Difference between revisions of "Errata: Example 8.10 missing factor of v, a1 and a2 flipped"

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(Created page with "{{Errata |Chapter=Output Feedback |Page=8-28 |Line=-4 |Version=3.1.5 |Date=6 Oct 2021 }} Example 8.10 (Steering control with velocity scheduling) is missing a factor of <math>...")
 
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Example 8.10 (Steering control with velocity scheduling) is missing a factor of <math>v</math> in the definition of <math>A_\text{d}</math> that propagates through the example.  In addition, the coefficients <math>a_1</math> and <math>a_2</math> are swapped in the definition of <math>w_2</math>.
 
Example 8.10 (Steering control with velocity scheduling) is missing a factor of <math>v</math> in the definition of <math>A_\text{d}</math> that propagates through the example.  In addition, the coefficients <math>a_1</math> and <math>a_2</math> are swapped in the definition of <math>w_2</math>.
 +
 +
The equation for <math>A_\text{d}</math> should read:
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<center><math>
 +
  \aligned
 +
    A_\text{d} &= \left. \pder{f}{x} \right|_{(x_\text{d}, u_\text{d})}
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      = \left.
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        \bmat{0 & 0 & -v \sin\theta \\ 0 & 0 & v \cos\theta \\ 0 & 0 & 0}
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        \right|_{(x_\text{d}, u_\text{d})}
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      = \bmat{0 & 0 & 0 \\ 0 & 0 & v_\text{r} \\ 0 & 0 & 0}, \\
 +
    B_\text{d} &= \left. \pder{f}{u} \right|_{(x_\text{d}, u_\text{d})}
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    = \bmat{1 & 0 \\ 0 & 0 \\ 0 & v_\text{r}/l}.
 +
  \endaligned
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</math></center>

Revision as of 04:42, 7 October 2021

Chapter Output Feedback
Page 8-28
Line -4
Version 3.1.5
Date 6 Oct 2021

Example 8.10 (Steering control with velocity scheduling) is missing a factor of in the definition of that propagates through the example. In addition, the coefficients and are swapped in the definition of .

The equation for should read:

Failed to parse (unknown function "\aligned"): {\displaystyle \aligned A_\text{d} &= \left. \pder{f}{x} \right|_{(x_\text{d}, u_\text{d})} = \left. \bmat{0 & 0 & -v \sin\theta \\ 0 & 0 & v \cos\theta \\ 0 & 0 & 0} \right|_{(x_\text{d}, u_\text{d})} = \bmat{0 & 0 & 0 \\ 0 & 0 & v_\text{r} \\ 0 & 0 & 0}, \\ B_\text{d} &= \left. \pder{f}{u} \right|_{(x_\text{d}, u_\text{d})} = \bmat{1 & 0 \\ 0 & 0 \\ 0 & v_\text{r}/l}. \endaligned }