Proper transfer function: Difference between revisions

Revision as of 21:57, 5 July 2009

Revision as of 13:54, 17 December 2009

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{{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.

== Example ==

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

:<math> \textbf{G}(s) = \frac{\textbf{N}(s)}{\textbf{D}(s)} = \frac{s^{4} + n_{1}s^{3} + n_{2}s^{2} + n_{3}s + n_{4}}{s^{4} + d_{1}s^{3} + d_{2}s^{2} + d_{3}s + d_{4}}</math>

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

== Implications ==

A proper transfer function will never grow unbounded as the frequency approaches infinity.

:<math> |\textbf{G}(\pm j\infty)| < \infty </math>

== See also ==

* [[Strictly proper]]

{{DEFAULTSORT:Proper Transfer Function}}

[[Category:Control theory]]

[[Category:Articles lacking sources (Erik9bot)]]

[[eo:Pozitiva tradona funkcio]]