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ufechner7 committed Jul 24, 2024
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## Winch model

First, we calculate the acceleration of the tether at the ground station. It can be calculated as
$$a_{t,o} = \frac{1}{I_w} \frac{r}{n} (\tau_g + \tau_d - \tau_f)$$

$$a_{t,o} = \frac{1}{I_w} \frac{r}{n} (\tau_g + \tau_d - \tau_f)$$

where $I_w$ is the winch inertia as seen from the generator, $r$ the drum radius $n$ the gearbox ratio, $\tau_g$ the generator torque, $\tau_d$ the torque exerted by the drum on the generator and $\tau_f$ the friction torque.

The torque exerted by the drum depends on the tether force $F$ as follows:

$$ \tau_d = \frac{r}{n}~F$$

The friction is modelled as the combination of a viscous friction component with the friction coefficient $c_f$ and the static friction $\tau_s$

$$ \tau_f = c_f v_{t,o} + \tau_s~\mathrm{sign}(v_{t,o})$$

### Torque controlled winch
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