Proper transfer function: Difference between revisions

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In [[control theory]], a '''proper transfer function''' is a [[transfer function]] in which the [[Degree (angle)of a 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 (angle)|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) and degree of the numerator is(number [[lessof than]]zeros) is the ''relative degree'' of the denominatortransfer function.

If the degree of the numerator equals the degree of the denominator, the transfer function is '''biproper'''.

The difference between the order of the denominator (number of poles) and order of the numerator (number of zeros) is the ''relative degree'' of the transfer function.

==Example==

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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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