501
edits
Control package: Difference between revisions
→Inverted Pendulum
| Line 531: | Line 531: | ||
\begin{align} | \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_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{ | G_2(s)&=\frac{\Theta(s)}{F(s)}=\frac{\gamma_1s}{\beta_4s^3+\beta_3s^2+\beta_2s+\beta_1} | ||
\end{align} | \end{align} | ||
</math> | </math> | ||
| Line 547: | Line 547: | ||
|- | |- | ||
|<math display="inline">\beta_3=(M+m)b+(ml^2+I)c\approx (M+m)b+ml^2c</math> | |<math display="inline">\beta_3=(M+m)b+(ml^2+I)c\approx (M+m)b+ml^2c</math> | ||
|- | |||
|<math display="inline">\beta_2=-(M+m)mgl+bc</math> | |||
|- | |||
|<math display="inline">\beta_1=-mglc</math> | |||
|- | |||
|<math display="inline">\gamma_1=-ml</math> | |||
|} | |} | ||