A Numerical Example of Alternator Model Reduction to Be Given in a Classroom

1988 ◽  
Vol 25 (4) ◽  
pp. 341-349
Author(s):  
Mohamed B. A. Kamoun ◽  
Michel Poloujadoff
Keyword(s):  
Transmission Line ◽  
Model Reduction ◽  
Stability Study ◽  
Computer Solution ◽  
Numerical Example

The authors give a numerical example of a stability study of an alternator connected to an infinite bus through a transmission line. Possible reductions of the model are carefully considered. This paper is intended to be the basis of exercises submitted to students for a computer solution.

A Unifying Theory of Least-Squares Padé Model Reduction Methods

1996 ◽  
Vol 210 (2) ◽  
pp. 95-102 ◽  
Author(s):  
I D Smith ◽  
T N Lucas
Keyword(s):  
Least Squares ◽  
Model Reduction ◽  
System Parameter ◽  
Reduced Model ◽  
Numerical Example ◽  
Parameter Matching ◽  
Reduction Methods ◽  
Error Index ◽  
Least Squares Approach

The apparently different approaches of least-squares parameter-matching Podé model reduction methods are shown to be related via a unifying theory. From the formulation it is possible to show several interesting features of the least-squares approach which lead to a fuller understanding of exactly how the reduced model approximates the system. An error index is derived for the general case and it is shown that a range of system parameter preservation options are available to the user. A numerical example illustrates the main points of the paper.

A Recursive Body-Body Formulation for Reducing the Computational Cost of Pairwise Coulomb Force Computation for Modeling and Simulation of Biopolymers, Using a Multibody Approach to Model Reduction

2013 ◽  
Author(s):  
Jeremy Laflin ◽  
Kurt Anderson
Keyword(s):  
Model Reduction ◽  
Charge Distribution ◽  
Computational Cost ◽  
Coulomb Force ◽  
Rigid Bodies ◽  
Inertia Tensor ◽  
Numerical Example ◽  
Pairwise Force ◽  
Body Formulation ◽  
Dynamics Simulations

This work presents a method for recursively assembling tensor-like quantities that parameterize the charge distribution of rigid bodies, which result from model reduction of biopolymeric systems using an articulated multibody approach. This is done with the goal of reducing the computational cost associated with the pairwise force determination encountered in molecular dynamics simulations. To achieve a linear computational cost complexity of the force determination, with respect to the number of bodies in the system (N), a recursive assembly and disassembly (evaluation) sweep is proposed. This work proposes assembling these tensor quantities (pseudo-inertia tensors), which are associated with the body’s charge distribution, with a method that uses the standard parallel axis theorem to shift these tensors to a common point so they may be summed. This work presents a preliminary numerical example that examines the accuracy of the force and moment computation using a pseudo-inertia tensor resulting after one level of recursive assembly. The Coulomb force and associated moment on a target body due to the assembled body is computed. The test problem approximates a system that is highly negatively or positively charged. The orientation of the bodies that are assembled is varied, along with the distance between the assembly and the target body. The preliminary results presented herein suggest that this is a viable method of efficiently representing the charge distribution of an assembly. The numerical example presented determines the Coulomb force and the associated moment, as a function of distance and the pseudo-inertia tensor. However, the approximation can be used for any force that is of the form 1/rs, where s is any power.

scholarly journals Modified Empirical Eigenfunctions and Its Applications for Model Reduction of Nonlinear Spatiotemporal Systems

2018 ◽  
Vol 2018 ◽  
pp. 1-12
Author(s):  
Mian Jiang ◽  
Shuangqi Liu ◽  
Jigang Wu
Keyword(s):  
Model Reduction ◽  
Temporal Dynamics ◽  
Control Design ◽  
Coefficient Matrix ◽  
Accurate Description ◽  
Reduced Model ◽  
Engineering Applications ◽  
Linear Combinations ◽  
Higher Modes ◽  
Numerical Example

Model reduction can greatly reduce complexity and difficulty of control design for spatiotemporal systems (STS) in engineering applications. Empirical eigenfunctions (EEFs) are widely used for the model reduction of spatiotemporal systems, however, truncation of higher modes may describe the behaviours of nonlinear spatiotemporal systems inaccurately. In this paper, modified EEFs are proposed and applied to model reduction of nonlinear spatiotemporal systems. Modified EEFs are obtained via modifying the weights matrix in the method of snapshots, which can be rewritten as linear combinations of initial EEFs. The coefficient matrix for combinations is computed according to the nonlinear temporal dynamics of STSs. Thus, the effects of higher modes are considered into modified EEFs with less computational requirements. The reduced model can give a more accurate description for behaviours of the system. The performance of the proposed method is further proved theoretically, and a numerical example demonstrates the effectiveness of the proposed method.

Suboptimal Model Reduction by Multi-Point Padé Approximation

1994 ◽  
Vol 208 (2) ◽  
pp. 131-134 ◽  
Author(s):  
T N Lucas
Keyword(s):  
Transfer Function ◽  
Model Reduction ◽  
Approximation Method ◽  
Padé Approximation ◽  
Order Reduction ◽  
Pade Approximation ◽  
Reduced Order ◽  
Numerical Example ◽  
Integral Square Error ◽  
Reduction Methods

A novel Padé approximation method is used to obtain a reduced-order transfer function, with a predetermined denominator, such that the integral square error between the time responses of the full and reduced models is minimized. The method is seen to be easy to apply compared with existing suboptimal order reduction methods. A numerical example is given to illustrate its application.

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