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 \begin{aligned} A_\text{d} &= \left. \frac{\partial f}{\partial 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. \frac{\partial f}{\partial u} \right|_{(x_\text{d}, u_\text{d})} = \bmat{1 & 0 \\ 0 & 0 \\ 0 & v_\text{r}/l}. \end{aligned} }
Line 11: | Line 11: | ||
<center><math> | <center><math> | ||
\begin{aligned} | \begin{aligned} | ||
− | A_\text{d} &= \left. \ | + | A_\text{d} &= \left. \frac{\partial f}{\partial x} \right|_{(x_\text{d}, u_\text{d})} |
= \left. | = \left. | ||
\bmat{0 & 0 & -v \sin\theta \\ 0 & 0 & v \cos\theta \\ 0 & 0 & 0} | \bmat{0 & 0 & -v \sin\theta \\ 0 & 0 & v \cos\theta \\ 0 & 0 & 0} | ||
\right|_{(x_\text{d}, u_\text{d})} | \right|_{(x_\text{d}, u_\text{d})} | ||
= \bmat{0 & 0 & 0 \\ 0 & 0 & v_\text{r} \\ 0 & 0 & 0}, \\ | = \bmat{0 & 0 & 0 \\ 0 & 0 & v_\text{r} \\ 0 & 0 & 0}, \\ | ||
− | B_\text{d} &= \left. \ | + | B_\text{d} &= \left. \frac{\partial f}{\partial u} \right|_{(x_\text{d}, u_\text{d})} |
= \bmat{1 & 0 \\ 0 & 0 \\ 0 & v_\text{r}/l}. | = \bmat{1 & 0 \\ 0 & 0 \\ 0 & v_\text{r}/l}. | ||
\end{aligned} | \end{aligned} | ||
</math></center> | </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: