Balanced Truncation of Networked Linear Passive Systems

This paper studies model order reduction of multi-agent systems consisting of identical linear passive subsystems, where the interconnection topology is characterized by an undirected weighted graph. Balanced truncation based on a pair of specifically selected generalized Gramians is implemented on the asymptotically stable part of the full-order network model, which leads to a reduced-order system preserving the passivity of each subsystem. Moreover, it is proven that there exists a coordinate transformation to convert the resulting reduced-order model to a state-space model of Laplacian dynamics. Thus, the proposed method simultaneously reduces the complexity of the network structure and individual agent dynamics, and it preserves the passivity of the subsystems and the synchronization of the network. Moreover, it allows for the a priori computation of a bound on the approximation error. Finally, the feasibility of the method is demonstrated by an example

Model reduction for linear delay systems using a delay-independent balanced truncation approach

A model reduction approach for asymptotically stable linear delay-differential equations is presented in this paper. Specifically, a balancing approach is developed on the basis of energy functionals that provide (bounds on) a measure of energy related to observability and controllability, respectively. The reduced-order model derived in this way is again a delay-differential equation, such that the method is structure preserving. In addition, asymptotic stability is preserved and an a priori bound on the reduction error is derived, providing a measure of accuracy of the reduction. The results are illustrated by means of application on an example

Doped microporous hybrid silica membranes for gas separation

Hybrid silica (i.e., bis-triethoxysilylethane: BTESE) membranes doped with B, Ta or Nb were made through a sol–gel process. Triethyl borate, tantalum (V) ethoxide (TPE) and niobium (V) ethoxide (NPE) were selected as doping precursors. The doping concentration was optimized to produce sols, suitable for membrane fabrication. Thermal stability, structural analysis, cross-sectional micrographs and single gas permeation experiments were performed on these membranes, and results are compared with an undoped BTESE membrane. It was observed that the synthesized doped BTESE materials and membranes resulted into a more open (and, in one occurrence, SF6 permeable) pore microstructure, showing high permeances of larger gas molecules, while having a cross-sectional thickness comparable to undoped BTESE membrane

Mode Selection for Component Mode Synthesis with Guaranteed Assembly Accuracy

In this work, a modular approach is introduced to select the most important eigenmodes for each component of a composed structural dynamics system to obtain the required accuracy of the reduced-order assembly model. To enable the use of models of complex (structural) dynamical systems in engineering practice, e.g., in a design, optimization and/or control context, the complexity of the models needs to be reduced. When the model consist of an assembly of multiple interconnected structural components, component mode synthesis is often the preferred model reduction method. The standard approach to component mode synthesis for such system is to select the eigenmodes of a component that are most important to accurately model the dynamic behavior of this component in a certain frequency range of interest. However, often, a more relevant goal is to obtain, in this frequency range, an accurate model of the assembly. In the proposed approach, accuracy requirements on the level of the assembly are translated to accuracy requirements on component level, by employing techniques from the field of systems and control. With these component-level requirements, the eigenmodes that are most important to accurately model the dynamic behavior of the assembly can be selected in a modular fashion. We demonstrate with two structural dynamics benchmark systems that this method based on assembly accuracy allows for a computationally efficient selection of eigenmodes that 1) guarantees satisfaction of the assembly accuracy requirements and 2) results in most cases in reduced-order models of significantly lower order with respect to the industrial standard approach in which component eigenmodes are selected using a frequency criterion

Translating Assembly Accuracy Requirements to Cut-Off Frequencies for Component Mode Synthesis

One of the most popular methods for reducing the complexity of assemblies of finite element models in the field of structural dynamics is component mode synthesis. A main challenge of component mode synthesis is balancing model complexity and model accuracy, because it is difficult to predict how component reduction influences assembly model accuracy. This work introduces an approach that allows for the translation of assembly model accuracy requirements in the frequency domain to the automatic selection of the cut-off frequencies for the model-order reduction (MOR) of components. The approach is based on a mathematical approach for MOR for coupled linear systems in the field of systems and control. We show how this approach is also applicable to structural dynamics models. We demonstrate the use of this approach in the scope of component mode synthesis (CMS) methods with the aim to reduce the complexity of component models while guaranteeing accuracy requirements of the assembly model. The proposed approach is illustrated on a mechanical, three-component structural dynamics system for which reduced-order models are computed that are reduced further compared to reduction using standard methods. This results in lower simulation cost, while maintaining the required accuracy

Modular Redesign of Mechatronic Systems: Formulation of Module Specifications Guaranteeing System Dynamics Specifications

Complex mechatronic systems are typically composed of interconnected modules, often developed by independent teams. This development process challenges the verification of system specifications before all modules are integrated. To address this challenge, a modular redesign framework is proposed in this paper. Herein, first, allowed changes in the dynamics (represented by frequency response functions (FRFs)) of the redesigned system are defined with respect to the original system model, which already satisfies system specifications. Second, these allowed changes in the overall system dynamics (or system redesign specifications) are automatically translated to dynamics (FRF) specifications on module level that, when satisfied, guarantee overall system dynamics (FRF) specifications. This modularity in specification management supports local analysis and verification of module design changes, enabling design teams to work in parallel without the need to iteratively rebuild the system model to check fulfilment of system FRF specifications. A modular redesign process results that shortens time-to-market and decreases redesign costs. The framework's effectiveness is demonstrated through three examples of increasing complexity, highlighting its potential to enable modular mechatronic system (re)design