Difference between revisions of "Errata: Last equation in Example 8.6 has sign error in the second term"

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In the last displayed equation of this example, there is a sign error in the term <math>1 + P(s) G_{uy}(s)</math> that appears in the denominator.  Because the compensator <math>G_{uy}</math> is in the feedback path and there is ''not'' a negative gain term in the loop, the correct expression is
 
In the last displayed equation of this example, there is a sign error in the term <math>1 + P(s) G_{uy}(s)</math> that appears in the denominator.  Because the compensator <math>G_{uy}</math> is in the feedback path and there is ''not'' a negative gain term in the loop, the correct expression is
 
<center><amsmath>
 
<center><amsmath>
   G_{y r} = \frac{k_r P(s)}{1 - P(s) G_{uy}(s)}  
+
   G_{y r} = \frac{P(s) {\color{blue} G_{ur}(s)}}{1 {\color{blue} -} P(s) G_{uy}(s)}  
     = \frac{k_1 (\gamma s + 1)}{s^2 + (k_1 \gamma + k_2) s + k_1}.
+
     = \frac{{\color{blue} k_r} (\gamma s + 1)}{s^2 + (k_1 \gamma + k_2) s + k_1}.
 
</amsmath></center>
 
</amsmath></center>
Note that the right hand side of the equation is unchanged; the negative sign in the expression for <math>G_{uy}</math> (at the end of the previous page) cancels out.
+
(additional errors reported [[Errata: Last equation in Example 8.6 has errors in numerator expressions|here]] are also shown).  Note that the right hand side of the equation is unchanged; the negative sign in the expression for <math>G_{uy}</math> (at the end of the previous page) cancels out.
 
}}
 
}}

Latest revision as of 18:09, 28 August 2011

Return to Errata page

Location: page 247, line 11

In the last displayed equation of this example, there is a sign error in the term that appears in the denominator. Because the compensator is in the feedback path and there is not a negative gain term in the loop, the correct expression is

math

(additional errors reported here are also shown). Note that the right hand side of the equation is unchanged; the negative sign in the expression for (at the end of the previous page) cancels out.

(Contributed by A. Tits, 4 Nov 2010)