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IEVref: | 351-50-03 | ID: | |||||||||||||||

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

Term: | second-order lag element | ||||||||||||||||

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Definition: | linear time-invariant transfer element the transfer function of which has exactly two poles with negative real parts which may be real or complex conjugate and no zeros Note 1 to entry: The transfer function of a second-order lag element is given as $\frac{V\left(s\right)}{U\left(s\right)}=\frac{{K}_{\text{\Rho}}}{\left(1+{T}_{1}\cdot s\right)\cdot \left(1+{T}_{2}\cdot s\right)}$ for two real poles and as $\frac{V\left(s\right)}{U\left(s\right)}=\frac{{K}_{\text{\Rho}}}{\frac{{s}^{2}}{{\omega}_{0}^{2}}+2\cdot \vartheta \cdot \frac{s}{{\omega}_{0}}+1}$ for a complex conjugate pair of poles where
Note 2 to entry: This entry was numbered 351-28-14 in IEC 60050-351:2006. | ||||||||||||||||

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

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Internal notes: | 2013-12-16: de term corrected in accordance with mail from "Seeger, Anne" <anne.seeger@vde.com>, 2013-12-16. JGO 2017-08-28: <mstyle displaystyle=true'> corrected to <mstyle displaystyle='true'>. LMO | ||||||||||||||||

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Note 1 to entry: The transfer function of a second-order lag element is given as

$\frac{V\left(s\right)}{U\left(s\right)}=\frac{{K}_{\text{\Rho}}}{\left(1+{T}_{1}\cdot s\right)\cdot \left(1+{T}_{2}\cdot s\right)}$ for two real poles

and as

$\frac{V\left(s\right)}{U\left(s\right)}=\frac{{K}_{\text{\Rho}}}{\frac{{s}^{2}}{{\omega}_{0}^{2}}+2\cdot \vartheta \cdot \frac{s}{{\omega}_{0}}+1}$ for a complex conjugate pair of poles

where

K_{P} | is the proportional action coefficient; |

T_{1}, T_{2} | are the time constants; |

$\vartheta $ | is the damping ratio; |

ω_{0} | is the characteristic angular frequency; |

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

U(s) | is the input transform; |

V(s) | is the output transform. |

Note 2 to entry: This entry was numbered 351-28-14 in IEC 60050-351:2006.