Proper transfer function: Difference between revisions

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In [[control theory]], a '''proper transfer function''' is a [[transfer function]] in which the [[degreeDegree of a (mathematics)polynomial|degree]] of the numerator does not exceed the degree of the denominator. A '''strictly proper''' transfer function is a transfer function where the degree of the numerator is [[less than]] the degree of the denominator.

{{Unreferenced|date=December 2009}}

In [[control theory]], a '''proper transfer function''' is a [[transfer function]] in which the [[degree (mathematics)|degree]] of the numerator does not exceed the degree of the denominator.

AThe '''strictlydifference proper'''between [[transferthe function]]degree isof athe transferdenominator function(number whereof thepoles) [[Degreeand (mathematics)|degree]] of the numerator is(number [[lessof than]]zeros) is the ''relative degree'' of the denominatortransfer function.

==Example==

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is '''proper''', because

:<math> \deg(\textbf{N}(s)) = 4 \leq \deg(\textbf{D}(s)) = 4 </math>.

is '''biproper''', because

:<math> \deg(\textbf{N}(s)) = 4 = \deg(\textbf{D}(s)) = 4 </math>.

but is '''not strictly proper''', because

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because

:<math> \deg(\textbf{N}(s)) = 4 \nleq \deg(\textbf{D}(s)) = 3 </math>.

A '''not proper''' transfer function can be made proper by using the method of long division.

The following transfer function is '''strictly proper'''

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Also, the integral of the real part of a strictly proper transfer function is zero.

==References==

* [https://web.archive.org/web/20160304220240/https://courses.engr.illinois.edu/ece486/documents/set5.pdf Transfer functions] - ECE 486: Control Systems Spring 2015, University of Illinois

* [http://www.ece.mcmaster.ca/~ibruce/courses/EE4CL4_lecture9.pdf ELEC ENG 4CL4: Control System Design Notes for Lecture #9], 2004, Dr. Ian C. Bruce, McMaster University

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[[Category:Control theory]]

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