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Fix for broken equation

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This commit is contained in:
Christian Risi 2025-02-16 12:20:46 +01:00
parent 2a63fb24ba
commit a6b3ab236e
1 changed files with 14 additions and 17 deletions
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docs/Chapters/1-MODERN-CONTROL.md
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@ -107,23 +107,20 @@ $$
> >
> Then, put all variables equal to the previous one derivated: > Then, put all variables equal to the previous one derivated:
> >
> $$ > $x(t) = \begin{bmatrix}
x(t) = \begin{bmatrix} > x_1(t)\\
x_1(t)\\ > x_2(t) = \dot{x_1}(t)\\
x_2(t) = \dot{x_1}(t)\\ > \dots\\
\dots\\ > x_n(t) = \dot{x}_{n-1}(t)
x_n(t) = \dot{x}_{n-1}(t) > \end{bmatrix}
\end{bmatrix} > \;
\; > \dot{x}(t) = \begin{bmatrix}
\dot{x}(t) = \begin{bmatrix} > \dot{x_1}(t) = x_2(t)\\
\dot{x_1}(t) = x_2(t)\\ > \dot{x_2}(t) = x_3(t)\\
\dot{x_2}(t) = x_3(t)\\ > \dots\\
\dots\\ > \dot{x}_{n-1}(t) = \dot{x}_{n}(t)\\
\dot{x}_{n-1}(t) = \dot{x}_{n}(t)\\ > \dot{x}_{n}(t) = \text{our formula}
\dot{x}_{n}(t) = \text{our formula} > \end{bmatrix}$
\end{bmatrix}
> $$
> >
Now in our state we may express `position` and `speed`, while in our Now in our state we may express `position` and `speed`, while in our