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

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Line 13: Line 13:
 
     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})}
 
       = \left.
 
       = \left.
         \bmat{0 & 0 & -v \sin\theta \\ 0 & 0 & v \cos\theta \\ 0 & 0 & 0}
+
         \begin{bmatrix} 0 & 0 & -v \sin\theta \\ 0 & 0 & v \cos\theta \\ 0 & 0 & 0 \end{bmatrix}
 
         \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}, \\
+
       = \begin{bmatrix} 0 & 0 & 0 \\ 0 & 0 & v_\text{r} \\ 0 & 0 & 0 \end{bmatrix}, \\
 
     B_\text{d} &= \left. \frac{\partial f}{\partial u} \right|_{(x_\text{d}, u_\text{d})}
 
     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}.
+
     = \begin{bmatrix} 1 & 0 \\ 0 & 0 \\ 0 & v_\text{r}/l \end{bmatrix}.
 
   \end{aligned}
 
   \end{aligned}
 
</math></center>
 
</math></center>

Revision as of 04:43, 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: