Update all figures

This commit is contained in:
Thomas Dehaeze 2020-06-19 11:08:16 +02:00
parent 858a3e862e
commit a2ec5ab10f
58 changed files with 1598 additions and 483 deletions

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matlab/figs-inkscape Symbolic link
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../inkscape/figs

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@ -65,7 +65,7 @@
- $k$: Actuator's Stiffness [N/m]
- $m$: Payload's mass [kg]
- $\omega_0 = \sqrt{\frac{k}{m}}$: Resonance of the (non-rotating) mass-spring system [rad/s]
- $\omega_r = \dot{\theta}$: rotation speed [rad/s]
- $\Omega = \dot{\theta}$: rotation speed [rad/s]
#+name: fig:rotating_xy_platform
@ -141,7 +141,7 @@ Without the coupling terms, each equation is the equation of a one degree of fre
Thus, the term $- m\dot{\theta}^2$ acts like a negative stiffness (due to *centrifugal forces*).
** Constant Rotating Speed
To simplify, let's consider a constant rotating speed $\dot{\theta} = \omega_r$ and thus $\ddot{\theta} = 0$.
To simplify, let's consider a constant rotating speed $\dot{\theta} = \Omega$ and thus $\ddot{\theta} = 0$.
#+NAME: eq:coupledplant
\begin{equation}
@ -154,13 +154,15 @@ To simplify, let's consider a constant rotating speed $\dot{\theta} = \omega_r$
\begin{bmatrix} F_u \\ F_v \end{bmatrix}
\end{equation}
# Explain each term
#+NAME: eq:coupled_plant
\begin{equation}
\begin{bmatrix} d_u \\ d_v \end{bmatrix} =
\frac{\frac{1}{k}}{\left( \frac{s^2}{{\omega_0}^2} + (1 - \frac{{\omega_r}^2}{{\omega_0}^2}) \right)^2 + \left( 2 \frac{{\omega_r} s}{{\omega_0}^2} \right)^2}
\frac{\frac{1}{k}}{\left( \frac{s^2}{{\omega_0}^2} + (1 - \frac{{\Omega}^2}{{\omega_0}^2}) \right)^2 + \left( 2 \frac{{\Omega} s}{{\omega_0}^2} \right)^2}
\begin{bmatrix}
\frac{s^2}{{\omega_0}^2} + 1 - \frac{{\omega_r}^2}{{\omega_0}^2} & 2 \frac{\omega_r s}{{\omega_0}^2} \\
-2 \frac{\omega_r s}{{\omega_0}^2} & \frac{s^2}{{\omega_0}^2} + 1 - \frac{{\omega_r}^2}{{\omega_0}^2} \\
\frac{s^2}{{\omega_0}^2} + 1 - \frac{{\Omega}^2}{{\omega_0}^2} & 2 \frac{\Omega s}{{\omega_0}^2} \\
-2 \frac{\Omega s}{{\omega_0}^2} & \frac{s^2}{{\omega_0}^2} + 1 - \frac{{\Omega}^2}{{\omega_0}^2} \\
\end{bmatrix}
\begin{bmatrix} F_u \\ F_v \end{bmatrix}
\end{equation}