scholarly journals Model reduction of unstable systems based on balanced truncation algorithm

2021 ◽  
Vol 11 (3) ◽  
pp. 2045
Author(s):  
Ngoc Kien Vu ◽  
Hong Quang Nguyen
Keyword(s):  
Model Reduction ◽  
Model Order Reduction ◽  
Order Reduction ◽  
Order System ◽  
Balanced Truncation ◽  
Model Order ◽  
Unstable Systems ◽  
Practical Applications ◽  
Simulation Results ◽  
Lower Order System

Model reduction of a system is an approximation of a higher-order system to a lower-order system while the dynamic behavior of the system is almost unchanged. In this paper, we will discuss model order reduction (MOR) strategies for unstable systems, in which the method based on the balanced truncation algorithm will be focused on. Since each MOR algorithm has its strengths and weakness, practical applications should be suitable for each specific requirement. Simulation results will demonstrate the correctness of the algorithms.

scholarly journals The Unifying Feature of Projection in Model Order Reduction

2014 ◽  
Vol 12 (3-4) ◽  
pp. 17-27 ◽  
Author(s):  
K. Perev
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Model Reduction ◽  
Model Order Reduction ◽  
Krylov Subspace ◽  
Order Reduction ◽  
Orthogonal Decomposition ◽  
Balanced Truncation ◽  
Model Order ◽  
Lanczos Procedure ◽  
Proper Orthogonal

Abstract This paper considers the problem of model order reduction of linear systems with the emphasis on the common features of the main approaches. One of these features is the unifying role of operator projection in model reduction. It is shown how projections are implemented for different methods of model reduction and what their properties are. The other common feature is the subspaces where projections are defined. The main approaches for model reduction which are considered in the paper are balanced truncation, proper orthogonal decomposition and the Lanczos procedure from the Krylov subspace methods. It is shown that the range spaces of system gramians for balanced truncation and the range space of the reachability and observability matrices for the Lanczos procedure coincide. The connection between balanced truncation and the proper orthogonal decomposition method is also established. Therefore, the methods for model reduction are similar in terms of general operational principles, and differ mostly in their technical implementation. Several numerical examples are considered showing the validity of the proposed conjectures.

scholarly journals A NOVEL MIXED METHOD FOR THE MODEL ORDER REDUCTION OF LINEAR SYSTEMS USING PARTICLE SWARM OPTIMIZATION AND POLYNOMIAL METHOD

2013 ◽  
pp. 75-77
Author(s):  
M. SUDHEER KUMAR ◽  
N. NAGENDRA ◽  
T. MADHUBABU
Keyword(s):  
Mixed Method ◽  
Model Order Reduction ◽  
Order Reduction ◽  
Original System ◽  
Pso Algorithm ◽  
Order System ◽  
Polynomial Method ◽  
Model Order ◽  
Reduced Order ◽  
Lower Order System

In this paper, a novel mixed method is used for reducing the higher order system to lower order system. The denominator polynomials are obtained by the PSO Algorithm and the numerator coefficients are derived by the polynomial method. This method is simple and computer oriented. If the original system is stable then reduced order system is also stable. The proposed method is illustrated with the help of typical numerical examples considered from the literature.

A new model order reduction method for the design of compensator by using moment matching algorithm

2019 ◽  
Vol 42 (3) ◽  
pp. 472-484 ◽  
Author(s):  
Arvind Kumar Prajapati ◽  
Rajendra Prasad
Keyword(s):  
Model Reduction ◽  
Lower Order ◽  
Large Scale ◽  
Order Reduction ◽  
Order System ◽  
Moment Matching ◽  
Matching Algorithm ◽  
New Model ◽  
Factor Division Algorithm ◽  
Lower Order System

The aim of this paper is the construction of a new model reduction technique for large scale stable linear dynamic systems. It is principally focused on the dominant modes and time moments retention. This reduction implicates the translation of the overall important features confined in the large scale complete order model into the lower order system, allowing the computation of approximant denominator by using generalized pole clustering method. The approximant numerator is obtained by means of the factor division algorithm. As a result, a lower order system is obtained. To demonstrate its effectiveness, to highlight some fundamental of its features, and to accomplish its accuracy, a comparative study is done. Two standard numerical examples are taken, where approximant model computed by the proposed method is compared with the reduced order models computed from the recently proposed methods as well as well-known model reduction schemes. The paper is also emphasized on the design of compensator by using moment matching algorithm with the help of the reduced model. The design of compensator is validated and illustrated with the help of a standard numerical example taken from the literature.

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