scholarly journals Discussion: “Model Reduction of Large-Scale Discrete Plants With Specified Frequency Domain Balanced Structure” (Zadegan, A., and Zilouchian, A., 2005, ASME J. Dyn. Syst. Meas., Control, 127, pp. 486–498)

2009 ◽  
Vol 131 (6) ◽  
Author(s):  
Hamid Reza Shaker ◽  
Rafael Wisniewski
Keyword(s):  
Model Reduction ◽  
Frequency Domain ◽  
Large Scale ◽  
Reduction Method ◽  
Order Reduction ◽  
Balanced Structure ◽  
Order Reduction Method

This work presents a commentary of the article published by A. Zadegan and A. Zilouchian (2005, ASME J. Dyn. Syst. Meas., Control, 127, pp. 486–498). We show their order reduction method is not always true and may lead to inaccurate results and is therefore erroneous. A framework for solving the problem is also suggested.

scholarly journals AN ITERATIVE MODEL ORDER REDUCTION METHOD FOR LARGE-SCALE DYNAMICAL SYSTEMS

2017 ◽  
Vol 59 (1) ◽  
pp. 115-133
Author(s):  
K. MOHAMED ◽  
A. MEHDI ◽  
M. ABDELKADER
Keyword(s):  
Dynamical Systems ◽  
Model Order Reduction ◽  
Large Scale ◽  
Reduction Method ◽  
Linear Time ◽  
Order Reduction ◽  
Lyapunov Equation ◽  
Model Order ◽  
Iterative Model ◽  
Order Reduction Method

We present a new iterative model order reduction method for large-scale linear time-invariant dynamical systems, based on a combined singular value decomposition–adaptive-order rational Arnoldi (SVD-AORA) approach. This method is an extension of the SVD-rational Krylov method. It is based on two-sided projections: the SVD side depends on the observability Gramian by the resolution of the Lyapunov equation, and the Krylov side is generated by the adaptive-order rational Arnoldi based on moment matching. The use of the SVD provides stability for the reduced system, and the use of the AORA method provides numerical efficiency and a relative lower computation complexity. The reduced model obtained is asymptotically stable and minimizes the error ($H_{2}$and$H_{\infty }$) between the original and the reduced system. Two examples are given to study the performance of the proposed approach.

scholarly journals A New MEMS Stochastic Model Order Reduction Method: Research and Application

2015 ◽  
Vol 2015 ◽  
pp. 1-10
Author(s):  
Bian Xiangjuan ◽  
Youping Gong ◽  
Chen Guojin ◽  
Lv Yunpeng
Keyword(s):  
Finite Element ◽  
Stochastic Model ◽  
Model Order Reduction ◽  
Large Scale ◽  
Reduction Method ◽  
Order Reduction ◽  
Fast Time ◽  
Random Input ◽  
Model Order ◽  
Order Reduction Method

Modeling and simulation of MEMS devices is a very complex tasks which involve the electrical, mechanical, fluidic, and thermal domains, and there are still some uncertainties that need to be accounted for during the robust design of MEMS actuators caused by uncertain material and/or geometric parameters. According to these problems, we put forward stochastic model order reduction method under random input conditions to facilitate fast time and frequency domain analyses; the method makes use of polynomial chaos expansions in terms of the random input variables for the matrices of a finite element model of the system and then uses its transformation matrix to reduce the model; the method is independent of the MOR algorithm, so it is seamlessly compatible with MOR method used in popular finite element solvers. The simulation results verify the method is effective in large scale MEMS design process.

Model Reduction of Large-Scale Discrete Plants With Specified Frequency Domain Balanced Structure

2004 ◽  
Vol 127 (3) ◽  
pp. 486-498 ◽  
Author(s):  
Abbas H. Zadegan ◽  
Ali Zilouchian
Keyword(s):  
Model Reduction ◽  
Frequency Domain ◽  
Large Scale ◽  
Linear Time ◽  
Model Simulation ◽  
Large Scale Systems ◽  
Linear Time Invariant ◽  
Balanced Structure ◽  
Linear Time Invariant Systems ◽  
Model Reduction Technique

A new model reduction technique for linear time-invariant systems is proposed. A new method that reduces the order of large-scale systems by integrating singular perturbation with specified frequency domain balanced structure is proposed. Considering a frequency range at which the system actually operates guarantees a good approximation of the original full order model. Simulation experiments for model reduction of several large-scale systems demonstrate the effectiveness of the proposed technique.

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