Pid fajli v torque formula. So, in a way, a position controller, a velocity controller, and an acceleration (torque) controller are all different implementations of each other because each is the of the next - position is the integral of velocity, and velocity is the integral of acceleration. This typically depends on what you're interested in. Torque is analogous to force for rotating systems, in that: $$ F = m a tau = I alpha $$ Where $ alpha$ is angular acceleration and $I$ is moment of inertia. $m$ and $a$ are mass and linear acceleration, respectively. Where these differ is how you apply the controller.

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