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eth-summaries/electives/amr/parts/05_planning-control/00_feedback-control/01_pid.tex
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\subsection{Proportional-Integral-Differential (PID)}
$u(t) = K_p e(t) + K_i \int_{t_0}^{t} e(\tau) \dx \tau + K_d \frac{\dx e(t)}{\dx t}$, where params $K_p$ (curr), $K_i$ (long-term), $K_d$ (trend) reduce corresp. errors,
with $e = r - y$
\bi{Drone Control} ${_B}\vec{F}$ and ${_B}\vec{M}$ as in sect. \ref{sec:rigid-body-dynamics}, use $\vec{u}' = {_B}\vec{M}$.