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 = R. M. Murray
+
| contributor = J. W. Kim
| date =  
+
| date = 4 Dec 2011
| rev = 2.10e
+
| 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}
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</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

Return to Errata page

Location: page 299, line -10

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

math

then the time constant works out to be

math

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