Difference between revisions of "Errata: In Example 6.10, the system input for the linearized model should be w instead of u"

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{{errata page
 
{{errata page
| chapter =  
+
| chapter = State Feedback
| page =  
+
| page = 196
| line =  
+
| line = 19, 23
| contributor = R. M. Murray
+
| contributor = J. W. Kim
| date =  
+
| date = 5 Nov 2011
| rev = 2.10e
+
| rev = 2.11a
 
| version = Third printing
 
| version = Third printing
| text =  
+
| text = The dynamics at the top of the example use the linearized input <amsmath>w = u-u_e</amsmath> and hence the input for the remainder of the example is <amsmath>w</amsmath> and not <amsmath>u</amsmath>.  This affects the two displayed equations in lines 19 and 23.  The first displayed equation should read
 +
<center><amsmath>
 +
  \frac{d}{t} \begin{bmatrix} x \\ z \end{bmatrix} = \begin{bmatrix}
 +
    a & 0 \\
 +
    1 & 0
 +
  \end{bmatrix} \begin{bmatrix} x \\ z \end{bmatrix} +
 +
  \begin{bmatrix} b \\ 0 \end{bmatrix} {\color{blue} w} + \begin{bmatrix}-b_g \\ 0 \end{bmatrix} \theta + \begin{bmatrix} 0 \\ v_e - v_r \end{bmatrix}.
 +
</amsmath></center>
 +
and the second should read
 +
<center><amsmath>
 +
  \aligned
 +
    \frac{dz}{dt} &= y - v_r, \qquad
 +
    {\color{blue} w} &= -k_p x - k_i z + k_r v_r,
 +
  \endaligned
 +
</amsmath></center>
 
}}
 
}}

Latest revision as of 17:34, 6 September 2012

Return to Errata page

Location: page 196, line 19, 23

The dynamics at the top of the example use the linearized input math and hence the input for the remainder of the example is math and not math. This affects the two displayed equations in lines 19 and 23. The first displayed equation should read

math

and the second should read

math

(Contributed by J. W. Kim, 5 Nov 2011)