# Difference between revisions of "Errata: Closed loop time constant after equation (10.6) has an extra factor of 2"

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{{errata page | {{errata page | ||

− | | chapter = | + | | chapter = PID Control |

− | | page = | + | | page = 299 |

− | | line = | + | | line = -10 |

− | | contributor = | + | | contributor = J. W. Kim |

− | | date = | + | | date = 4 Dec 2011 |

− | | rev = 2. | + | | rev = 2.11a |

| version = Third printing | | version = Third printing | ||

| text = | | text = | ||

+ | The derivation for the closed loop time constant <amsmath>T_\text{cl}</amsmath> is not correct. Using the loop transfer function | ||

+ | <center><amsmath> | ||

+ | L(s) = k_i P'(0) + \frac{k_i P(0)}{s} | ||

+ | </amsmath></center> | ||

+ | then the time constant works out to be | ||

+ | <center><amsmath> | ||

+ | T_{cl}\approx \frac{1 + k_i P'(0)}{k_i P(0)} = -P'(0)/P(0) \quad\text{(when}\quad k_i P′(0) = −0.5). | ||

+ | </amsmath></center> | ||

}} | }} |

## Latest revision as of 03:57, 29 September 2012

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Location: page 299, line -10

The derivation for the closed loop time constant is not correct. Using the loop transfer function

then the time constant works out to be

(Contributed by J. W. Kim, 4 Dec 2011)