Difference between revisions of "Errata: Example 8.10 missing factor of v, a1 and a2 flipped"
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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 | + | The equation for <math>A_\text{d}</math> should read |
<center><math> | <center><math> | ||
A_\text{d} = \left. \frac{\partial f}{\partial x} \right|_{(x_\text{d}, u_\text{d})} | A_\text{d} = \left. \frac{\partial f}{\partial x} \right|_{(x_\text{d}, u_\text{d})} | ||
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= \begin{bmatrix} 0 & 0 & 0 \\ 0 & 0 & {\color{blue} v_\text{r}} \\ 0 & 0 & 0 \end{bmatrix}, | = \begin{bmatrix} 0 & 0 & 0 \\ 0 & 0 & {\color{blue} v_\text{r}} \\ 0 & 0 & 0 \end{bmatrix}, | ||
</math></center> | </math></center> | ||
− | This leads to an error in the definition of <math>w_2</math> later in the example. In addition, the coefficients <math>a_1</math> and <math>a_2</math> are swapped and there was an error in the sign, so the definition of <math>w_2</math> should be | + | This leads to an error in the definition of <math>w_2</math> later in the example. In addition, the coefficients <math>a_1</math> and <math>a_2</math> are swapped and there was an error in the sign, so the definition of <math>w_2</math> should be |
<center><math> | <center><math> | ||
w_2 = {\color{blue} -} \frac{l}{v_\text{r}}(\frac{\color{blue} a_2}{\color{blue} v_\text{r}} e_y + {\color{blue} a_1} e_\theta). | w_2 = {\color{blue} -} \frac{l}{v_\text{r}}(\frac{\color{blue} a_2}{\color{blue} v_\text{r}} e_y + {\color{blue} a_1} e_\theta). | ||
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+ \begin{bmatrix} v_\text{r} \\ 0 \end{bmatrix}. | + \begin{bmatrix} v_\text{r} \\ 0 \end{bmatrix}. | ||
</math></center> | </math></center> | ||
+ | |||
+ | These corrections also change the controller response in Figure 8.13. The corrected response is | ||
+ | <center> | ||
+ | [[Image:outputfbk-steering-gainsched.png]] | ||
+ | </center> |
Revision as of 05:07, 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
This leads to an error in the definition of later in the example. In addition, the coefficients and are swapped and there was an error in the sign, so the definition of should be
The final controller then becomes
These corrections also change the controller response in Figure 8.13. The corrected response is