechanical Engineering

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“…Equation 1 Alternative to passively increasing the maximum bearable compressive load of an individual bar, active buckling control may be used. Active buckling control provides a possibility to increase the maximum bearable load of slender bars by the integration of piezoelectric stack actuators in compact piezo-elastic supports at the bar ends, Fig.2(a), [11,12]. In this particular setup, the circular bar is made of aluminum alloy EN AW-7075 with a length of 400 mm, diameter of 8 mm and Young's modulus 71.0 kN/mm 2 .…”

mentioning

confidence: 99%

Optimal Placement of Active Bars for Buckling Control in Truss Structures under Bar Failures

Gally

Kuttich

Pfetsch³

et al. 2018

AMM

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Buckling of slender bars subject to axial compressive loads represents a critical design constraint for light-weight truss structures. Active buckling control by actuators provides a possibility to increase the maximum bearable axial load of individual bars and, thus, to stabilize the truss structure.For reasons of cost, it is in general not economically viable to use such actuators in each bar of the truss structure. Hence, it is an important practical question where to place these active bars. Optimized structures, especially when coupled with active elements to further decrease the number of necessary bars, however, lead to designs, which, while cost-efficient, are especially prone to bardamages, caused, e.g., by material failures. Therefore, this paper presents a mathematical optimization approach to optimally place active bars for buckling control in a way that secures both buckling and general stability constraints even after failure of any combination of a certain number of bars. This allows us to increase the resilience of the system and guarantee stable behavior even in case of failures.

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Adequate Mathematical Beam-Column Model for Active Buckling Control in a Tetrahedron Truss Structure

Schaeffner

Platz

Melz

2020

Model Validation and Uncertainty Quantification, Volume 3

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Gain-scheduled ${{\mathscr{H}}}_{\infty }$ buckling control of a circular beam-column subject to time-varying axial loads

Cited by 7 publications

References 24 publications

Forward vs. Bayesian Inference Parameter Calibration: Two Approaches for Non-deterministic Parameter Calibration of a Beam-Column Model

Forward vs. Bayesian Inference Parameter Calibration: Two Approaches for Non-deterministic Parameter Calibration of a Beam-Column Model

Optimal Placement of Active Bars for Buckling Control in Truss Structures under Bar Failures

Adequate Mathematical Beam-Column Model for Active Buckling Control in a Tetrahedron Truss Structure

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