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IEVref: | 351-45-51 | ID: | |||||||||

Language: | en | Status: Standard | |||||||||

Term: | rational transfer element | ||||||||||

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Definition: | linear time-invariant transfer element the transfer function of which may be written as a quotient of two polynomials in s$G\left(s\right)=\frac{V\left(s\right)}{U\left(s\right)}=\frac{{b}_{0}+{b}_{1}\cdot s+\dots +{b}_{m}\cdot {s}^{m}}{{a}_{0}+{a}_{1}\cdot s+\dots +{a}_{n}\cdot {s}^{n}}$ with b real, _{j}a ≠ 0, _{n}b ≠ 0_{m}where
Note 1 to entry: In real controlled systems, Note 2 to entry: An element with dead time is an example for a non-rational transfer element. Note 3 to entry: This entry was numbered 351-24-43 in IEC 60050-351:2006. | ||||||||||

Publication date: | 2013-11 | ||||||||||

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$G\left(s\right)=\frac{V\left(s\right)}{U\left(s\right)}=\frac{{b}_{0}+{b}_{1}\cdot s+\dots +{b}_{m}\cdot {s}^{m}}{{a}_{0}+{a}_{1}\cdot s+\dots +{a}_{n}\cdot {s}^{n}}$ with *a _{j}* and

where

a, _{i}b_{i} | are the polynomial coefficients; |

s | is the complex variable of the Laplace transform; |

U(s) | is the input transform; |

V(s) | is the output transform. |

Note 1 to entry: In real controlled systems, *m* < *n*. With respect to mathematical denomination these elements would have to be called "proper-fractional rational transfer element" which is not usage.

Note 2 to entry: An element with dead time is an example for a non-rational transfer element.

Note 3 to entry: This entry was numbered 351-24-43 in IEC 60050-351:2006.