Difference between revisions of "Errata: Example 8.10 missing factor of v, a1 and a2 flipped"
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Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\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 }
(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: | ||
+ | <center><math> | ||
+ | \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 | ||
+ | </math></center> |
Revision as of 04:42, 7 October 2021
Chapter | Output Feedback |
---|---|
Page | |
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: