Model Order Reduction of 1D Diffusion Systems Via Residue Grouping

2008 ◽  
Vol 130 (1) ◽  
Author(s):  
Kandler A. Smith ◽  
Christopher D. Rahn ◽  
Chao-Yang Wang
Keyword(s):  
Model Order Reduction ◽  
State Space Model ◽  
Lithium Ion ◽  
Computation Time ◽  
Order Reduction ◽  
Optimization Procedure ◽  
Model Order ◽  
Diffusion Systems ◽  
Spatially Distributed ◽  
Order Reduction Method

A model order reduction method is developed and applied to 1D diffusion systems with negative real eigenvalues. Spatially distributed residues are found either analytically (from a transcendental transfer function) or numerically (from a finite element or finite difference state space model), and residues with similar eigenvalues are grouped together to reduce the model order. Two examples are presented from a model of a lithium ion electrochemical cell. Reduced order grouped models are compared to full order models and models of the same order in which optimal eigenvalues and residues are found numerically. The grouped models give near-optimal performance with roughly 1∕20 the computation time of the full order models and require 1000–5000 times less CPU time for numerical identification compared to the optimization procedure.

An Automated Model-Order Reduction Method for Automatic Transmissions

2017 ◽  
Vol 139 (7) ◽  
Author(s):  
Vanja Ranogajec ◽  
Joško Deur
Keyword(s):  
State Space ◽  
Model Order Reduction ◽  
Reduction Method ◽  
State Space Model ◽  
Order Reduction ◽  
Torque Converter ◽  
State Variables ◽  
Model Order ◽  
Automatic Transmissions ◽  
Order Reduction Method

New generation of torque converter automatic transmissions (AT) includes a large number of gears for improved fuel economy and vehicle performance, which leads to exponentially increasing number of shift types and shift events. In order to facilitate various numerical/simulation analyses of AT dynamics, shift control optimization, and control strategy design, a full-order AT model is usually reduced by eliminating state variables related to locked clutches in particular gears or shifts. The paper proposes an automated model-order reduction method for an arbitrary, user-specified clutch state, and demonstrates its application on an example of ten-speed AT. The method is based on determining the locked-clutch torque variables and their substitution into the full-order state-space model input vector, as well as finding a linear relation between the reduced-order and full-order model state-space variables.

scholarly journals The Model Order Reduction Method as an Effective Way to Implement GPC Controller for Multidimensional Objects

Algorithms ◽  
2020 ◽  
Vol 13 (8) ◽  
pp. 178
Author(s):  
Sebastian Plamowski ◽  
Richard W Kephart
Keyword(s):  
Predictive Control ◽  
Model Order Reduction ◽  
Order Reduction ◽  
High Order ◽  
Double Precision ◽  
Model Order ◽  
Numerical Errors ◽  
Multiple Input ◽  
Multidimensional Objects ◽  
Order Reduction Method

The paper addresses issues associated with implementing GPC controllers in systems with multiple input signals. Depending on the method of identification, the resulting models may be of a high order and when applied to a control/regulation law, may result in numerical errors due to the limitations of representing values in double-precision floating point numbers. This phenomenon is to be avoided, because even if the model is correct, the resulting numerical errors will lead to poor control performance. An effective way to identify, and at the same time eliminate, this unfavorable feature is to reduce the model order. A method of model order reduction is presented in this paper that effectively mitigates these issues. In this paper, the Generalized Predictive Control (GPC) algorithm is presented, followed by a discussion of the conditions that result in high order models. Examples are included where the discussed problem is demonstrated along with the subsequent results after the reduction. The obtained results and formulated conclusions are valuable for industry practitioners who implement a predictive control in industry.

Model of induction brazing of nonmagnetic metals using model order reduction approach

2018 ◽  
Vol 37 (4) ◽  
pp. 1515-1524 ◽  
Author(s):  
Pavel Karban ◽  
David Pánek ◽  
Ivo Doležel
Keyword(s):  
Heat Treatment ◽  
Model Order Reduction ◽  
Computation Time ◽  
Order Reduction ◽  
Nonlinear Problems ◽  
Model Order ◽  
Content Type ◽  
Weakly Nonlinear ◽  
Induction Brazing ◽  
Multiphysics Problems

Purpose A novel technique for control of complex physical processes based on the solution of their sufficiently accurate models is presented. The technique works with the model order reduction (MOR), which significantly accelerates the solution at a still acceptable uncertainty. Its advantages are illustrated with an example of induction brazing. Design/methodology/approach The complete mathematical model of the above heat treatment process is presented. Considering all relevant nonlinearities, the numerical model is reduced using the orthogonal decomposition and solved by the finite element method (FEM). It is cheap compared with classical FEM. Findings The proposed technique is applicable in a wide variety of linear and weakly nonlinear problems and exhibits a good degree of robustness and reliability. Research limitations/implications The quality of obtained results strongly depends on the temperature dependencies of material properties and degree of nonlinearities involved. In case of multiphysics problems characterized by low nonlinearities, the results of solved problems differ only negligibly from those solved on the full model, but the computation time is lower by two and more orders. Yet, however, application of the technique in problems with stronger nonlinearities was not fully evaluated. Practical implications The presented model and methodology of its solution may represent a basis for design of complex technologies connected with induction-based heat treatment of metal materials. Originality/value Proposal of a sophisticated methodology for solution of complex multiphysics problems established the MOR technology that significantly accelerates their solution at still acceptable errors.

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