Difference between revisions of "Errata: Example 8.10 missing factor of v, a1 and a2 flipped"
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Failed to parse (unknown function "\begin{bmatrix}"): {\displaystyle \begin{bmatrix} v \\ \phi \end{bmatrix} = -\underbrace{\begin{bmatrix} \lambda_1 & 0 & 0 \\ 0 & \dfrac{a_2 l}{v_\text{r}^2} & \dfrac{a_1 l}{v_\text{r} \end{bmatrix} }_{K_\text{d}} \underbrace{\begin{bmatrix} x - v_\text{r} t \\ y - y_\text{r} \\ \theta} \end{bmatrix}}_{e} + \underbrace{\begin{bmatrix} v_\text{r} \\ 0 \end{bmatrix} \vphantom{\begin{bmatrix} 0 \\ 0 \\ 0 \end{bmatrix}}}}_{u_\text{d}}. }
Line 27: | Line 27: | ||
0 & \dfrac{a_2 l}{v_\text{r}^2} & \dfrac{a_1 l}{v_\text{r} \end{bmatrix} | 0 & \dfrac{a_2 l}{v_\text{r}^2} & \dfrac{a_1 l}{v_\text{r} \end{bmatrix} | ||
}_{K_\text{d}} | }_{K_\text{d}} | ||
− | \underbrace{\begin{bmatrix} x - v_\text{r} t \\ y - y_\text{r} \\ \theta} \end{bmatrix}_{e} + | + | \underbrace{\begin{bmatrix} x - v_\text{r} t \\ y - y_\text{r} \\ \theta} \end{bmatrix}}_{e} + |
− | \underbrace{\begin{bmatrix} v_\text{r} \\ 0}\vphantom{\begin{bmatrix} 0 \\ 0 \\ 0 \end{bmatrix}} | + | \underbrace{\begin{bmatrix} v_\text{r} \\ 0 \end{bmatrix} \vphantom{\begin{bmatrix} 0 \\ 0 \\ 0 \end{bmatrix}}}}_{u_\text{d}}. |
</math></center> | </math></center> |
Revision as of 04:53, 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:
This leads to an error in the definition of later in the example. In addition, the coefficients and are swapped, so the definition of should be:
The final controller then becomes