Feedforward gains

Theoretical kV and kA for a drivetrain, elevator or roller, from motor specs and gearing.

Inputs

Motor

12 V vendor specs; see the motor database.

Number of motors

Gear reduction

Motor rotations per output rotation, e.g. 8.45 for 8.45:1.

Wheel or drum diameter

Mass moved

Result

2.538

kA: 0.195
Free speed: 4.729
Acceleration at stall: 61.54

How it’s calculated

Formula

k_V = \frac{V_\text{nom}}{v_\text{free}}, \qquad v_\text{free} = \frac{\omega_\text{free}}{R} \frac{d}{2}

k_A = \frac{V_\text{nom}}{a_\text{stall}}, \qquad a_\text{stall} = \frac{n \, \tau_\text{stall} \, R}{m \, d/2}

With your numbers (converted to SI units)

v_\text{free} = \frac{628.3}{6.75} \times 0.0508 = 4.729\,\text{m/s}, \quad k_V = \frac{12}{4.729} = 2.538

a_\text{stall} = \frac{4 \times 7.09 \times 6.75}{61.23 \times 0.0508} = 61.54\,\text{m/s}^2, \quad k_A = \frac{12}{61.54} = 0.195

What it means

Feedforward predicts the voltage a mechanism needs: V = kS + kV·v + kA·a. kV is the voltage per unit of speed and kA the voltage per unit of acceleration. These theoretical values are a good starting point; characterise the real mechanism with SysId to get kS and refine kV and kA.

Assumptions

Ideal motor model at 12 V: no friction, so kS is 0 here.
Gearing losses and rotating inertia are ignored, so the real kA is higher.
Free current is ignored; on a real mechanism it shows up in kS and makes kV slightly lower (about 0.5–2%).
For an elevator, add kG (gravity) separately; for a drivetrain, rotation needs its own gains.

Learn the concepts behind this on resources.simbotics.org · All formulas