Use feed-forward in a winch controller

[1-Bart-1]

To improve the dynamic performance of the winch control system, a feed-forward contribution can be calculated using the set (commanded) torque and the measured states: angular position, angular velocity, and angular acceleration of the winch drum. This approach enables more accurate tracking of desired speed or force and simplifies the tuning of the controller, as no proportional gain is needed, just an integral gain to reject measurement and model errors.

[ufechner7]

Fine with me, but before implementing such a controller we need solid controller performance indicators.

[ufechner7]

@1-Bart-1 Feed-forward for which signal? For the set speed signal?

[1-Bart-1]

Using the measured states you can directly calculate the input needed to achieve a certain speed or winch force.

[ufechner7]

Which measured states?

[1-Bart-1]

I think the following works for a torque controlled winch:

Input Torque $\tau$ for Desired Tether Force $F$

Solve for $\tau$:
$\tau = F \cdot r + b \omega + I \alpha$

Formula:
$\tau = F \cdot r + b \omega + I \alpha$

Input Torque $\tau$ for Desired Tether Speed $v$

Tether speed: $v = \omega \cdot r$, so $\omega = \frac{v}{r}$.
Substitute:
$\tau = F \cdot r + b \cdot \frac{v}{r} + I \alpha$

Formula:
$\tau = F \cdot r + b \cdot \frac{v}{r} + I \alpha$

Parameters:

• $F$: Tether force (N) not needed in force control, optionally measured in speed control
• $\tau$: Input torque (N·m)
• $b$: Viscous friction coefficient (N·m·s/rad)
• $\omega$: Angular velocity (rad/s) has to be measured
• $v$: Tether speed (m/s) has to be measured
• $I$: Moment of inertia (kg·m²)
• $\alpha$: Angular acceleration (rad/s²)
• $r$: Drum radius (m)

Tether Force $F$ needed in speed control can be estimated from $\omega$ and $\alpha$

1. Net torque: $\tau_{\text{net}} = I \alpha$
2. Input torque $\tau$ opposed by tether torque ($F \cdot r$) and viscous friction ($b \omega$):
   $\tau_{\text{net}} = \tau - F \cdot r - b \omega$
3. Solve:
   $\tau - F \cdot r - b \omega = I \alpha$
   $F = \frac{\tau - b \omega - I \alpha}{r}$

Formula:
$F = \frac{\tau - b \omega - I \alpha}{r}$

[ufechner7]

Nice!

But:

• we don't have a controller for a torque controlled winch yet (see: Add support for TorqueControlledWinch #2 )
• static friction is not taken into account
• the mass of the kite is not taken into account (not clear if/how it should be included for feed forward control)
• the aerodynamic force is not taken into account (not clear if that is needed)

Of course, point 2 to 4 could be treated as disturbances, but should somehow appear in the formulas.

Finally, #16 must be implemented first to be able to quantify the advantage of feed-forward control.

[1-Bart-1]

we don't have a controller for a torque controlled winch yet (see:

Yes, it makes sense to use a torque controlled winch here. A speed controlled winch is just a torque controlled winch with an internal pid right?

static friction is not taken into account

We can easily add that to the torque formula. Didn't add the gearbox yet either.

the mass of the kite is not taken into account (not clear if/how it should be included for feed forward control)

The kite can be ignored, we just care about the tether force and winch state.

the aerodynamic force is not taken into account (not clear if that is needed)

Same as above, not needed. The aerodynamic force is a cause of the winch force, but for the control itself you just care about the winch force.