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→Inverted Pendulum
| Line 524: | Line 524: | ||
mlsX(s)+(ml^2+I)s^2\Theta(s)+bs\Theta(s)-mgl\Theta(s)&=0 | mlsX(s)+(ml^2+I)s^2\Theta(s)+bs\Theta(s)-mgl\Theta(s)&=0 | ||
\end{cases} | \end{cases} | ||
</math> | |||
and by dividing the state variables by the input one obtains the transfer functions | |||
<math> | |||
\begin{align} | |||
G_1(s)&=\frac{X(s)}{F(s)}=\frac{\alpha_2s^2+\alpha_1s+\alpha_0}{\beta_4s^4+\beta_3s^3+\beta_2s^2+\beta_1s}\\ | |||
G_2(s)&=\frac{\Theta(s)}{F(s)}=\frac{c_2s}{\beta_4s^3+\beta_3s^2+\beta_2s+\beta_1} | |||
\end{align} | |||
</math> | </math> | ||