- #1
Linder88
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Homework Statement
The task is to write the following equations of motion as in equation (2) considering the inputs and outputs as in equation (3)
\begin{equation}
\begin{cases}
(I_b+m_bl_b^2)\ddot{\theta}_b=m_bl_bg\theta_b-m_bl_b\ddot{x}_w-\frac{K_t}{R_m}v_m+\bigg(\frac{K_eK_t}{R_m}+b_f\bigg)\bigg(\frac{\dot{x}_w}{l_w}-\dot{\theta}_b\bigg)\\
\bigg(\frac{J_w}{l_w}+l_wm_b+l_wm_w\bigg)\ddot{x}_w=-m_bl_bl_w\ddot{\theta}_b+\frac{K_t}{R_m}v_m-\bigg(\frac{K_eK_t}{R_M}+b_f\bigg)\bigg(\frac{\dot{x}_w}{l_w}-\dot{\theta}_b\bigg)
\end{cases}
\end{equation}
Homework Equations
Since this course is focused on control based State-Space (SS) models, we do now rewrite our EOM as
\begin{equation}
\begin{cases}
\dot{x}=Ax+Bu
Cx+Du
\end{cases}
\end{equation}
for oppurtune x, A, B, C and D. As for the input and output, assume for now
\begin{equation}
u=v_m\\
y=\theta_b
\end{equation}
The Attempt at a Solution
Equation (3) in (2)
\begin{equation}
\begin{cases}
\dot{x}=Ax+Bv_m\\
\theta_b=Cx+Dv_m
\end{cases}
\end{equation}