New Gramians for Switched Linear Systems: Reachability, Observability, and Model Reduction

Duff, Igor Pontes; Grundel, Sara; Benner, Peter

doi:10.1109/tac.2019.2934020

Cited by 8 publications

(2 citation statements)

References 36 publications

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“…With P 0 = P σ k−1 (s − k ), P 1 = P k (t), and F 1 = e A k (t−s k ) J k , this identity equals exactly the desired relationship (9).…”

Section: A Reachability Gramianmentioning

confidence: 81%

“…Generalized Gramians-based approaches are proposed, e.g., in [4], [5], [6], [7], [8], and [9]; these approaches are considered only for quadratically stable systems, and the Gramians are then the solutions of certain linear matrix inequalities. Furthermore, an improvement of the underlying approaches was reviewed in [10], [11], [12], [13], [14], and [15] by introducing new Gramians and their system theoretical properties; again, certain stability assumptions are made.…”

Section: Introductionmentioning

confidence: 99%

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Midpoint-Based Balanced Truncation for Switched Linear Systems With Known Switching Signal

Hossain

Trenn

2024

IEEE Trans. Automat. Contr.

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“…With P 0 = P σ k−1 (s − k ), P 1 = P k (t), and F 1 = e A k (t−s k ) J k , this identity equals exactly the desired relationship (9).…”

Section: A Reachability Gramianmentioning

confidence: 81%

Section: Introductionmentioning

confidence: 99%

Midpoint-Based Balanced Truncation for Switched Linear Systems With Known Switching Signal

Hossain

Trenn

2024

IEEE Trans. Automat. Contr.

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Model order reduction via substructuring for a nonlinear, differential‐algebraic machine tool model with moving loads

Aumann

Benner

Saak

et al. 2023

Proc Appl Math and Mech

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Machine tools are permanently exposed to complex static, dynamic and thermic loads. This often results in an undesired displacement of the tool center point (TCP), causing errors in the production process and thus limiting the achievable workpiece quality. Recent research efforts try to counter these effects by process-parallel solutions utilizing machine internal data. Therefore, fast simulation models are a fundamental requirement. Here, model order reduction (MOR) becomes crucial. The resulting low-dimensional models are required for various applications, e.g., in digital twins, the correction of thermally induced errors at the TCP during the production process as well as for lifetime calculations in predictive maintenance. In this contribution, we present a strategy of MOR for a coupled thermo-mechanical model with a nonlinear subsystem and moving loads, using the example of a feed axis with nonlinear machine components. Applying tailored substructuring techniques, we are able to separate the linear and nonlinear system components. This allows to apply classic linear MOR methods to the much larger linear part, whereas the small nonlinear part is kept, and thus enables drastically reduced computing times. The relative movement is considered by a switched system approach. Transient thermo-mechanical interactions of the feed axis are calculated in a final investigation, comparing the performance of the resulting reduced-order model and the original one.

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Model Order Reduction of Switched Linear Systems with Constrained Switching

Gosea

Duff

Benner

et al. 2019

IUTAM Symposium on Model Order Reduction of Coupled Systems, Stuttgart, Germany, May 22–25, 2018

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New Gramians for Switched Linear Systems: Reachability, Observability, and Model Reduction

Cited by 8 publications

References 36 publications

Midpoint-Based Balanced Truncation for Switched Linear Systems With Known Switching Signal

Midpoint-Based Balanced Truncation for Switched Linear Systems With Known Switching Signal

Model order reduction via substructuring for a nonlinear, differential‐algebraic machine tool model with moving loads

Model Order Reduction of Switched Linear Systems with Constrained Switching

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