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

From FBSwiki
Jump to navigation Jump to search
Line 11: Line 11:
 
<center><math>
 
<center><math>
 
   \begin{aligned}
 
   \begin{aligned}
     A_\text{d} &= \left. \pder{f}{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}
 
         \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. \pder{f}{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}.
 
     = \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:

Failed to parse (unknown function "\bmat"): {\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} }