# The sandbox

This is the sandbox, so I'm assuming I can edit this as I please.

Test0

# Test1

## test

$(-3dB point) = \frac{1}{2\pi}(R1*R2*C1*C2)^\frac{1}{2}$

$x[n+1] = x[n] + \gamma(u[n]-x[n]) - K_P\sum_{j=1}^N(\frac{1}{N}x_j[n]) + K_I\sum_{j=1}^N(\frac{1}{N}w_j[n])$

$w[n+1] = w[n] - K_I\sum_{j=1}^N(\frac{1}{N}x_j[n])$

$\begin{bmatrix} \dot u_x \\ \dot u_y \\ \end{bmatrix} = \begin{bmatrix} 1 & 0 & 2(R_x-x_{Mx}) & (R_y-x_{My}) & 0 \\ 0 & 1 & 0 & (R_x-x_{Mx}) & 2(R_y-x_{My})\\ \end{bmatrix} \begin{bmatrix} k_{Mx} & 0 & 0 & 0 & 0 \\ 0 & k_{My} & 0 & 0 & 0 \\ 0 & 0 & k_{Mxx} & 0 & 0 \\ 0 & 0 & 0 & k_{Myy} & 0 \\ 0 & 0 & 0 & 0 & k_{Mxy} \\ \end{bmatrix} \begin{bmatrix} g_{Mx}-x_{Mx} \\ g_{My}-x_{My}\\ g_{Mxx}-x_{Mxx} \\ g_{Myy}-x_{Myy} \\ g_{Mxy}-x_{Mxy} \\ \end{bmatrix}$