DocumentCode :
1441759
Title :
Teaching linear systems theory using Cramer´s rule
Author :
Klein, Richard E.
Author_Institution :
Dept. of Mech. & Ind. Eng., Illinois Univ., Urbana, IL, USA
Volume :
33
Issue :
3
fYear :
1990
fDate :
8/1/1990 12:00:00 AM
Firstpage :
258
Lastpage :
267
Abstract :
A pedagogical approach based upon Cramer´s rule is outlined for the presentation of linear systems theory in a first course for engineering students. The Laplace complex variable, or the Heaviside derivative operator, is used with Cramer´s rule from elementary mathematics to allow students to expeditiously gain a foothold on linear dynamic systems theory. The approach applies to the broad class of finite-dimensional linear time invariant systems as they can be readily expressed as a square system of equations in the form Ax=Bu . The elements of the system´s A and B matrices are, in general, polynomials in the Laplace complex variable or the Heaviside derivative operator. Cramer´s rule permits an explicit solution for this square nonhomogeneous system for a desired unknown, or output, with respect to an input of interest. Consequently, Cramer´s rule gives rise to a general method with pedagogical appeal for obtaining desired system transfer functions. The computational tasks may be done initially by hand and then by appropriate software as problems of greater complexity are examined
Keywords :
control system analysis; education; linear systems; Cramer´s rule; Heaviside derivative operator; Laplace complex variable; engineering students; finite-dimensional linear time invariant systems; linear systems theory; pedagogical approach; polynomials; transfer functions; Algebra; Application software; Concrete; Education; Laplace equations; Linear systems; Mathematics; Polynomials; Transfer functions;
fLanguage :
English
Journal_Title :
Education, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-9359
Type :
jour
DOI :
10.1109/13.57070
Filename :
57070
Link To Document :
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