9,046 research outputs found
Dynamics of aerospace vehicles
The focus of this research was to address the modeling, including model reduction, of flexible aerospace vehicles, with special emphasis on models used in dynamic analysis and/or guidance and control system design. In the modeling, it is critical that the key aspects of the system being modeled be captured in the model. In this work, therefore, aspects of the vehicle dynamics critical to control design were important. In this regard, fundamental contributions were made in the areas of stability robustness analysis techniques, model reduction techniques, and literal approximations for key dynamic characteristics of flexible vehicles. All these areas are related. In the development of a model, approximations are always involved, so control systems designed using these models must be robust against uncertainties in these models
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
Modeling of Transitional Channel Flow Using Balanced Proper Orthogonal Decomposition
We study reduced-order models of three-dimensional perturbations in
linearized channel flow using balanced proper orthogonal decomposition (BPOD).
The models are obtained from three-dimensional simulations in physical space as
opposed to the traditional single-wavenumber approach, and are therefore better
able to capture the effects of localized disturbances or localized actuators.
In order to assess the performance of the models, we consider the impulse
response and frequency response, and variation of the Reynolds number as a
model parameter. We show that the BPOD procedure yields models that capture the
transient growth well at a low order, whereas standard POD does not capture the
growth unless a considerably larger number of modes is included, and even then
can be inaccurate. In the case of a localized actuator, we show that POD modes
which are not energetically significant can be very important for capturing the
energy growth. In addition, a comparison of the subspaces resulting from the
two methods suggests that the use of a non-orthogonal projection with adjoint
modes is most likely the main reason for the superior performance of BPOD. We
also demonstrate that for single-wavenumber perturbations, low-order BPOD
models reproduce the dominant eigenvalues of the full system better than POD
models of the same order. These features indicate that the simple, yet accurate
BPOD models are a good candidate for developing model-based controllers for
channel flow.Comment: 35 pages, 20 figure
Passivity-preserving parameterized model order reduction using singular values and matrix interpolation
We present a parameterized model order reduction method based on singular values and matrix interpolation. First, a fast technique using grammians is utilized to estimate the reduced order, and then common projection matrices are used to build parameterized reduced order models (ROMs). The design space is divided into cells, and a Krylov subspace is computed for each cell vertex model. The truncation of the singular values of the merged Krylov subspaces from the models located at the vertices of each cell yields a common projection matrix per design space cell. Finally, the reduced system matrices are interpolated using positive interpolation schemes to obtain a guaranteed passive parameterized ROM. Pertinent numerical results validate the proposed technique
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