Animals use proportional-integral-derivative (PID) controllers to control their muscles.
Actually, the integral term is missing so they’re just “PD” controllers.
(wikipedia link)
Force encoding in muscle spindles during stretch of passive muscle.
Blum KP, Lamotte D’Incamps B, Zytnicki D, Ting LH (2017)
https://doi.org/10.1371/journal.pcbi.1005767
This article finds that muscle proprioceptive receptors can sense both the force on the muscle as well as the derivative of the force.
To demonstrate an interesting effect: please tap on your knee, just below you knee cap, to trigger your knee jerk reflex.
Now slowly and firmly press on the same spot that triggered the reflex. Observe that the vigour of your response is proportional to the speed of the press.