On the Relative Gain Array (RGA) with singular and rectangular matrices

被引：7

作者：

Uhlmann, Jeffrey ^{[1
]}

机构：

[1] Univ Missouri, 201 Naka Hall, Columbia, MO 65211 USA

来源：

APPLIED MATHEMATICS LETTERS | 2019年 / 93卷

关键词：

Control systems; Moore-Penrose pseudoinverse; Process control; Relative Gain Array (RGA); UC inverse; Unit consistency;

D O I：

10.1016/j.aml.2019.01.031

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper identifies a significant deficiency in the literature on the application of the Relative Gain Array (RGA) formalism in the case of singular matrices. Specifically, it is shown that the conventional use of the Moore-Penrose pseudoinverse is inappropriate because it fails to preserve critical properties that can be assumed in the nonsingular case. It is then shown that such properties can be rigorously preserved using an alternative generalized matrix inverse. (C) 2019 Elsevier Ltd. All rights reserved.

引用

页码：52 / 57

页数：6

共 10 条

[1]

[Anonymous], TOPICS MATRIX ANAL

[2] An effective procedure for sensor variable selection and utilization in plasma etching for semiconductor manufacturing [J].

Baek, Kye Hyun ;

Edgar, Thomas F. ;

Song, Kiwook ;

Choi, Gilheyun ;

Cho, Han Ku ;

Han, Chonghun .

COMPUTERS & CHEMICAL ENGINEERING, 2014, 61 :20-29

[3] ON A NEW MEASURE OF INTERACTION FOR MULTIVARIABLE PROCESS CONTROL [J].

BRISTOL, EH .

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 1966, AC11 (01) :133-+

[4] THE RELATIVE GAIN FOR NONSQUARE MULTIVARIABLE SYSTEMS [J].

CHANG, JW ;

YU, CC .

CHEMICAL ENGINEERING SCIENCE, 1990, 45 (05) :1309-1323

[5] MATHEMATICAL ASPECTS OF THE RELATIVE GAIN ARRAY A-DEGREE-A-T [J].

JOHNSON, CR ;

SHAPIRO, HM .

SIAM JOURNAL ON ALGEBRAIC AND DISCRETE METHODS, 1986, 7 (04) :627-644

[6]

Skogestad S., 2005, POSTLETHWAITE MULTIV

[7]

Uhlmann J., 2017, ARXIV160408476V2CSNA

[8] A GENERALIZED MATRIX INVERSE THAT IS CONSISTENT WITH RESPECT TO DIAGONAL TRANSFORMATIONS [J].

Uhlmann, Jeffrey .

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 2018, 39 (02) :781-800

[9]

Uhlmann Jeffrey, 2018, IEEE CONTROL SYST LE

[10]

Zhang B., 2018, ARXIV180601776V1EESS

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